In mathematics , the graphstructure theorem is a major result in the area of graph theory . The result establishes a deep and fundamental connection between the theory of minor graph theory graph minors and graph embedding topological embeddings . The theorem is stated in the seventeenth of a series ... . Intuitively, a huge graph G has small tree width if and only if G takes the structure of a huge ... width of G is not very large. The graphstructure theorem implies that this reason always ... 4 sub , the complete graph on four vertices, for which k 3 . This is one reason that the graphstructure ... enough for the graphstructure theorem. Two more notions are required clique sums and vortices ... non planar graph having 8 vertices. We point out that Theorem 2 is an exact structure theorem since the precise structure of K sub 5 sub free graphs is determined. Such results are rare within graph theory. The graphstructure theorem is not precise in this sense because, for most graphs H , the structural ... of F appears in more than k of the intervals in &Lambda . Statement of the graphstructure theorem Graphstructure theorem. For any graph H, there exists a positive integer k such that every H free graph ... with Corollary 1. Refinements Strengthened versions of the graphstructure theorem are possible ... Structure Theory Proc. AMS IMS SIAM Joint Summer Research Conference on Graph Minors volume 147 ... and motivation for the theorem A minor graph theory minor of a graph G is any graph H that is isomorphic to a graph that can be obtained from a subgraph of G by edge contraction contracting some edges. If G does not have a graph H as a minor, then we say that G is H free . Let H be a fixed graph. Intuitively, if G is a huge H free graph, then there ought to be a good reason for this. The graphstructure theorem provides such a good reason in the form of a rough description of the structure of G . In essence, every H free graph G suffers from one of two structural deficiencies either G is too ... more details
Image 6n graf.svg thumb 250px A labeled graph of 6 vertices and 7 edges. refimprove date October 2010 In computer science , a graph is an abstract data type that is meant to implement the graph mathematics graph and hypergraph concepts from mathematics . A graphdatastructure consists of a finite and possibly ... . The nodes may be part of the graphstructure, or may be external entities represented by integer indices or reference computer science reference s. A graphdatastructure may also associate to each ... out Maximum flow problem the maximum flow from a source to a sink in a graph. Operations The basic operations provided by a graphdatastructure G usually include code adjacent code G , x , y tests ... graph s See also Graph traversal for graph walking strategies Graph database for graphdatastructure persistency Graph rewriting for rule based transformations of graphs graphdata structures GraphStream Graphviz yEd Graph Editor Java based diagram editor for creating and editing graphs References ... vertices. This datastructure allows the storage of additional data on the vertices. Incidence list ... edge stores its incident vertices. This datastructure allows the storage of additional data on vertices ... notes notes 18.pdf publisher Bell College chapter 18 GraphData Structures Dead link date September ... Data structures Categories DEFAULTSORT Graph Abstract Data Type Category Graph theory Category Graph ... Graph algorithms are a significant field of interest within computer science. Typical higher ... in the form of the Floyd Warshall algorithm . A directed graph can be seen as a flow network , where ... Different data structures for the representation of graphs are used in practice Adjacency list ... and columns represent destination vertices. Data on edges and vertices must be stored externally ... lists are generally preferred because they efficiently represent sparse graph s. An adjacency matrix is preferred if the graph is dense, that is the number of edges E is close to the number of vertices ... more details
about the musical computer architecture mobile telephony standard Enhanced Data Rates for GSM Evolution Explicit DataGraph Execution , or EDGE , is an instruction set architecture ISA which intends to greatly ... the graph is the string of blocks connected by the data flowing between them. Another advantage of the EDGE ... architecture it Explicit DataGraph Execution ja Explicit DataGraph Execution ... that convert data from one form to another. Most instructions require several internal ... encoded instructions and data in order to better utilize this resource. For instance, the code add ..., reducing the program s needs and leaving more room for data. An instruction set that tried to provide ... data, so by adding additional functional units these instructions can be run at the same time. A new ... types of data and adding units dedicated to that sort of data this has led to the introduction ... take five cycles if the data is in the cache could take hundreds if it is not, but the compiler has no way to know whether that data will be in the cache at runtime that s determined by overall system ... bottleneck in traditional designs is that the data and the instructions that operate on them are theoretically ... by the CPU. EDGE thus combines the advantages of the VLIW concept of looking for independent data at compile time, with the superscalar RISC concept of executing the instructions when the data for them becomes available. In the vast majority of real world programs, the linkage of data and instructions ... points where data is passed in or out. This information is lost as the high level language is converted ..., but can have predicated instructions. The dataflow graph is encoded using these blocks, by specifying the flow of data from one block of instructions to another, or to some storage area. The basic ... so that the output of one block feeds directly into the one that will consume its data. This eliminates ... at any time after its operands are available. Due the isolation of data, similar to EDGE, dataflow ... more details
Image Hash table 3 1 1 0 1 0 0 SP.svg thumb 315px right a hash table In computer science , a datastructure ... be used algorithmic efficiency efficiently . ref Paul E. Black ed. , entry for datastructure in Dictionary ... May 21, 2009. ref ref Entry datastructure in the Encyclop dia Britannica 2009 http www.britannica.com EBchecked topic 152190 datastructure Online entry accessed on May 21, 2009. ref Different kinds ... factor in software design. Overview An array datastructure stores a number of elements of the same ... set is an abstract datastructure that can store specific values, without any particular sequence ... them. Data structures not containing code, like those above, are called plain old datastructure ... and manipulated by the program. Thus the record computer science record and Array datastructure ... while the linked datastructure s are based on storing addresses of data items within the structure ... linked list XOR linking The implementation of a datastructure usually requires writing a set of subroutine procedures that create and manipulate instances of that structure. The efficiency of a data ... concept of an abstract data type , a datastructure that is defined indirectly by the operations ... that allows datastructure implementations to be reused by different programs. Modern languages .... Many known data structures have concurrent datastructure concurrent versions that allow multiple computing threads to access the datastructure simultaneously. See also Wikipedia books Data structures List of data structures Plain old datastructure Concurrent datastructureData model Dynamization Linked datastructure Persistent datastructure References Reflist Further reading Peter Brass, Advanced ... Structures , Prentice Hall , 1985. External links Sister project links wikt datastructure commons ... csonline DataStructures Lessons index.html Datastructure tutorials with animations http ... Analysis Data structures Data types Data model DEFAULTSORT DataStructure Category Data structures ... more details
Selfref For information about graphs on Wikipedia, see Wikipedia Graphs and charts . Wiktionary Graph may refer to A Information graphics graphic such as a line chart , Plot graphics plot , chart or diagram depicting the relationship between two or more variables used, for instance, in visualising scientific data. In mathematics Graph mathematics , is a set of vertices and edges. Graph theory Graph of a function In computer science Graphdatastructure , an abstract data type representing relationships or connections Graph software , the name of a software application for mathematical plotting Conceptual graph , a model for knowledge representation and reasoning Other uses HMS Graph P715 , a submarine of the Royal Navy United Kingdom See also Grapheme linguistics Graphemics wiktionary graphy graphy suffix Latin for to write or draw Graf Graff disambiguation List of information graphics software Disambiguation de Graph es Grafo desambiguaci n eu Grafo argipena fr Graphe hu Gr f egy rtelm s t lap ms Graf ja ru uk ur Graph ... more details
Orphan date November 2006 Image s graph.gif right thumb 275px Visual representation of an S graph to efficiently solving batch process scheduling problems in chemical plant s. ref Cite journal last Holczinger first T. coauthors J Romero, L Puigjaner, F Friedler title Scheduling of Multipurpose Batch Processes with Multiple Batches of the Products volume 30 pages 305 312 date 2002 12 02 unused data Hungarian Journal for Industrial Chemistry ref ref name AICE Cite journal last Romero first Javier coauthors Luis Puigjaner, Tibor Holczinger, Ferenc Friedler title Scheduling intermediate storage multipurpose batch plants using the S graph journal American Institute of Chemical Engineers volume 50 issue 2 pages 403 417 date 2004 02 18 ref S graph is especially developed for the problems with non intermediate storage NIS policy, which often appears in chemical productions, but it is also capable to solve problems with unlimited intermediate storage UIS policy. ref name AICE Overview S graph representation has the advantage of exploiting problem specific knowledge to develop efficient scheduling algorithm s. ref name AICE There are products, and a set of task, which have to be performed to produce a product. There are dependencies between the tasks, and every task has a set of equipments, that can perform the task. Different processing times can be set for the same task in different equipments. It is also possible to have more equipment units from the same type, or define changeover times between two task in one equipment. There are two types of the scheduling problems The number of batches to produce is set, and we try to minimize the makespan processing time . Every product has a revenue, and a time horizon is set. The objective is to maximize the revenue in this fixed time horizon. S graph framework also contains Combinatorics combinatoric algorithm s to solve both of these problems. References Reflist External links http www.s graph.com S graph website Category Job scheduling ... more details
. Trees and graphs The tree datastructure can be generalized to represent directed graph s by removing ... replaced by different terminology for example, source and target . Different graphdatastructure Representations implementation strategies exist, for example adjacency list s. In graph theory , a tree graph theory tree is a connected acyclic Graphdatastructuregraph unless stated otherwise, trees and graphs are undirected. There is no one to one correspondence between such trees and trees as datastructure. We can take an arbitrary undirected tree, arbitrarily pick one of its vertex graph theory ..., at the top, has no parent. In computer science , a tree is a widely used datastructure that simulates a hierarchical tree structure with a set of linked Vertex graph theory nodes . Mathematically, it is an tree graph theory Definitions ordered directed tree , more specifically an Arborescence graph theory arborescence an acyclic connected graph mathematics graph where each node has zero or more .... Terminology A node computer science node is a structure which may contain a value, a condition, or represent a separate datastructure which could be a tree of its own . Each node in a tree has ... drawn at the top. In some trees, such as heap datastructure heaps , the root node has special properties ... with pointers to their children, their parents, or both, or as items in an Array datastructure ... producing an Arborescence graph theory arborescence and assign an order to all the nodes. The result corresponds to a tree datastructure. Picking a different root or different ordering produces a different ... images for visual effects Routing algorithms See also Tree structure Tree graph theory Tree set theory ... C. elegans javascript CS Trees Data structures DEFAULTSORT Tree DataStructure Category ... definition of subtree used in graph theory. ref Eric W. Weisstein Subtree. From MathWorld ... Finding the root for any node Common uses Representing hierarchical data Storing data in a way ... more details
In computing , a persistent datastructure is a datastructure which always preserves the previous version of itself when it is modified such data structures are effectively Immutable object immutable , as their operations do not visibly update the structure in place, but instead always yield a new updated structure. A persistent datastructure is not a datastructure committed to persistent storage , such as a disk this is a different and unrelated sense of the word persistent. A datastructure .... The datastructure is fully persistent if every version can be both accessed and modified. If there is also a meld or merge operation that can create a new version from two previous versions, the data ... make only small changes to a datastructure. A better method is to exploit the similarity between ... persistent In partially persistence model, we may query any previous version of the datastructure ... Array datastructure array . For access time , we must find the right version at each node ... to the root. Maintain an array of roots indexed by timestamp. The datastructure pointed to by time ... up with a way to combine the advantages of Persistent datastructure fat nodes and Persistent data ... the access time. The access time specifies the version of the datastructure that we care about. If the modification .... br With this algorithm , given any time t, at most one modification box exists in the datastructure ..., both updates and queries are allowed on any version of the datastructure. br Confluently persistent ... a Directed acyclic graph DAG direct acyclic graphstructure on the version graph. br Examples of persistent data structures Perhaps the simplest persistent datastructure is the linked list singly ... doi 10.1145 6138.6151 ref and Stack datastructure stack s, ref name okasaki Cite journal author ... effort, for example Queue datastructure Queue , Double ended queue s dequeue , Min Dequeue which have ... and butter datastructure in functional languages. In ML programming language ML derived languages ... more details
In computer science , a linked datastructure is a datastructure which consists of a set of record computer science data records node computer science nodes linked together and organized by reference computer science references links or pointer computer programming pointer s . In linked data structures, the links are usually treated as special data type s that can only be reference computer science dereferenced or compared for equality. Linked data structures are thus contrasted with Array datastructure arrays and other data structures that require performing arithmetic operations on pointers ... 2012 as long as no arithmetic is done on those indices, the datastructure is essentially a linked ... data structures include linked list s, search tree s, expression tree s, and many other widely used data structures. They are also key building blocks for many efficient algorithms, such as topological sort ref name knuth Donald Knuth , The Art of Computer Programming ref and disjoint set datastructure ... links that are stored as part of the data in the structure itself. It is not necessary that it should be stored in the adjacent memory locations. Every structure has a data field and a address ... datastructure in whose nodes data values can be stored from some ordered set , which is such that in an in order ... datastructure is built dynamically and never needs to be bigger than the programmer requires. It also requires no guessing in terms of how much space you must allocate when using a linked datastructure ... connected and sequential portion of memory. But in linked datastructure, the reference ... to one part of a datastructure even while other processes are working on other parts. On the other hand, access to any particular node in a linked datastructure requires following a chain of references ... of the number of entries. Broadly the implementation of these linked datastructure is through .... In arrays, nth element can be accessed immediately, while in a linked datastructure we have to follow ... more details
datastructure so that it is convenient for writing programs that traverse the structure arbitrarily ... that it can be adapted to List computing lists , Tree datastructure trees , and other Inductive Definition inductively defined data structures. Such modified data structures are usually referred to as a tree with zipper or a list with zipper to emphasize that the structure is conceptually a tree ... the scenes the zipper are efficient when making functional changes to a datastructure, where a new, slightly changed, datastructure is returned from an edit operation instead of making a change in the current datastructure . Example Bidirectional list traversal Many common data structures in computer science can be expressed as the structure generated by a few primitive constructor operation s or observer operation s. These include the structure of finite lists, which can be generated by two ... from the order of the original datastructure. Specifically, the context of 3 in the list 1, 2, 3 is represented as 2, 1 . A list with a zipper represents the entire structure, and a location within the structure. This is a pair consisting of the location s context, and the part of the structure ... datastructure and modify it directly perhaps after object copy deep cloning it, to avoid affecting ... the same goal as the conventional zipper without creating any type specific datastructure ... programming in Haskell generic programming to generate a traversal function for any datastructure ... concept of Focus computing focus or of moving around in some set of data, since its semantics reflect ... between an internal substructure and its next containing structure. When the types are described in a particular ... Type indexed data types . 23 July 2003 External links http www.haskell.org haskellwiki Zipper Zipper ... nr pubs zipcfg abstract.html An Applicative Control Flow Graph Based on Huet s Zipper http sigfpe.blogspot.com ... Functional programming Category Data structures th ... more details
21 ref This datastructure is used by the Boost Graph Library to implement its http www.boost.org ...In computing , a disjoint set datastructure is a datastructure that keeps track of a Set mathematics ... these two operations, a disjoint set datastructure is sometimes called a union find datastructure ... set datastructure is to create a linked list for each set. The element at the head of each list ... Hill, 2001. ISBN 0 262 03293 7. Chapter 21 Data structures for Disjoint Sets, pp. 498&ndash 524. ref For asymptotically faster operations, a different datastructure is needed. Analysis of the na ve ... O 1 math for this structure because each node contains the name of the list to which it belongs. A similar argument holds for merging the trees in the data structures discussed below, additionally it helps explain the time analysis of some operations in the binomial heap and Fibonacci heap data structures. Disjoint set forests Disjoint set forests are data structures where each set is represented by a tree datastructure , in which each node holds a reference to its parent node see spaghetti ... Omega alpha n math words must be accessed by any disjoint set datastructure per operation ... developed a persistent datastructure persistent version of the disjoint set forest datastructure ... Union Find DataStructure. In ACM SIGPLAN Workshop on ML, Freiburg, Germany, October 2007. ref See also Partition refinement , a different datastructure for maintaining disjoint sets, with updates that split ... union find datastructure Python implementation Category Data structures de Union Find Struktur fa ... subsets. A union find algorithm is an algorithm that performs two useful operations on such a datastructure Find Determine which subset a particular element is in. This can be used for determining ... . So for any given element of any given list in the structure described, it will need to be updated ... xRoot.rank xRoot.rank 1 The second improvement, called path compression , is a way of flattening the structure ... more details
About the programming datastructure the dynamic memory area Dynamic memory allocation Image Max Heap.svg thumb right 240px Example of a complete binary max heap In computer science , a heap is a specialized tree datastructure tree based datastructure that satisfies the heap property if B is a child node of A , then key A key B . This implies that an element with the greatest key is always in the root node, and so such a heap is sometimes called a max heap . Alternatively, if the comparison is reversed, the smallest element is always in the root node, which results in a min heap . The maximum ... two. The heap is one maximally efficient implementation of an abstract data type called a priority queue . Heaps are crucial in several efficient graph theory graph algorithm s such as Dijkstra s algorithm , and in the sorting algorithm heapsort . A heap datastructure should not be confused with the heap ... was originally used only for the datastructure. Some early popular languages such as Lisp programming language Lisp provided dynamic memory allocation using heap data structures, which gave the memory ... The heap datastructure has many applications. Heapsort One of the best sorting methods being in place ... space efficient way using an array datastructure array alone. The first or last element will contain ... structure. See also Sorting algorithm Stack datastructure Queue datastructure Tree datastructure ... bottom up in O n . ref cite book title Data Structures and Algorithms in Java first1 Michael T. last1 ... reports 1991 TR 2091 027.pdf ref List of algorithms Graph algorithms Graph algorithms By using heaps as internal traversal data structures, run time will be reduced by polynomial order. Examples of such problems ... Commons category Heaps Wikibooks Data Structures Min and Max Heaps http mathworld.wolfram.com Heap.html Heap at Wolfram MathWorld CS Trees Data structures DEFAULTSORT Heap DataStructure Category Heaps data structures cs Halda datov struktura da Hob datastruktur de Heap Datenstruktur et Kuhi es Mont culo ... more details
wiktionarypar Periodic Graph Periodic graph periodic graph Periodic graphs periodic graphs Periodic graph can mean Periodic graph crystallography or crystal net , a Euclidean graph representing the atomic or molecular structure of a crystal. Periodic graph geometry , a Euclidean graph preserved under a lattice of translations. Periodic graphgraph theory , a graph that is periodic with respect to a graph theoretic operator disambig ... more details
In computer science , a succinct datastructure is datastructure which uses an amount of space that is close to the information theoretic lower bound, but unlike other compressed representations still allows for efficient query operations. The concept was originally introduced by Jacobson ref name jacobson1988succinct to encode bit vector s, unlabeled tree datastructure trees , and planar graph s. Unlike general lossless data compression algorithms, succinct data structures retain the ability to use them in place, without decompressing them first. A related notion is that of a compressed datastructure , in which the size of the datastructure depends upon the particular data being represented. Suppose that math Z math is the information theoretical optimal number of bits needed to store some data. A representation of this data is called implicit datastructure implicit if it takes math ... of storage space. Thus, since each of these auxiliary tables take math o n math space, this datastructure ... ref references DEFAULTSORT Succinct DataStructure Category Data structures ja ... using some permutation of the input data the most well known example of this is the heap. Succinct dictionaries ... math bits of storage space the original bit array and an math o n math auxiliary structure and supports ... find the number of bits set in the small blocks. This is often beneficial, since succinct data structures find their uses in large data sets, in which case cache misses become much more frequent ... structure used for rank however, this takes math O lg n math time in the worst case. A more complicated structure using math 3n lg lg n O sqrt n lg n lg lg n o n math bits of additional storage ... name brodnik1999membership This structure can be extended to support rank and select queries and takes ... last Jacobson first G. J title Succinct static data structures year 1988 ref ref name raman2002succinct ... title Squeezing succinct data structures into entropy bounds booktitle Proceedings of the seventeenth ... more details
Image Aggregate DataStructure Diagram.jpg thumb 240px Example of a DataStructure Diagram. A DataStructure Diagram DSD is a data model used to describe Conceptual schema conceptual data models by providing graphical notations which document entity entities and their Relational model relationship s, and the Integrity constraints constraint s that binds them. The basic graphic elements of DSDs are box es, representing entities, and arrow s, representing relationships. Datastructure diagrams are most useful for documenting complex data entities. Overview Image DataStructure Diagram.jpg thumb left DataStructure Diagram. DataStructure Diagram is a diagram type that is used to depict the structure of data elements in the data dictionary . The datastructure diagram is a graphical alternative to the composition specifications within such data dictionary entries. ref http knowledge.fhwa.dot.gov tam aashto.nsf All Documents 4825476B2B5C687285256B1F00544258 FILE DIGloss.pdf Data Integration Glossary , U.S. Department of Transportation, August 2001. ref Datastructure diagrams are an extension of the entity relationship model E R model . In DSDs, Attribute computing attribute s are specified inside the entity boxes rather than outside of them, while relationships are drawn as boxes composed of attributes which specify the constraints that bind entities together. The E R model, while ... between each entity. There are several styles for representing datastructure diagrams, with the notable difference in the manner of defining Cardinality data modeling cardinality . The choices are between ... of the cardinality. Data flow diagram Entity relationship diagram Unified Modeling Language References Reflist Refimprove date November 2008 Further reading commons category DataStructure Diagrams Charles W. Bachman . Datastructure diagrams . Data Base, 1969, 1 2 4 10. Tom DeMarco . Structured ... Wiki . Data model DEFAULTSORT DataStructure Diagram Category Data modeling diagrams de Datenstrukturdiagramm ... more details
In computer science , an implicit datastructure is a datastructure that uses very little memory besides the actual data elements i.e. very little information other than main data is stored in these structures. These are storage schemes which retain no pointers and represent the file of n k key records as a simple n by k array n thus retrieve faster. In implicit data structures the only structural information to be given is to allow the array to grow and shrink as n. No extra information is required. It is called implicit because most of the structure of the elements is expressed implicitly by their order ... and can mean from O 1 to O log n extra space. Implicit datastructure encodes data efficiently ... at various position in data. To achieve optimal coding, we use bits instead of bytes. Implicit data structures are frequently also succinct datastructure s. Although one may argue that disk space is no longer ... I O devices. Hence, if a larger chunk of an implicit datastructure fits in main memory the operations ... of this structure takes average time.The same result obtain for the data structures in which ... that implicit data structures are designed to improve is main memory utilization. Hard disks, or any other means of large data capacity, I O devices, are orders of magnitudes slower than main memory. Hence ... data structures can improve cache efficiency and thus running speed, especially if the method used improves locality. Keys are scanned very efficiently. Downloading indexed data in mobiles becomes easier. Implicit datastructure for weighted element For presentation of elements with different weight several data structures are required.The structure uses one more location besides required for values of elements.The first structure supports worst case search time in terms of rank of weight ... data structures include Binary heap Beap Further reading See publications of http photon.poly.edu ... gnf Greg Frederickson Category Data structures ... more details
The term compressed datastructure arises in the computer science subfields of algorithms , data structures , and theoretical computer science . It refers to a datastructure whose operations are roughly as fast as those of a conventional datastructure for the problem, but whose size can be substantially smaller. The size of the compressed datastructure is typically highly dependent upon the entropy of the data being represented. Important examples of compressed data structures include the compressed suffix array ref R. Grossi and J. S. Vitter, Compressed Suffix Arrays and Suffix Trees with Applications to Text Indexing and String Matching , Proceedings of the 32nd ACM Symposium on Theory of Computing , May 2000, 397 406. Journal version in SIAM Journal on Computing , 35 2 , 2005, 378 407. ref ref R. Grossi, A. Gupta, and J. S. Vitter, High Order Entropy Compressed Text Indexes, Proceedings of the 14th Annual SIAM ACM Symposium on Discrete Algorithms , January 2003, 841 850. ref and the FM index , ref P. Ferragina and G. Manzini, Opportunistic Data Structures with Applications, Proceedings of the 41st IEEE Symposium on Foundations of Computer Science , November 2000, 390 398. Journal version in Indexing Compressed Text, Journal of the ACM , 52 4 , 2005, 552 581. ref both of which can represent an arbitrary text of characters T for pattern matching . Given any input pattern P , they support ... the self indexing feature. An important related notion is that of a succinct datastructure , which ... needed to represent the data. In contrast, the size of a compressed datastructure depends upon the particular data being represented. When the data are compressible, as is often the case in practice for natural language text, the compressed datastructure can occupy substantially less space than the information theoretic minimum. References references Category Data structures ..., both data structures are self indexing, in that they can reconstruct the text T in a random access ... more details
Refimprove date November 2009 In computer science , a concurrent datastructure is a particular way of storing and organizing data for access by multiple computing Thread computer science threads or process computing processes on a computer . Historically, such data structures were used on uniprocessor ... of multi core processors , the term has come to stand mainly for data structures that can be accessed by multiple threads which may actually access the data simultaneously because they run on different processors that communicate with one another. The concurrent datastructure sometimes also called a shared datastructure is usually considered to reside in an abstract storage environment ... environment one specifies the datastructure s properties and checks that they are implemented ... of liveness requirements tend to define the datastructure. The method computer science method calls can be Blocking computing blocking or Non blocking algorithm non blocking . Data structures are not restricted ... approaches for arguing the safety properties of a concurrent datastructure such as serializability ... difficult to design and verify a correct datastructure implementation. A key measure for performance ... one can scale the performance of a concurrent datastructure is captured by a formula known as Amdahl ... schema DEFAULTSORT Concurrent DataStructure Category Data structures Category Concurrent ... operations on the data by the operating system, even though the processors never issued two operations that accessed the data simultaneously. Today, as multiprocessor computer architectures ... or a distributed collection of storage modules. Basic principles Concurrent data structures, intended for use in parallel or distributed computing environments, differ from sequential data structures ... Moir and Nir Shavit title Handbook of Data Structures and Applications chapter http www.cs.tau.ac.il shanir concurrent data structures.pdf Concurrent Data Structures edition 1st editor Dinesh Metha and Sartaj ... more details
Refimprove date March 2009 Datastructure alignment is the way data is arranged and accessed in computer memory. It consists of two separate but related issues data alignment and datastructure padding . When a modern computer reads from or writes to a memory address, it will do this in Word data type ... bytes between the end of the last datastructure and the start of the next, which is datastructure ... error alignment fault . Even though the previous datastructure ends at the 14th byte, the next datastructure should start at the 16th byte. Two padding bytes are inserted between the two data structures to align the next datastructure to the 16th byte. Although datastructure alignment is a fundamental ... language allow at least partial control of datastructure padding, which may be useful in certain ... aggregate a datastructure or array is aligned if and only if each primitive datum in the aggregate ... or words contained the data and extract the equivalent value. Datastructure padding Although the compiler ... aligned. In addition the datastructure as a whole may be padded with a final unnamed member ... the members of a structure to a certain level of alignment, e.g. pack 2 means align data members ... structures is most frequently used to conserve memory space , it may also be used to format a datastructure ... the start of a datastructure where mod is the Modulo operation modulo operator pseudo code, see ... of C structs on x86 Datastructure members are stored sequentially in a memory so that in the structure ... of memory then each member of the datastructure depicted above would be 2 byte aligned. Data1 would ... Data2 int Data3 char Data4 source After compilation the datastructure will be supplemented with padding ... Datastructure alignment least common multiple requires at least 2 args and http en.wikipedia.org wiki Talk Datastructure alignment calculation of whole structure alignment and paddings . date February ... Family The Programming Environments for 32 Bit Microprocessors DEFAULTSORT DataStructure Alignment ... more details
A plain old datastructure POD is a datastructure that is represented only as passive collections of field values, without using encapsulation computer science encapsulation or other object oriented features. Plain old data structures are appropriate when there is a part of a system where it should be clearly indicated that the detailed logic for data manipulation and integrity are elsewhere. PODs are often found at the boundaries of a system, where information is being moved to and from other systems or persistent storage and the business logic that is found in other parts of the system is not relevant. For example, PODs would be convenient for representing the field values of objects that are being constructed from external data, in a part of the system where the semantic checks and interpretations needed for valid objects have not yet been applied. A POD type in C is defined as either a scalar type or a POD class. A POD class has no user defined copy assignment operator, no user defined destructor, and no non static data members that are not themselves PODs. Moreover, a POD class must be an aggregate, meaning it has no user declared constructors, no private nor protected non static data, no base classes and no virtual functions. The standard includes statements about how PODs must behave in C . In certain contexts, C allows only POD types to be used. For example, a tt union tt in C cannot contain a class that has virtual function s or nontrivial constructors or destructors ... concept corresponds to a class with public data members and no methods Java Code Conventions 10.1 , http www.oracle.com technetwork java codeconventions 137265.html 177 i.e., a data transfer object . Others ... data representations such as XML or JSON can also be used as PODs if no significant semantic restrictions ... 29, 1999. http www.oracle.com technetwork java codeconventions 137265.html 177 Java Language Data ... C Category Composite data types ru zh POD ... more details
In computer science , a search datastructure is any datastructure that allows the efficient retrieval of specific items from a set mathematics set of items, such as a specific record computer science record from a database . The simplest, most general, and least efficient search structure is merely an unordered sequential list computing list of all the items. Locating the desired item in such a list, by the linear search method, inevitably requires a number of operations proportional to the number n of items, in the worst case complexity worst case as well as in the average case complexity average case . Useful search data structures allow faster retrieval however, they are limited to queries of some specific kind. Moreover, since the cost of building such structures is at least proportional to n , they only pay off if several queries are to be performed on the same database or on a database that changes little between queries . Static search structures are designed for answering many Information retrieval queries on a fixed database dynamic structures also allow insertion, deletion ... 50,000 and 100,000 and hired between 1995 and 2007 . Single ordered keys Array datastructure Array ... Heap datastructure Heap Asymptotic amortized worst case analysis In this table, the asymptotic ... n O log n O log n O log n O n Heap datastructure Heap O log n O log n sup sup O n O 1 O n Hash table ... is only an approximate summary for each datastructure there are special situations and variants that may lead to different costs. Also two or more data structures can be combined to obtain lower costs. Footnotes reflist See also List of data structures Category Data structures ... of fixing the search structure to account for the changes in the database. Classification The simplest ... case. class wikitable Insert Delete Search Find maximum Space usage Unsorted Array datastructure array Constant time O 1 O 1 Linear time O n O n O n Value indexed array O 1 O 1 O 1 O n O ... more details
Distinguish Array data type Refimprove date September 2008 In computer science , an array datastructure or simply array is a datastructure consisting of a collection of elements value computer science ... datastructure are required to have the same size and should use the same data representation ... to implement other data structures, such as heap datastructure heaps , hash table s, double ended queue deque s, queue datastructure queue s, stack datastructure stacks , String computer science ... List datastructure comparison Dynamic array Growable array s are similar to arrays but add the ability ... Data Structures Arrays Commons category Array datastructureData structures Use dmy dates date September 2010 DEFAULTSORT Array DataStructure Category Arrays Category Data structures az Massiv bn ... Paul E. date 13 November 2008 work Dictionary of Algorithms and Data Structures publisher National ... integer variables, with indices 0 through 9, may be stored as 10 Word data type words at memory addresses ... R. Richardson 2002 , The Book on Data Structures. iUniverse, 112 pages. ISBN 0 595 24039 9, 9780595240395 ... important data structures, and are used by almost every program. They are also used to implement many other data structures, such as list computing list s and string computer science string s. They effectively .... The term array is often used to mean array data type , a kind of data type provided by most high ... s, or other data structures. The term is also used, especially in the description of algorithm s, to mean associative array or abstract array , a theoretical computer science model an abstract data type ... used machine language programming to set up and access array structures for data tables, vector and matrix ... element identifier and addressing formulas When data objects are stored in an array, individual objects ... scalar computing scalar data types like Enumerated type enumerations , or Character computing characters ... require only amortized constant time. Some array data structures do not reallocate storage, but do ... more details
theory set theoretic definitions of a graph it is the ordered pair of empty set s , and in recursive definition recursively defined datastructure s math K 0 math is useful for defining the base case base case for recursion by treating the null tree datastructure tree as the child node of a tree child ...In the mathematics mathematical field of graph theory , the null graph may refer either to the order graph theory order zero graph mathematics graph , or alternatively, to any edgeless graph the latter is sometimes called an empty graph . Order zero graph infobox graph name Order zero graph null graph ... index 0 genus 0 spectral gap undefined notation math K 0 math properties Integral graph Integral br Symmetric graph Symmetric The order graph theory order zero graph mathematics graph math K 0 math is the unique graph of order zero having zero vertex graph theory vertices . As a consequence, it also has zero edge graph theory edges . In some contexts, math K 0 math is excluded from being considered a graph either by definition, or more simply as a matter of convenience . The order zero graph ... of a category of graphs. Its inclusion within the definition of graph theory is more useful in some ... . On the negative side, most well defined formulas for graph properties must include exceptions for math K 0 math if it is included as a graph counting all strongly connected component s of a graph would become counting all non null strongly connected components of a graph . Due to the undesirable aspects, it is usually assumed in literature that the term graph implies graph with at least one vertex unless context suggests otherwise. ref MathWorld urlname EmptyGraph title Empty Graph ref ref MathWorld urlname NullGraph title Null Graph ref When acknowledged, math K 0 math fulfills vacuous truth vacuously most of the same basic graph properties as math K 1 math the graph with one vertex and no edges it has a size graph theory size of zero, it is equal to its complement graph math bar K 0 ... more details
otheruses4 the 3 regular graph the graph associated with a Coxeter group Coxeter diagram infobox graph name Coxeter graph image Image Coxeter graph.svg 250px image caption The Coxeter graph namesake vertices ... 4 chromatic number 3 chromatic index 3 properties Symmetric graph Symmetric br distance regular graph Distance regular br distance transitive graph Distance transitive br Cubic graph Cubic br Hypohamiltonian graph Hypohamiltonian In the mathematics mathematical field of graph theory , the Coxeter graph is a 3 regular graph with 28 vertices and 42 edges. ref MathWorld urlname CoxeterGraph title Coxeter Graph ref All the cubic graph cubic distance regular graph s are known. ref Brouwer, A. E. Cohen ... graph is one of the 13 such graphs. Properties The Coxeter graph has chromatic number 3, chromatic index 3, radius 4, diameter 4 and girth graph theory girth 7. It is also a 3 k vertex connected graph vertex connected graph and a 3 k edge connected graph edge connected graph . The Coxeter graph is hypohamiltonian graph hypohamiltonian it does not itself have a Hamiltonian cycle but every graph formed by removing a single vertex from it is Hamiltonian. It has Crossing number graph theory rectilinear crossing number 11, and is the smallest cubic graph with that crossing number currently known, but an 11 crossing, 26 vertex graph may exist OEIS id A110507 . The Coxeter graph may be constructed from the smaller distance regular Heawood graph by constructing a vertex for each 6 cycle in the Heawood graph and an edge for each disjoint pair of 6 cycles. ref citation first Italo J. last Dejter title From the Coxeter graph to the Klein graph journal Journal of Graph Theory year 2011 doi 10.1002 jgt.20597 arxiv 1002.1960 . ref Algebraic properties The automorphism group of the Coxeter graph is a group of order 336. ref Royle, G. http www.csse.uwa.edu.au gordon foster F028A.html F028A data ref It acts transitively on the vertices, on the edges and on the arcs of the graph. Therefore the Coxeter ... more details
In combinatorics combinatorial mathematics , a Levi graph or incidence graph is a bipartite graph associated with an incidence structure . ref MathWorld urlname LeviGraph title Levi Graph ref ...infobox graph name Levi graph image Image Pappus.png 240px image caption The Pappus graph , a Levi graph ... a graph with one vertex per point, one vertex per line, and an edge for every incidence between ... Levi, F. W. title Finite geometrical systems year 1942 publisher Calcutta . ref The Levi graph of a system of points and lines usually has girth graph theory girth at least six Any 4 Cycle graph cycles would correspond to two lines through the same two points. Conversely any bipartite graph with girth at least six can be viewed as the Levi graph of an abstract incidence structure. Levi graphs may also be defined for other types of incidence structure, such as the incidences between points and planes in Euclidean space . For every Levi graph, there is an equivalent hypergraph , and vice versa . Examples The Desargues graph is the Levi graph of the Desargues configuration , composed of 10 points ... graph can also be viewed as the generalized Petersen graph G 10,3 or the Kneser graph bipartite Kneser graph with parameters 5,2. It is 3 regular with 20 vertices. The Heawood graph is the Levi graph of the Fano plane . It is also known as the 3,6 cage graph theory cage , and is 3 regular with 14 vertices. The M bius Kantor graph is the Levi graph of the M bius Kantor configuration , a system ... regular with 16 vertices. The Pappus graph is the Levi graph of the Pappus configuration , composed ... passing through each point. It is 3 regular with 18 vertices. The Gray graph is the Levi graph of a configuration ... lines through them. The Tutte eight cage is the Levi graph of the Cremona Richmond configuration ... graph Q sub 4 sub is the Levi graph of the M bius configuration formed by the points and planes of two mutually incident tetrahedra. The Ljubljana graph on 112 vertices is the Levi graph of the Ljubljana ... more details
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