On computing the transitive closure of a relation

Eve, J.; Kurki-Suonio, Reino

doi:10.1007/bf00271339

Cited by 53 publications

(20 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This is because in a graph with cycles, a simple DFS cannot construct the sets H s (v) for all states v. This difficulty, however, may be resolved if we use, instead of a plain DFS, a transitive closure algorithm based on Tarjan's algorithm to compute the SCCs of a graph (Aho et al 1974). Many such algorithms are known in the literature (Purdom 1970;Eve and Kurki-Suonio 1977;Schmitz 1983). Let Reach(v) denote the set of nodes reachable from a node v in a graph.…”

Section: All-pairs Reachability In Bounded-stack Rsmsmentioning

confidence: 99%

“…Such algorithms have a sizable literature (Purdom 1970;Eve and Kurki-Suonio 1977;Schmitz 1983). Their attraction in our setting is that they perform one depth-first traversal of the input graph, computing closure using set operations along the way, so that it is possible to weave the treatment of added edges into the discovery of edges in the original graph.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Subcubic algorithms for recursive state machines

Chaudhuri

2008

Proceedings of the 35th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

View full text Add to dashboard Cite

show abstract

Section: All-pairs Reachability In Bounded-stack Rsmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Subcubic algorithms for recursive state machines

Chaudhuri

2008

Proceedings of the 35th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

View full text Add to dashboard Cite

show abstract

“…In the context of the transitive-closure computation, the call multigraph can be represented by a relation R such that (P, Q) E R iff there is an edge from P to Q in G. Eve and Kurki-Suonio [28] present an algorithm for computing the transitive closure of an arbitrary relation based on Tarjan's algorithm for finding the strongly connected components of a directed graph [59]. This algorithm, like the data-flow analysis described above, performs O(e) union operations on inputs of length n. Zadeck [67] has developed a data-flow technique, based on Tarjan's algorithm for identifying the strongly connected regions of a graph, that can be applied to fast data-flow problems for which each member of a strongly connected region has the same solution.…”

Section: Acm Transactions On Programmingmentioning

confidence: 99%

An interval-based approach to exhaustive and incremental interprocedural data-flow analysis

Burke

1990

ACM Trans. Program. Lang. Syst.

105

View full text Add to dashboard Cite

We reformulate interval analysis so that it can he applied to any monotone data-flow problem, including the nonfast problems of flow-insensitive interprocedural analysis. We then develop an incremental interval analysis technique that can be applied to the same class of problems. When applied to flow-insensitive interprocedural data-flow problems, the resulting algorithms are simple, practical, and efficient. With a single update, the incremental algorithm can accommodate any sequence of program changes that does not alter the structure of the program call graph. It can also accommodate a large class of structural changes. For alias analysis, we develop an incremental algorithm that obtains the exact solution as computed by an exhaustive algorithm. Finally, we develop a transitive closure algorithm that is particularly well suited to the very sparse matrices associated with the problems we address.

show abstract

“…It should be pointed out that this CPU-time complexity is comparable with the classical algorithms like those in [13,12,43). A discussion in detail can be found in [28].…”

Section: W€smentioning

confidence: 78%

“…"ek" in [13], "eb" in [12], "sm" in [43], "ir" in [25]; "bfs" for PTC" in section 2, "dfs" for a usual depth-first searcher;…”

Section: W€smentioning

confidence: 99%

A suitable algorithm for computing partial transitive closures in databases

Jiang

[1990] Proceedings. Sixth International Conference on Data Engineering

View full text Add to dashboard Cite

T h e computation of partial transitive closures is considered as an elementary operation for implementing deductive database systems. A new algorithm supporting this operation is presented. Unlike previously published algorithms, which are based either on matrix-manipulations or on depth-first search strategy, the algorithm presented here uses breadth-first search as its dominant traversal strategy, a graph compression method t o minimize temporary results and Tarjan's technique in a new way t o deal with strongly connected components. We show that this algorithm is especially suitable for computing partial transitive closures in databases, for it also aims a t the minimization of disk I/O. Preliminary results of a simulation confirm this suitability.In addition, we present considerations about the implementation.

show abstract

On computing the transitive closure of a relation

Cited by 53 publications

References 5 publications

Subcubic algorithms for recursive state machines

Subcubic algorithms for recursive state machines

An interval-based approach to exhaustive and incremental interprocedural data-flow analysis

A suitable algorithm for computing partial transitive closures in databases

Contact Info

Product

Resources

About