An Efficient Transitive Closure Algorithm for Cyclic Digraphs

A Space-Economic Representation of Transitive Closures in Relational Databases

A composite object represented as a directed graph (digraph for short) is an important data structure that requires efficient support in CAD/CAM, CASE, office systems, software management, web databases, and document databases. It is cumbersome to handle such objects in relational database systems when they involve ancestor-descendant relationships (or say, recursive relationships). In this pap...

Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs

This paper presents the first fully dynamic algorithms for maintaining all-pairs shortest paths in digraphs with positive integer weights less than b. For approximate shortest paths with an error factor of (2 + ), for any positive constant , the amortized update time isO(n2 log n= log logn); for an error factor of (1 + ) the amortized update time is O(n2 log3(bn)= 2). For exact shortest paths t...

Efficient Parallel Implementation of Transitive Closure of Digraphs

Turán theorems and convexity invariants for directed graphs

This paper is motivated by the desire to evaluate certain classical convexity invariants (specifically, the Helly and Radon numbers) in the context of transitive closure of arcs in the complete digraph. To do so, it is necessary to establish several new Turán type results for digraphs and characterize the associated extremal digraphs. In the case of the Radon number, we establish the following ...

Improved Deterministic Algorithms for Decremental Transitive Closure and Strongly Connected Components

This paper presents a new deterministic algorithm for decremental maintenance of the transitive closure in a directed graph. The algorithm processes any sequence of edge deletions in O(mn) time and answers queries in constant time. Until now such time bound has only been achieved by a randomized Las Vegas algorithm. In addition to that, a few decremental algorithms for maintaining strongly conn...