An Efficient Strongly Connected Components Algorithm in the Fault Tolerant Model

An Efficient Strongly Connected Components Algorithm in the Fault Tolerant Model

In this paper we study the problem of maintaining the strongly connected components of a graph in the presence of failures. In particular, we show that given a directed graph G = (V,E) with n = |V | and m = |E|, and an integer value k ≥ 1, there is an algorithm that computes in O(2n log2 n) time for any set F of size at most k the strongly connected components of the graph G \ F . The running t...

A space-efficient algorithm for finding strongly connected components

Tarjan’s algorihm for finding the strongly connected components of a directed graph is widely used and acclaimed. His original algorithm required at most v(2 + 5w) bits of storage, where w is the machine’s word size, whilst Nuutila and Soisalon-Soininen reduced this to v(1 + 4w). Many real world applications routinely operate on very large graphs where the storage requirements of such algorithm...

Verified Efficient Implementation of Gabow's Strongly Connected Components Algorithm

We present an Isabelle/HOL formalization of Gabow’s algorithm for finding the strongly connected components of a directed graph. Using data refinement techniques, we extract efficient code that performs comparable to a reference implementation in Java. Our style of formalization allows for re-using large parts of the proofs when defining variants of the algorithm. We demonstrate this by verifyi...

An efficient algorithm for fault-tolerant geocoding

Strongly connected components-Algorithm for finding the strongly connected components of a graph

A directed graph G (V, E) is strongly connected if and only if, for any pair of vertices X and Y from V, there exists a path from X to Y and a path from Y to X. In Computer Science, the partition of a graph in strongly connected components is represented by the partition of all vertices from the graph, so that for any two vertices, X and Y, from the same partition, there exists a path from X to...