Papers › $2$-Fault-Tolerant Strong Connectivity Oracles
$2$-Fault-Tolerant Strong Connectivity Oracles
Loukas Georgiadis, Evangelos Kosinas, Daniel Tsokaktsis
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We study the problem of efficiently answering strong connectivity queries under two vertex failures. Given a directed graph G with n vertices, we provide a data structure with O(nh) space and O(h) query time, where h is the height of a decomposition tree of G into strongly connected subgraphs. This immediately implies data structures with O(n logn) space and O(logn) query time for graphs of constant treewidth, and O(n^(3/2)) space and O(√(n)) query time for planar graphs. For general directed graphs, we give a refined version of our data structure that achieves O(n√(m)) space and O(√(m)) query time, where m is the number of edges of the graph. We also provide some simple BFS-based heuristics that seem to work remarkably well in practice. In the experimental part, we first evaluate various methods to construct a decomposition tree with small height h in practice. Then we provide efficient implementations of our data structures, and evaluate their empirical performance by conducting an extensive experimental study on graphs taken from real-world applications.
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