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International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 238-249 | Cite as

Speeding up Graph Algorithms via Switching Classes

  • Nathan LindzeyEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8986)

Abstract

Given a graph G, a vertex switch of \(v \in V(G)\) results in a new graph where neighbors of v become nonneighbors and vice versa. This operation gives rise to an equivalence relation over the set of labeled digraphs on n vertices. The equivalence class of G with respect to the switching operation is commonly referred to as G’s switching class. The algebraic and combinatorial properties of switching classes have been studied in depth; however, they have not been studied as thoroughly from an algorithmic point of view. The intent of this work is to further investigate the algorithmic properties of switching classes. In particular, we show that switching classes can be used to asymptotically speed up several super-linear unweighted graph algorithms. The current techniques for speeding up graph algorithms are all somewhat involved insofar that they employ sophisticated pre-processing, data-structures, or use “word tricks” on the RAM model to achieve at most a \(O(\log (n))\) speed up for sufficiently dense graphs. Our methods are much simpler and can result in super-polylogarithmic speedups. In particular, we achieve better bounds for diameter, transitive closure, bipartite maximum matching, and general maximum matching.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Computer Science DepartmentColorado State UniversityFort CollinsUSA

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