Chapter

Experimental and Efficient Algorithms

Volume 3503 of the series Lecture Notes in Computer Science pp 240-252

Algorithm Engineering for Optimal Graph Bipartization

  • Falk HüffnerAffiliated withInstitut für Informatik, Friedrich-Schiller-Universität Jena

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Abstract

We examine exact algorithms for the NP-complete Graph Bipartization problem that asks for a minimum set of vertices to delete from a graph to make it bipartite. Based on the “iterative compression” method recently introduced by Reed, Smith, and Vetta, we present new algorithms and experimental results. The worst-case time complexity is improved from O(3 k · kmn) to O(3 k · mn), where n is the number of vertices, m is the number of edges, and k is the number of vertices to delete. Our best algorithm can solve all problems from a testbed from computational biology within minutes, whereas established methods are only able to solve about half of the problems within reasonable time.