Hariharan, Ramesh and Kavitha, Telikepalli and Mehlhorn, Kurt
(2006)
*A Faster Deterministic Algorithm for Minimum Cycle Bases in Directed Graphs.*
In: 33rd ICALP 2006, 10 July 2006, Venice, Italy, pp. 250-261.

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## Abstract

We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph G whose edges have non-negative weights. A cycle in this graph is actually a cycle in the underlying undirected graph with edges traversable in both directions. A {−1, 0, 1} edge incidence vector is associated with each cycle: edges traversed by the cycle in the right direction get 1 and edges traversed in the opposite direction get -1. The vector space over Q generated by these vectors is the cycle space of G. A minimum cycle basis is a set of cycles of minimum weight that span the cycle space of G. The current fastest algorithm for computing a minimum cycle basis in a directed graph with m edges and n vertices runs in $\'{O}(m^{ω+1}n)$ time (where ω < 2.376 is the exponent of matrix multiplication). Here we present an $O(m^3n + m^2n^2 log n)$ algorithm. We also slightly improve the running time of the current fastest randomized algorithm from $O(m^2n log n)$ to $O(m^2n + {mn}^2 log n)$.

Item Type: | Conference Paper |
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Additional Information: | Copyright of this article belongs to Springer-Verlag. |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation) |

Date Deposited: | 06 Nov 2007 |

Last Modified: | 19 Sep 2010 04:41 |

URI: | http://eprints.iisc.ernet.in/id/eprint/12416 |

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