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# An (O)over-bar(m(2)n) randomized algorithm to compute a minimum cycle basis of a directed graph

Kavitha, T (2005) An (O)over-bar(m(2)n) randomized algorithm to compute a minimum cycle basis of a directed graph. In: 32nd International Colloquium on Automata, Languages and Programming (ICALP 2005), JUL 11-15, 2005, Lisbon, PORTUGAL.  Preview
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10.1.1.109.7698.pdf - Accepted Version

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## Abstract

We consider the problem of computing a minimum cycle basis in a directed graph G. The input to this problem is a directed graph whose arcs have positive weights. In this problem a {- 1, 0, 1} incidence vector is associated with each cycle and the vector space over Q generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of weights of the cycles is minimum is called a minimum cycle basis of G. The current fastest algorithm for computing a minimum cycle basis in a directed graph with m arcs and n vertices runs in O(m(w+1)n) time (where w < 2.376 is the exponent of matrix multiplication). If one allows randomization, then an (O) over tilde (m(3)n) algorithm is known for this problem. In this paper we present a simple (O) over tilde (m(2)n) randomized algorithm for this problem. The problem of computing a minimum cycle basis in an undirected graph has been well-studied. In this problem a {0, 1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of the graph. The fastest known algorithm for computing a minimum cycle basis in an undirected graph runs in O(m(2)n + mn(2) logn) time and our randomized algorithm for directed graphs almost matches this running time.

Item Type: Conference Paper Copyright of this article belongs to Springer. Division of Electrical Sciences > Computer Science & Automation Ms V Mangala 02 Mar 2012 11:06 02 Mar 2012 11:53 http://eprints.iisc.ac.in/id/eprint/43747

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