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  A Faster Algorithm for Minimum Cycle Basis of Graphs

Mehlhorn, K., Michail, D., Telikepalli, K., & Paluch, K. (2004). A Faster Algorithm for Minimum Cycle Basis of Graphs. In Automata, languages and programming: 31st International Colloquium, ICALP 2004 (pp. 846-857). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2A07-0 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2A09-C
Genre: Conference Paper

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 Creators:
Mehlhorn, Kurt1, Author           
Michail, Dimitrios1, Author           
Telikepalli, Kavitha2, Author
Paluch, Katarzyna1, Author           
Díaz, Josep2, Editor
Karhumäki, Juhani, Editor
Lepistö, Arto, Editor
Sannella, Donald, Editor
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              
2Max Planck Society, ou_persistent13              

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 Abstract: In this paper we consider the problem of computing a minimum cycle basis in a graph $G$ with $m$ edges and $n$ vertices. The edges of $G$ have non-negative weights on them. The previous best result for this problem was an $O(m^{\omega}n)$ algorithm, where $\omega$ is the best exponent of matrix multiplication. It is presently known that $\omega < 2.376$. We obtain an $O(m^2n + mn^2\log n)$ algorithm for this problem. Our algorithm also uses fast matrix multiplication. When the edge weights are integers, we have an $O(m^2n)$ algorithm. For unweighted graphs which are reasonably dense, our algorithm runs in $O(m^{\omega})$ time. For any $\epsilon > 0$, we also design a $1+\epsilon$ approximation algorithm to compute a cycle basis which is at most $1+\epsilon$ times the weight of a minimum cycle basis. The running time of this algorithm is $O(\frac{m^{\omega}}{\epsilon}\log(W/{\epsilon}))$ for reasonably dense graphs, where $W$ is the largest edge weight.

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Language(s): eng - English
 Dates: 2005-05-012004
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 231968
Other: Local-ID: C1256428004B93B8-158CD04BC22EDE8AC1256F4F00523BF7-KMMP2004c
 Degree: -

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Title: Untitled Event
Place of Event: Turku, Finland
Start-/End Date: 2004-07-12

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Title: Automata, languages and programming : 31st International Colloquium, ICALP 2004
Source Genre: Proceedings
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Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 846 - 857 Identifier: -

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Pages: - Volume / Issue: 3142 Sequence Number: - Start / End Page: - Identifier: ISSN: 0302-9743