Approximating the minimum cycle mean
We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that the algorithmic question is reducible in O(n^2) time to the p...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2013-07-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1307.4473v1 |
| _version_ | 1811305971451953152 |
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| author | Krishnendu Chatterjee Monika Henzinger Sebastian Krinninger Veronika Loitzenbauer |
| author_facet | Krishnendu Chatterjee Monika Henzinger Sebastian Krinninger Veronika Loitzenbauer |
| author_sort | Krishnendu Chatterjee |
| collection | DOAJ |
| description | We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that the algorithmic question is reducible in O(n^2) time to the problem of a logarithmic number of min-plus matrix multiplications of n-by-n matrices, where n is the number of vertices of the graph. (2) Second, when the weights are nonnegative, we present the first (1 + ε)-approximation algorithm for the problem and the running time of our algorithm is ilde(O)(n^ω log^3(nW/ε) / ε), where O(n^ω) is the time required for the classic n-by-n matrix multiplication and W is the maximum value of the weights. |
| first_indexed | 2024-04-13T08:36:07Z |
| format | Article |
| id | doaj.art-e625870770494720b8b7b9b1486a3ed1 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-04-13T08:36:07Z |
| publishDate | 2013-07-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-e625870770494720b8b7b9b1486a3ed12022-12-22T02:54:07ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802013-07-01119Proc. GandALF 201313614910.4204/EPTCS.119.13Approximating the minimum cycle meanKrishnendu ChatterjeeMonika HenzingerSebastian KrinningerVeronika LoitzenbauerWe consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that the algorithmic question is reducible in O(n^2) time to the problem of a logarithmic number of min-plus matrix multiplications of n-by-n matrices, where n is the number of vertices of the graph. (2) Second, when the weights are nonnegative, we present the first (1 + ε)-approximation algorithm for the problem and the running time of our algorithm is ilde(O)(n^ω log^3(nW/ε) / ε), where O(n^ω) is the time required for the classic n-by-n matrix multiplication and W is the maximum value of the weights.http://arxiv.org/pdf/1307.4473v1 |
| spellingShingle | Krishnendu Chatterjee Monika Henzinger Sebastian Krinninger Veronika Loitzenbauer Approximating the minimum cycle mean Electronic Proceedings in Theoretical Computer Science |
| title | Approximating the minimum cycle mean |
| title_full | Approximating the minimum cycle mean |
| title_fullStr | Approximating the minimum cycle mean |
| title_full_unstemmed | Approximating the minimum cycle mean |
| title_short | Approximating the minimum cycle mean |
| title_sort | approximating the minimum cycle mean |
| url | http://arxiv.org/pdf/1307.4473v1 |
| work_keys_str_mv | AT krishnenduchatterjee approximatingtheminimumcyclemean AT monikahenzinger approximatingtheminimumcyclemean AT sebastiankrinninger approximatingtheminimumcyclemean AT veronikaloitzenbauer approximatingtheminimumcyclemean |