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- Publisher Website: 10.1137/1.9781611973402.82
- Scopus: eid_2-s2.0-84902096396
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Conference Paper: Ranking on Arbitrary Graphs: Rematch via Continuous LP with Monotone and Boundary Condition Constraints
Title | Ranking on Arbitrary Graphs: Rematch via Continuous LP with Monotone and Boundary Condition Constraints |
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Authors | |
Keywords | Continuous linear programming Maximum matching Oblivious algorithms Primal-dual methods |
Issue Date | 2014 |
Publisher | Society for Industrial and Applied Mathematics (SIAM). |
Citation | Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms: Portland, Oregon, USA, 5-7 January 2014, p. 1112-1122 How to Cite? |
Abstract | Motivated by online advertisement and exchange settings, greedy randomized algorithms for the maximum matching problem have been studied, in which the algorithm makes (random) decisions that are essentially oblivious to the input graph. Any greedy algorithm can achieve performance ratio 0.5, which is the expected number of matched nodes to the number of nodes in a maximum matching.
Since Aronson, Dyer, Frieze and Suen proved that the Modified Randomized Greedy algorithm achieves performance ratio 0.5+ ∊ (where ) on arbitrary graphs in the mid-nineties, no further attempts in the literature have been made to improve this theoretical ratio for arbitrary graphs until two papers were published in FOCS 2012.
In this paper, we revisit the Ranking algorithm using the LP framework. Special care is given to analyze the structural properties of the Ranking algorithm in order to derive the LP constraints, of which one known as the boundary constraint requires totally new analysis and is crucial to the success of our LP.
We use continuous LP relaxation to analyze the limiting behavior as the finite LP grows. Of particular interest are new duality and complementary slackness characterizations that can handle the monotone and the boundary constraints in continuous LP. Our work achieves the currently best theoretical performance ratio of on arbitrary graphs. Moreover, experiments suggest that Ranking cannot perform better than 0.724 in general. |
Persistent Identifier | http://hdl.handle.net/10722/201102 |
ISBN |
DC Field | Value | Language |
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dc.contributor.author | Chan, HTH | en_US |
dc.contributor.author | Chen, F | en_US |
dc.contributor.author | Wu, X | en_US |
dc.contributor.author | Zhao, Z | en_US |
dc.date.accessioned | 2014-08-21T07:13:34Z | - |
dc.date.available | 2014-08-21T07:13:34Z | - |
dc.date.issued | 2014 | en_US |
dc.identifier.citation | Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms: Portland, Oregon, USA, 5-7 January 2014, p. 1112-1122 | en_US |
dc.identifier.isbn | 9781611973389 | - |
dc.identifier.uri | http://hdl.handle.net/10722/201102 | - |
dc.description.abstract | Motivated by online advertisement and exchange settings, greedy randomized algorithms for the maximum matching problem have been studied, in which the algorithm makes (random) decisions that are essentially oblivious to the input graph. Any greedy algorithm can achieve performance ratio 0.5, which is the expected number of matched nodes to the number of nodes in a maximum matching. Since Aronson, Dyer, Frieze and Suen proved that the Modified Randomized Greedy algorithm achieves performance ratio 0.5+ ∊ (where ) on arbitrary graphs in the mid-nineties, no further attempts in the literature have been made to improve this theoretical ratio for arbitrary graphs until two papers were published in FOCS 2012. In this paper, we revisit the Ranking algorithm using the LP framework. Special care is given to analyze the structural properties of the Ranking algorithm in order to derive the LP constraints, of which one known as the boundary constraint requires totally new analysis and is crucial to the success of our LP. We use continuous LP relaxation to analyze the limiting behavior as the finite LP grows. Of particular interest are new duality and complementary slackness characterizations that can handle the monotone and the boundary constraints in continuous LP. Our work achieves the currently best theoretical performance ratio of on arbitrary graphs. Moreover, experiments suggest that Ranking cannot perform better than 0.724 in general. | - |
dc.language | eng | en_US |
dc.publisher | Society for Industrial and Applied Mathematics (SIAM). | - |
dc.relation.ispartof | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms | en_US |
dc.subject | Continuous linear programming | - |
dc.subject | Maximum matching | - |
dc.subject | Oblivious algorithms | - |
dc.subject | Primal-dual methods | - |
dc.title | Ranking on Arbitrary Graphs: Rematch via Continuous LP with Monotone and Boundary Condition Constraints | en_US |
dc.type | Conference_Paper | en_US |
dc.identifier.email | Chan, HTH: hubert@cs.hku.hk | en_US |
dc.identifier.authority | Chan, HTH=rp01312 | en_US |
dc.description.nature | link_to_OA_fulltext | - |
dc.identifier.doi | 10.1137/1.9781611973402.82 | - |
dc.identifier.scopus | eid_2-s2.0-84902096396 | - |
dc.identifier.hkuros | 232589 | en_US |
dc.identifier.spage | 1112 | - |
dc.identifier.epage | 1122 | - |
dc.publisher.place | Philadelphia | - |