Difference between revisions of "CATS-Mar-15-2013"
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== Title == | == Title == | ||
| − | + | Revisiting the Ranking Algorithm for Greedy Randomized Matching on Arbitrary Graphs | |
== Speaker == | == Speaker == | ||
| − | + | Hubert Chan, Department of Computer Science, The University of Hong Kong | |
== Abstract == | == 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 (MRG) algorithm achieves performance ratio 0.5000025 | ||
| + | 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 talk, 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. We believe our work achieves the currently best | ||
| + | theoretical performance ratio of 0.523 on arbitrary graphs. | ||
Revision as of 15:06, 18 July 2013
Title[edit]
Revisiting the Ranking Algorithm for Greedy Randomized Matching on Arbitrary Graphs
Speaker[edit]
Hubert Chan, Department of Computer Science, The University of Hong Kong
Abstract[edit]
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 (MRG) algorithm achieves performance ratio 0.5000025 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 talk, 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. We believe our work achieves the currently best theoretical performance ratio of 0.523 on arbitrary graphs.
