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Reading group meeting: Randomized Primal-Dual analysis of RANKING for Online Bipartite Matching

Time: 1:00pm Tuesday 30 April.

Location: SIT 402

Speaker: Julian Mestre, University of Sydney

Paper: Randomized Primal-Dual analysis of RANKING for Online Bipartite Matching by Devanur, Jain, and Kleinberg.  

Abstract: We give a simple proof that the RANKING algorithm of Karp, Vazirani and Vazirani [KVV90] is 1-1/e competitive for the online bipartite matching problem. The proof is via a randomized primal-dual argument. Primal-dual algorithms have been successfully used for many online algorithm problems, but the dual constraints are always satisfied deterministically. This is the first instance of a non-trivial randomized primal-dual algorithm in which the dual constraints only hold in expectation. The approach also generalizes easily to the vertex-weighted version considered by Agarwal et al. [AGKM11]. Further we show that the proof is very similar to the deterministic primal-dual argument for the online budgeted allocation problem with small bids (also called the AdWords problem) of Mehta et al. [MSVV05].

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