Online Matching in a Ride-Sharing Platform
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We propose a formal graph-theoretic model for studying the problem of matching rides online in a ride-sharing platform. Unlike most of the literature on online matching, our model, that we call Online Windowed Non-Bipartite Matching (OWNBM), pertains to online matching in non-bipartite graphs. We show that the edge-weighted and vertex-weighted versions of our model arise naturally in ride-sharing platforms. We provide a randomized 1/4-competitive algorithm for the edge-weighted case using a beautiful result of Lehmann, Lehmann and Nisan (EC 2001) for combinatorial auctions. We also provide an 1/2 (1 - 1/e)-competitive algorithm for the vertex-weighted case (with some constraint relaxation) using insights from an elegant randomized primal-dual analysis technique of Devanur, Jain and Kleinberg (SODA 2013).
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