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We propose a formal graph-theoretic model for studying the problem ofmatching rides online in a ride-sharing platform. Unlike most of the literatureon online matching, our model, that we call {\em Online Windowed Non-BipartiteMatching} ($\mbox{OWNBM}$), pertains to online matching in {\em non-bipartite}graphs. We show that the edge-weighted and vertex-weighted versions of ourmodel arise naturally in ride-sharing platforms. We provide a randomized$\frac{1}{4}$-competitive algorithm for the edge-weighted case using abeautiful result of Lehmann, Lehmann and Nisan (EC 2001) for combinatorialauctions. We also provide an $\frac{1}{2} (1 - \frac{1}{e})$-competitivealgorithm for the vertex-weighted case (with some constraint relaxation) usinginsights from an elegant randomized primal-dual analysis technique of Devanur,Jain and Kleinberg (SODA 2013).

Online Matching in a Ride-Sharing Platform