Abstract
We study a version of the online min-cost perfect matching with delays (MPMD) problem recently introduced by Emek et al. (STOC 2016). In this problem, requests arrive in a continuous time online fashion and should be matched to each other. Each request emerges from one out of n sources, with metric inter-source distances. The algorithm is allowed to delay the matching of requests, but with a cost: when matching two requests, it pays the distance between their respective sources and the time each request has waited from its arrival until it was matched. In this paper, we consider the special case of \(n = 2\) sources that captures the essence of the match-or-wait challenge (cf. rent-or-buy). It turns out that even for this degenerate metric space, the problem is far from trivial. Our results include a deterministic 3-competitive online algorithm for this problem, a proof that no deterministic online algorithm can have competitive ratio smaller than 3, and a proof that the same lower bound applies also for the restricted family of memoryless randomized algorithms.
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Aggarwal, G., Goel, G., Karande, C., Mehta, A.: Online vertex-weighted bipartite matching and single-bid budgeted allocations. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, pp. 1253–1264 (2011)
Azar, Y., Chiplunkar, A., Kaplan, H.: Polylogarithmic bounds on the competitiveness of min-cost perfect matching with delays. In: Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, pp. 1051–1061 (2017)
Birnbaum, B.E., Mathieu, C.: On-line bipartite matching made simple. SIGACT News 39(1), 80–87 (2008)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998). 62(1), 1–20
Devanur, N.R., Jain, K., Kleinberg, R.D.: Randomized primal-dual analysis of RANKING for online bipartite matching. In: Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, pp. 101–107 (2013)
Edmonds, J.: Maximum matching and a polyhedron with 0, 1-vertices. J. Res. Natl. Bur. Stand. B 69, 125–130 (1965)
Edmonds, J.: Paths, trees, and flowers. Can. J. Math. 17, 449–467 (1965)
Emek, Y., Kutten, S., Wattenhofer, R.: Online matching: haste makes waste! In: 48th Annual Symposium on Theory of Computing (STOC), June 2016. A full version can be obtained from http://ie.technion.ac.il/yemek/Publications/omhw.pdf
Goel, G., Mehta, A.: Online budgeted matching in random input models with applications to adwords. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, pp. 982–991 (2008)
Kalyanasundaram, B., Pruhs, K.: Online weighted matching. J. Algorithms 14(3), 478–488 (1993)
Karp, R.M., Vazirani, U.V., Vazirani, V.V.: An optimal algorithm for on-line bipartite matching. In: Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, pp. 352–358 (1990)
Khuller, S., Mitchell, S.G., Vazirani, V.V.: On-line algorithms for weighted bipartite matching and stable marriages. Theor. Comput. Sci. 127(2), 255–267 (1994)
Mehta, A.: Online matching and ad allocation. Found. Trends Theor. Comput. Sci. 8(4), 265–368 (2013)
Mehta, A., Saberi, A., Vazirani, U.V., Vazirani, V.V.: AdWords and generalized on-line matching. In: 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 264–273 (2005)
Meyerson, A., Nanavati, A., Poplawski, L.J.: Randomized online algorithms for minimum metric bipartite matching. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA (2006)
Miyazaki, S.: On the advice complexity of online bipartite matching and online stable marriage. Inf. Process. Lett. 114(12), 714–717 (2014)
Naor, J., Wajc, D.: Near-optimum online ad allocation for targeted advertising. In: Proceedings of the Sixteenth ACM Conference on Economics and Computation, EC, pp. 131–148 (2015)
Wang, Y., Wattenhofer, R.: Perfect Bipartite Matching with Delays (submitted)
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We are indebted to Shay Kutten and Roger Wattenhofer for their help in making this paper happen.
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Emek, Y., Shapiro, Y., Wang, Y. (2017). Minimum Cost Perfect Matching with Delays for Two Sources. In: Fotakis, D., Pagourtzis, A., Paschos, V. (eds) Algorithms and Complexity. CIAC 2017. Lecture Notes in Computer Science(), vol 10236. Springer, Cham. https://doi.org/10.1007/978-3-319-57586-5_18
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DOI: https://doi.org/10.1007/978-3-319-57586-5_18
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