@inproceedings{4b79c541f9f740e28d5b1270d3a90d30,

title = "Online matching: Haste makes waste!",

abstract = "This paper studies a new online problem, referred to as mincost perfect matching with delays (MPMD), defined over a finite metric space (i.e., a complete graph with positive edge weights obeying the triangle inequality) M that is known to the algorithm in advance. Requests arrive in a continuous time online fashion at the points of M and should be served by matching them to each other. The algorithm is allowed to delay its request matching commitments, but this does not come for free: the total cost of the algorithm is the sum of metric distances between matched requests plus the sum of times each request waited since it arrived until it was matched. A randomized online MPMD algorithm is presented whose competitive ratio is O(log2 n + log Δ), where n is the number of points in M and Δ is its aspect ratio. The analysis is based on a machinery developed in the context of a new stochastic process that can be viewed as two interleaved Poisson processes; surprisingly, this new process captures precisely the behavior of our algorithm. A related problem in which the algorithm is allowed to clear any unmatched request at a fixed penalty is also addressed. It is suggested that the MPMD problem is merely the tip of the iceberg for a general framework of online problems with delayed service that captures many more natural problems.",

keywords = "Alternate poisson process, Delayed service, Metric min-cost perfect matching, Online matching",

author = "Yuval Emek and Shay Kutten and Roger Wattenhofer",

note = "Publisher Copyright: {\textcopyright} 2016 ACM.; 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016 ; Conference date: 19-06-2016 Through 21-06-2016",

year = "2016",

month = jun,

day = "19",

doi = "https://doi.org/10.1145/2897518.2897557",

language = "الإنجليزيّة",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

pages = "333--344",

editor = "Yishay Mansour and Daniel Wichs",

booktitle = "STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing",

}