TY - GEN

T1 - Online matching

T2 - 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016

AU - Emek, Yuval

AU - Kutten, Shay

AU - Wattenhofer, Roger

N1 - Publisher Copyright:
© 2016 ACM.

PY - 2016/6/19

Y1 - 2016/6/19

N2 - 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.

AB - 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.

KW - Alternate poisson process

KW - Delayed service

KW - Metric min-cost perfect matching

KW - Online matching

UR - http://www.scopus.com/inward/record.url?scp=84979285004&partnerID=8YFLogxK

U2 - 10.1145/2897518.2897557

DO - 10.1145/2897518.2897557

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AN - SCOPUS:84979285004

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 333

EP - 344

BT - STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing

A2 - Mansour, Yishay

A2 - Wichs, Daniel

Y2 - 19 June 2016 through 21 June 2016

ER -