Deterministic Min-Cost Matching with Delays

We consider the online Minimum-Cost Perfect Matching with Delays (MPMD) problem introduced by Emek et al. (STOC 2016), in which a general metric space is given, and requests for points in space are submitted in different times in this space by an adversary. The goal is to match requests, while minim...

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Bibliographic Details
Published in:Theory of computing systems Vol. 64; no. 4; pp. 572 - 592
Main Authors: Azar, Yossi, Jacob Fanani, Amit
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2020
Springer Nature B.V
Subjects:
Algorithms
Competition
Computer Science
Matching
Metric space
Special Issue on Approximation and Online Algorithms 2018
Theory of Computation
Matching
Delayed service
Bipartite matching
Online algorithm
Competitive analysis
ISSN:1432-4350, 1433-0490
Online Access:Get full text
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Summary:We consider the online Minimum-Cost Perfect Matching with Delays (MPMD) problem introduced by Emek et al. (STOC 2016), in which a general metric space is given, and requests for points in space are submitted in different times in this space by an adversary. The goal is to match requests, while minimizing the sum of distances between matched pairs in addition to the time intervals passed from the moment each request appeared until it is matched. In the online Minimum-Cost Bipartite Perfect Matching with Delays (MBPMD) problem introduced by Ashlagi et al. (APPROX/RANDOM 2017), each request is also associated with one of two classes, and requests can only be matched with requests of the other class. Previous algorithms for the problems mentioned above, include randomized O ( log ( n ) ) -competitive algorithms for known and finite metric spaces, n being the size of the metric space, and a deterministic O m -competitive algorithm, m being the number of requests. We introduce O 1 𝜖 m log 2 3 2 + 𝜖 -competitive deterministic algorithms for both problems and for any fixed 𝜖 > 0. In particular, for a small enough 𝜖 the competitive ratio becomes O m 0.59 . These are the first deterministic algorithms for the mentioned online matching problems, achieving a sub-linear competitive ratio. We also show that the analysis of our algorithms is tight. Our algorithms do not need to know the metric space in advance.
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-019-09963-7