TY - GEN

T1 - Stochastic online metric matching

AU - Gupta, Anupam

AU - Guruganesh, Guru

AU - Peng, Binghui

AU - Wajc, David

N1 - Publisher Copyright:
© Graham Cormode, Jacques Dark, and Christian Konrad; licensed under Creative Commons License CC-BY

PY - 2019/7/1

Y1 - 2019/7/1

N2 - We study the minimum-cost metric perfect matching problem under online i.i.d arrivals. We are given a fixed metric with a server at each of the points, and then requests arrive online, each drawn independently from a known probability distribution over the points. Each request has to be matched to a free server, with cost equal to the distance. The goal is to minimize the expected total cost of the matching. Such stochastic arrival models have been widely studied for the maximization variants of the online matching problem; however, the only known result for the minimization problem is a tight O(log n)-competitiveness for the random-order arrival model. This is in contrast with the adversarial model, where an optimal competitive ratio of O(log n) has long been conjectured and remains a tantalizing open question. In this paper, we show that the i.i.d model admits substantially better algorithms: our main result is an O((log log log n)2)-competitive algorithm in this model, implying a strict separation between the i.i.d model and the adversarial and random order models. Along the way we give a 9-competitive algorithm for the line and tree metrics - the first O(1)-competitive algorithm for any non-trivial arrival model for these much-studied metrics.

AB - We study the minimum-cost metric perfect matching problem under online i.i.d arrivals. We are given a fixed metric with a server at each of the points, and then requests arrive online, each drawn independently from a known probability distribution over the points. Each request has to be matched to a free server, with cost equal to the distance. The goal is to minimize the expected total cost of the matching. Such stochastic arrival models have been widely studied for the maximization variants of the online matching problem; however, the only known result for the minimization problem is a tight O(log n)-competitiveness for the random-order arrival model. This is in contrast with the adversarial model, where an optimal competitive ratio of O(log n) has long been conjectured and remains a tantalizing open question. In this paper, we show that the i.i.d model admits substantially better algorithms: our main result is an O((log log log n)2)-competitive algorithm in this model, implying a strict separation between the i.i.d model and the adversarial and random order models. Along the way we give a 9-competitive algorithm for the line and tree metrics - the first O(1)-competitive algorithm for any non-trivial arrival model for these much-studied metrics.

KW - Metric matching

KW - Online

KW - Online matching

KW - Stochastic

UR - http://www.scopus.com/inward/record.url?scp=85069182490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069182490&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ICALP.2019.67

DO - 10.4230/LIPIcs.ICALP.2019.67

M3 - Conference contribution

AN - SCOPUS:85069182490

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019

A2 - Baier, Christel

A2 - Chatzigiannakis, Ioannis

A2 - Flocchini, Paola

A2 - Leonardi, Stefano

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019

Y2 - 9 July 2019 through 12 July 2019

ER -