TY - GEN

T1 - Deterministic min-cost matching with delays

AU - Azar, Yossi

AU - Jacob Fanani, Amit

N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2018.

PY - 2018

Y1 - 2018

N2 - 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 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 (formula presented) -competitive deterministic algorithms for both problems and for any fixed ɛ>0. In particular, for a small enough ɛ 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. Our algorithms do not need to know the metric space in advance.

AB - 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 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 (formula presented) -competitive deterministic algorithms for both problems and for any fixed ɛ>0. In particular, for a small enough ɛ 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. Our algorithms do not need to know the metric space in advance.

KW - Bipartite matching

KW - Competitive analysis

KW - Delayed service

KW - Matching

KW - Online algorithm

UR - http://www.scopus.com/inward/record.url?scp=85058444437&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-04693-4_2

DO - 10.1007/978-3-030-04693-4_2

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AN - SCOPUS:85058444437

SN - 9783030046927

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 21

EP - 35

BT - Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers

A2 - Epstein, Leah

A2 - Erlebach, Thomas

PB - Springer Verlag

T2 - 16th Workshop on Approximation and Online Algorithms, WAOA 2018

Y2 - 23 August 2018 through 24 August 2018

ER -