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In the Min-cost Perfect Matching with Delays (MPMD) problem, 2 m requests arrive over time at points of a metric space. An online algorithm has to connect these requests in pairs, but a decision to match may be postponed till a more…

Data Structures and Algorithms · Computer Science 2018-09-11 Marcin Bienkowski , Artur Kraska , Hsiang-Hsuan Liu , Paweł Schmidt

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.…

Data Structures and Algorithms · Computer Science 2018-08-08 Yossi Azar , Amit Jacob-Fanani

In the online metric bipartite matching problem, we are given a set $S$ of server locations in a metric space. Requests arrive one at a time, and on its arrival, we need to immediately and irrevocably match it to a server at a cost which is…

Computational Geometry · Computer Science 2018-03-21 Sharath Raghvendra

We consider the problem of online Min-cost Perfect Matching with Delays (MPMD) introduced by Emek et al. (STOC 2016). In this problem, an even number of requests appear in a metric space at different times and the goal of an online…

Data Structures and Algorithms · Computer Science 2017-04-25 Marcin Bienkowski , Artur Kraska , Paweł Schmidt

In the online Min-cost Perfect Matching with Delays (MPMD) problem, $m$ requests in a metric space are submitted at different times by an adversary. The goal is to match all requests while (i) minimizing the sum of the distances between…

Data Structures and Algorithms · Computer Science 2025-10-24 Marc Dufay , Roger Wattenhofer

In this paper, we study the Min-cost Perfect $k$-way Matching with Delays ($k$-MPMD), recently introduced by Melnyk et al. In the problem, $m$ requests arrive one-by-one over time in a metric space. At any time, we can irrevocably make a…

Data Structures and Algorithms · Computer Science 2023-10-30 Naonori Kakimura , Tomohiro Nakayoshi

We consider the problem of online min-cost perfect matching with concave delays. We begin with the single location variant. Specifically, requests arrive in an online fashion at a single location. The algorithm must then choose between…

Data Structures and Algorithms · Computer Science 2020-11-05 Yossi Azar , Runtian Ren , Danny Vainstein

We investigate the problem of Min-cost Perfect Matching with Delays (MPMD) in which requests are pairwise matched in an online fashion with the objective to minimize the sum of space cost and time cost. Though linear-MPMD (i.e., time cost…

Data Structures and Algorithms · Computer Science 2022-03-08 Xingwu Liu , Zhida Pan , Yuyi Wang , Roger Wattenhofer

This paper presents a new research direction for the Min-cost Perfect Matching with Delays (MPMD) - a problem introduced by Emek et al. (STOC'16). In the original version of this problem, we are given an $n$-point metric space, where…

Data Structures and Algorithms · Computer Science 2025-01-07 Mathieu Mari , Michał Pawłowski , Runtian Ren , Piotr Sankowski

We consider the problem of online Min-cost Perfect Matching with Delays (MPMD) recently introduced by Emek et al, (STOC 2016). This problem is defined on an underlying $n$-point metric space. An adversary presents real-time requests online…

Data Structures and Algorithms · Computer Science 2016-10-18 Yossi Azar , Ashish Chiplunkar , Haim Kaplan

This paper studies a new online problem, referred to as \emph{min-cost perfect matching with delays (MPMD)}, defined over a finite metric space (i.e., a complete graph with positive edge weights obeying the triangle inequality)…

Data Structures and Algorithms · Computer Science 2016-03-10 Yuval Emek , Shay Kutten , Roger Wattenhofer

In this paper, we introduce the problem of Online Matching with Delays and Size-based Costs (OMDSC). The OMDSC problem involves $m$ requests arriving online. At any time, a group can be formed by matching any number of these requests that…

Data Structures and Algorithms · Computer Science 2024-08-19 Yasushi Kawase , Tomohiro Nakayoshi

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…

Data Structures and Algorithms · Computer Science 2019-04-22 Anupam Gupta , Guru Guruganesh , Binghui Peng , David Wajc

We initiate the study of online problems with set delay, where the delay cost at any given time is an arbitrary function of the set of pending requests. In particular, we study the online min-cost perfect matching with set delay (MPMD-Set)…

Data Structures and Algorithms · Computer Science 2023-07-11 Lindsey Deryckere , Seeun William Umboh

We study the online metric matching problem. There are $m$ servers and $n$ requests located in a metric space, where all servers are available upfront and requests arrive one at a time. Upon the arrival of a new request, it needs to be…

Data Structures and Algorithms · Computer Science 2025-10-16 Mingwei Yang , Sophie H. Yu

In online minimum cost matching on the line, $n$ requests appear one by one and have to be matched immediately and irrevocably to a given set of servers, all on the real line. The goal is to minimize the sum of distances from the requests…

Data Structures and Algorithms · Computer Science 2020-01-10 Nicole Megow , Lukas Nölke

We study the problem of online facility location with delay. In this problem, a sequence of $n$ clients appear in the metric space, and they need to be eventually connected to some open facility. The clients do not have to be connected…

Data Structures and Algorithms · Computer Science 2022-09-30 Marcin Bienkowski , Martin Böhm , Jarosław Byrka , Jan Marcinkowski

We study the on-line minimum weighted bipartite matching problem in arbitrary metric spaces. Here, $n$ not necessary disjoint points of a metric space $M$ are given, and are to be matched on-line with $n$ points of $M$ revealed one by one.…

Data Structures and Algorithms · Computer Science 2007-06-06 Béla Csaba , András S. Pluhár

In the classical Online Metric Matching problem, we are given a metric space with $k$ servers. A collection of clients arrive in an online fashion, and upon arrival, a client should irrevocably be matched to an as-yet-unmatched server. The…

Data Structures and Algorithms · Computer Science 2019-12-02 Varun Gupta , Ravishankar Krishnaswamy , Sai Sandeep

In the online matching on the line problem, the task is to match a set of requests $R$ online to a given set of servers $S$. The distance metric between any two points in $R\,\cup\, S$ is a line metric and the objective for the online…

Data Structures and Algorithms · Computer Science 2017-12-20 Antonios Antoniadis , Carsten Fischer , Andreas Tönnis
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