A Randomized O(log2k)-Competitive Algorithm for Metric Bipartite Matching

We consider the online metric matching problem in which we are given a metric space, k of whose points are designated as servers. Over time, up to k requests arrive at an arbitrary subset of points in the metric space, and each request must be matched to a server immediately upon arrival, subject to...

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Bibliographic Details
Published in:Algorithmica Vol. 68; no. 2; pp. 390 - 403
Main Authors: Bansal, Nikhil, Buchbinder, Niv, Gupta, Anupam, Naor, Joseph (Seffi)
Format: Journal Article
Language:English
Published: Boston Springer US 01.02.2014
Springer
Subjects:
Algorithm Analysis and Problem Complexity
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computer Science
Computer science; control theory; systems
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Exact sciences and technology
Information retrieval. Graph
Mathematics of Computing
Theoretical computing
Theory of Computation
Online algorithm
Metric matching
Randomized algorithm
Competitive analysis
Metric space
Competitiveness
Competitive algorithms
Randomization
List
Metric
Bipartite graph
Data structure
Pairing
Deterministic algorithms
Graph matching
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:We consider the online metric matching problem in which we are given a metric space, k of whose points are designated as servers. Over time, up to k requests arrive at an arbitrary subset of points in the metric space, and each request must be matched to a server immediately upon arrival, subject to the constraint that at most one request is matched to any particular server. Matching decisions are irrevocable and the goal is to minimize the sum of distances between the requests and their matched servers. We give an O (log 2 k )-competitive randomized algorithm for the online metric matching problem. This improves upon the best known guarantee of O (log 3 k ) on the competitive factor due to Meyerson, Nanavati and Poplawski (SODA ’06, pp. 954–959, 2006 ). It is known that for this problem no deterministic algorithm can have a competitive better than 2 k −1, and that no randomized algorithm can have a competitive ratio better than ln k .
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-012-9676-9