Maintaining Near-Popular Matchings

Hoefer, M. (author): Max Planck Gesellschaft zur Förderung der Wissenschaften e.V. (MPG),Max Planck Society for the Advancement of Science (MPG)

Huang, Chien-Chung, 1976 (author): Chalmers tekniska högskola,Chalmers University of Technology

Wagner, L. (author): Rheinisch-Westfaelische Technische Hochschule Aachen,RWTH Aachen University

Institute of Mathematical Sciences India Max Planck Gesellschaft zur Förderung der Wissenschaften eV. (MPG) (creator_code:org_t)

ISBN 9783662476666
2015-06-20
2015
English.
In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - Berlin, Heidelberg : Springer Berlin Heidelberg. - 1611-3349 .- 0302-9743. - 9783662476666 ; 9135, s. 504-515

Related links:: http://dx.doi.org/10...; show more...; http://wrap.warwick....; https://research.cha...; https://doi.org/10.1...; show less...

Abstract Subject headings

We study dynamic matching problems in graphs among agents with preferences. Agents and/or edges of the graph arrive and depart iteratively over time. The goal is to maintain matchings that are favorable to the agent population and stable over time. More formally, we strive to keep a small unpopularity factor by making only a small amortized number of changes to the matching per round. Our main result is an algorithm to maintain matchings with unpopularity factor (Delta + k) by making an amortized number of O(Delta + Delta(2) /k) changes per round, for any k > 0. Here Delta denotes the maximum degree of any agent in any round. We complement this result by a variety of lower bounds indicating that matchings with smaller factor do not exist or cannot be maintained using our algorithm. As a byproduct, we obtain several additional results that might be of independent interest. First, our algorithm implies existence of matchings with small unpopularity factors in graphs with bounded degree. Second, given any matching M and any value alpha >= 1, we provide an efficient algorithm to compute a matching M' with unpopularity factor a over M if it exists. Finally, our results show the absence of voting paths in two-sided instances, even if we restrict to sequences of matchings with larger unpopularity factors (below Delta).

By the author/editor: Bhattacharya, S.; Hoefer, M.; Huang, Chien-Chu ...; Kavitha, T.; Wagner, L.

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Computer and Inf ...; and Computer Enginee ...

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