文章基本信息

标题：Solving Packing Problems with Few Small Items Using Rainbow Matchings
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作者：Max Bannach ; Sebastian Berndt ; Marten Maack 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：170
页码：11:1-11:14
DOI：10.4230/LIPIcs.MFCS.2020.11
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：An important area of combinatorial optimization is the study of packing and covering problems, such as Bin Packing, Multiple Knapsack, and Bin Covering. Those problems have been studied extensively from the viewpoint of approximation algorithms, but their parameterized complexity has only been investigated barely. For problem instances containing no "small" items, classical matching algorithms yield optimal solutions in polynomial time. In this paper we approach them by their distance from triviality, measuring the problem complexity by the number k of small items. Our main results are fixed-parameter algorithms for vector versions of Bin Packing, Multiple Knapsack, and Bin Covering parameterized by k. The algorithms are randomized with one-sided error and run in time 4^kâ<. k!â<. n^{O(1)}. To achieve this, we introduce a colored matching problem to which we reduce all these packing problems. The colored matching problem is natural in itself and we expect it to be useful for other applications. We also present a deterministic fixed-parameter algorithm for Bin Covering with run time O((k!)Â² â<. k â<. 2^k â<. n log(n)).
关键词：Bin Packing; Knapsack; matching; fixed-parameter tractable