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Solving packing problems with few small items using rainbow matchings
Citation Link: https://doi.org/10.15480/882.2882
Publikationstyp
Conference Paper
Publikationsdatum
2020
Sprache
English
Institut
TORE-URI
First published in
Number in series
170
Start Page
11:1
End Page
11:14
Citation
International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Contribution to Conference
Publisher DOI
Scopus ID
2-s2.0-85090505183
ArXiv ID
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 4k · k! · nO(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 Packing with run time O((k!)2 · k · 2k · n log(n)).
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 4k · k! · nO(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 Packing with run time O((k!)2 · k · 2k · n log(n)).
Schlagworte
Bin Packing
Knapsack
matching
fixed-parameter tractable
DDC Class
004: Informatik