The Minimum Feasible Tileset Problem

Yann Disser; Stefan Kratsch; Manuel Sorge

doi:10.1007/s00453-018-0460-3

The Minimum Feasible Tileset Problem

Yann Disser, Stefan Kratsch, Manuel Sorge

Department of Industrial Engineering and Management

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce and study the Minimum Feasible Tileset problem: given a set of symbols and subsets of these symbols (scenarios), find a smallest possible number of pairs of symbols (tiles) such that each scenario can be formed by selecting at most one symbol from each tile. We show that this problem is APX-hard and that it is NP-hard even if each scenario contains at most three symbols. Our main result is a 4/3-approximation algorithm for the general case. In addition, we show that the Minimum Feasible Tileset problem is fixed-parameter tractable both when parameterized with the number of scenarios and with the number of symbols.

Original language	English
Pages (from-to)	1126-1151
Number of pages	26
Journal	Algorithmica
Volume	81
Issue number	3
DOIs	https://doi.org/10.1007/s00453-018-0460-3
State	Published - 15 Mar 2019

Keywords

APX hardness
Approximation algorithm
Minimum feasible tileset
Parameterized complexity
Set packing

ASJC Scopus subject areas

General Computer Science
Computer Science Applications
Applied Mathematics

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10.1007/s00453-018-0460-3

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title = "The Minimum Feasible Tileset Problem",

abstract = "We introduce and study the Minimum Feasible Tileset problem: given a set of symbols and subsets of these symbols (scenarios), find a smallest possible number of pairs of symbols (tiles) such that each scenario can be formed by selecting at most one symbol from each tile. We show that this problem is APX-hard and that it is NP-hard even if each scenario contains at most three symbols. Our main result is a 4/3-approximation algorithm for the general case. In addition, we show that the Minimum Feasible Tileset problem is fixed-parameter tractable both when parameterized with the number of scenarios and with the number of symbols.",

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AB - We introduce and study the Minimum Feasible Tileset problem: given a set of symbols and subsets of these symbols (scenarios), find a smallest possible number of pairs of symbols (tiles) such that each scenario can be formed by selecting at most one symbol from each tile. We show that this problem is APX-hard and that it is NP-hard even if each scenario contains at most three symbols. Our main result is a 4/3-approximation algorithm for the general case. In addition, we show that the Minimum Feasible Tileset problem is fixed-parameter tractable both when parameterized with the number of scenarios and with the number of symbols.

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KW - Approximation algorithm

KW - Minimum feasible tileset

KW - Parameterized complexity

KW - Set packing

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The Minimum Feasible Tileset Problem

Abstract

Keywords

ASJC Scopus subject areas

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