The Maximum Matrix Contraction Problem

Dimitri Watel; Pierre-Louis Poirion

doi:10.1007/978-3-319-45587-7_37

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arXiv · 2306.01349

The Maximum Matrix Contraction Problem

Dimitri Watel·Pierre-Louis Poirion

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Abstract

In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem. Especially, we prove this problem to be NP-Complete and that every algorithm solving this problem is at most a $2\sqrt{n}$-approximation algorithm where n is the number of ones in the matrix. We then focus on efficient algorithms to solve the problem: an integer linear program and three heuristics.

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Dimitri Watel, Pierre-Louis Poirion. 2023-06-02. The Maximum Matrix Contraction Problem. https://doi.org/10.1007/978-3-319-45587-7_37

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