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arXiv · 1704.02836

The quadratic M-convexity testing problem

Yuni Iwamasa
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Abstract

M-convex functions, which are a generalization of valuated matroids, play a central role in discrete convex analysis. Quadratic M-convex functions constitute a basic and important subclass of M-convex functions, which has a close relationship with phylogenetics as well as valued constraint satisfaction problems. In this paper, we consider the quadratic M-convexity testing problem (QMCTP), which is the problem of deciding whether a given quadratic function on $\{0,1\}^n$ is M-convex. We show that QMCTP is co-NP-complete in general, but is polynomial-time solvable under a natural assumption. Furthermore, we propose an $O(n^2)$-time algorithm for solving QMCTP in the polynomial-time solvable case.

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Yuni Iwamasa. 2017-04-10. The quadratic M-convexity testing problem. https://doi.org/10.1016/j.dam.2017.12.004

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