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The Black-and-White Coloring (BWC) problem seeks a coloring of a graph’s vertices, minimizing the number of edges with endpoints of different colors, given a fixed number of black and white vertices. This problem is known to be NP-complete. We prove that no polynomial-time algorithm can achieve an additive approximation for this problem, unless P = NP.

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Non-existence of Additive Approximations for the Black-and-White Coloring Problem

  • 会议论文

  • 发表日期：

    2026年

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  • Shira Zucker

摘要

The Black-and-White Coloring (BWC) problem seeks a coloring of a graph’s vertices, minimizing the number of edges with endpoints of different colors, given a fixed number of black and white vertices. This problem is known to be NP-complete. We prove that no polynomial-time algorithm can achieve an additive approximation for this problem, unless P = NP.