Two-Class (r,k)-Coloring: Coloring with Service Guarantees

Pál András Papp; Roland Schmid; Valentin Stoppiello; Roger Wattenhofer

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arXiv · 2108.03882

Two-Class (r,k)-Coloring: Coloring with Service Guarantees

Pál András Papp·Roland Schmid·Valentin Stoppiello·Roger Wattenhofer

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Abstract

This paper introduces the Two-Class ($r$,$k$)-Coloring problem: Given a fixed number of $k$ colors, such that only $r$ of these $k$ colors allow conflicts, what is the minimal number of conflicts incurred by an optimal coloring of the graph? We establish that the family of Two-Class ($r$,$k$)-Coloring problems is NP-complete for any $k \geq 2$ when $(r, k) \neq (0,2)$. Furthermore, we show that Two-Class ($r$,$k$)-Coloring for $k \geq 2$ colors with one ($r = 1$) relaxed color cannot be approximated to any constant factor ($\notin$ APX). Finally, we show that Two-Class ($r$,$k$)-Coloring with $k \geq r \geq 2$ colors is APX-complete.

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BibTeX RIS

Pál András Papp, Roland Schmid, Valentin Stoppiello, Roger Wattenhofer. 2021-08-09. Two-Class (r,k)-Coloring: Coloring with Service Guarantees. https://arxiv.org/abs/2108.03882

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