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A 116/13-Approximation Algorithm for L(2, 1)-Labeling of Unit Disk Graphs

  • Hirotaka OnoEmail author
  • Hisato YamanakaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11376)

Abstract

Given a graph, an L(2, 1)-labeling of the graph is an assignment \(\ell \) from the vertex set to the set of nonnegative integers such that for any pair of vertices (uv), \(|\ell (u) - \ell (v)| \ge 2\) if u and v are adjacent, and \(\ell (u) \ne \ell (v)\) if u and v are at distance 2. The L(2, 1)-labeling problem is to minimize the span of \(\ell \) (i.e., \(\max _{u \in V}(\ell (u)) - \min _{u \in V}(\ell (u)) + 1\)). In this paper, we propose a new polynomial-time 116/13-approximation algorithm for L(2, 1)-labeling of unit disk graphs. This improves the previously best known ratio 12.

Keywords

Frequency/channel assignment Graph algorithm L(2, 1)-labeling Approximation algorithm Unit disk graphs 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical Informatics, Graduate School of InformaticsNagoya UniversityNagoyaJapan

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