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Max-Coloring Paths: Tight Bounds and Extensions

  • Telikepalli Kavitha
  • Julián Mestre
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)

Abstract

The max-coloring problem is to compute a legal coloring of the vertices of a graph G = (V,E) with a non-negative weight function w on V such that \(\sum_{i=1}^k \max_{v\in C_i} w(v_i)\) is minimized, where C 1,...,C k are the various color classes. Max-coloring general graphs is as hard as the classical vertex coloring problem, a special case where vertices have unit weight. In fact, in some cases it can even be harder: for example, no polynomial time algorithm is known for max-coloring trees. In this paper we consider the problem of max-coloring paths and its generalization, max-coloring a broad class of trees and show it can be solved in time \(O(|V| + \text{time for sorting the vertex weights})\). When vertex weights belong to ℝ, we show a matching lower bound of Ω(|V|log|V|) in the algebraic computation tree model.

Keywords

Candidate Solution Polynomial Time Algorithm Legal Coloring Color Class Tight Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Telikepalli Kavitha
    • 1
  • Julián Mestre
    • 2
  1. 1.Indian Institute of ScienceBangaloreIndia
  2. 2.Max-Plank-Institut für InformatikSaarbrückenGermany

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