Computing

, Volume 80, Issue 3, pp 255–274 | Cite as

Path multicoloring with fewer colors in spiders and caterpillars

Article

Abstract

We study a recently introduced path coloring problem with applications to wavelength assignment in all-optical networks with multiple fibers. In contrast to classical path coloring, it is, in this setting, possible to assign a color more than once to paths that pass through the same edge; the number of allowed repetitions per edge is given and the goal is to minimize the number of colors used.

We present algorithms and hardness results for tree topologies of special interest. Our algorithms achieve approximation ratio of 2 in spiders and 3 in caterpillars, whereas the best algorithm for trees so far, achieves an approximation ratio of 4. We also study the directed version of the problem and show that it admits a 3-approximation algorithm in caterpillars, while it can be solved exactly in spiders.

AMS Subject Classifications

68U05 68R10 05C05 05C15 90B18 05C85 90C59 94C15 

Keywords

Path coloring multifiber all-optical networks approximation algorithms spiders caterpillars 

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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Department of Computer Science, School of Electrical and Computer EngineeringNational Technical University of AthensAthensGreece
  2. 2.Computer and Information ScienceBrooklyn CollegeBrooklynUSA

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