Path Multicoloring with Fewer Colors in Spiders and Caterpillars

Publication Date

July 2007

Document Type

Article

Publication Title

Computing

Volume

80

DOI

10.1007/s00607-007-0234-2

First Page

255

Last Page

274

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.

Keywords

Path coloring, multifiber all-optical networks, approximation algorithms, spiders, caterpillars

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