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Scheduling Connections via Path and Edge Multicoloring

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9143)

Abstract

We consider path multicoloring problems, in which one is given a collection of paths defined on a graph and is asked to color some or all of them so as to optimize certain objective functions. Typical objectives are: (a) the minimization of the average, over all edges, of the maximum-multiplicity color when the number of colors is given (MinAvgMult-PMC), (b) the minimization of the number of colors when the maximum multiplicity for each edge is given (Min-PMC), or (c) the maximization of the number of colored paths when both the number of colors and a maximum multiplicity constraint for each edge are given (Max-PMC). Such problems also capture edge multicoloring variants (such as MinAvgMult-EMC, Min-EMC, and MaxEMC) as special cases and find numerous applications in resource allocation, most notably in optical and wireless networks, and in communication task scheduling.

Our contribution is two-fold: On the one hand, we give an exact polynomial-time algorithm for Min-PMC on spider networks with even admissible color multiplicities on each edge. On the other hand, we present an approximation algorithm for MinAvgMult-PMC in star networks, with a ratio strictly better than 2; our algorithm uses an appropriate path orientation. We also show that any algorithm which is based on path orientation cannot achieve an approximation ratio better than \(\frac{7}{6}\). Our results apply to the corresponding edge multicoloring problems as well.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LaBRI, UMR 5800Univ. BordeauxTalenceFrance
  2. 2.LIF, Aix-Marseille University and CNRSMarseilleFrance
  3. 3.School of Electrical and Computer EngineeringNational Technical University of AthensAthensGreece
  4. 4.Santa Clara UniversitySanta ClaraUSA

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