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Generating and Radiocoloring Families of Perfect Graphs

  • M. I. Andreou
  • V. G. Papadopoulou
  • P. G. Spirakis
  • B. Theodorides
  • A. Xeros
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)

Abstract

In this work we experimentally study the min order Radiocoloring problem (RCP) on Chordal, Split and Permutation graphs, which are three basic families of perfect graphs. This problem asks to find an assignment using the minimum number of colors to the vertices of a given graph G, so that each pair of vertices which are at distance at most two apart in G have different colors. RCP is an NP-Complete problem on chordal and split graphs [4]. For each of the three families, there are upper bounds or/and approximation algorithms known for minimum number of colors needed to radiocolor such a graph [4,10].

We design and implement radiocoloring heuristics for graphs of above families, which are based on the greedy heuristic. Also, for each one of the above families, we investigate whether there exists graph instances requiring a number of colors in order to be radiocolored, close to the best known upper bound for the family. Towards this goal, we present a number generators that produce graphs of the above families that require either (i) a large number of colors (compared to the best upper bound), in order to be radiocolored, called “extremal” graphs or (ii) a small number of colors, called “non-extremal”instances. The experimental evaluation showed that random generated graph instances are in the most of the cases “non-extremal” graphs. Also, that greedy like heuristics performs very well in the most of the cases, especially for “non-extremal” graphs.

Keywords

Polynomial Time Maximum Degree Greedy Heuristic Chordal Graph Const Color 
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 2005

Authors and Affiliations

  • M. I. Andreou
    • 1
  • V. G. Papadopoulou
    • 2
  • P. G. Spirakis
    • 2
  • B. Theodorides
    • 2
  • A. Xeros
    • 2
  1. 1.IntercollegeNicosiaCyprus
  2. 2.Research Academic Computer Technology Institute (RACTI) and Patras University, Greece.PatrasGreece

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