Approximating the Range Sum of a Graph on CREW PRAM

  • Saurabh Srivastava
  • Phalguni Gupta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2571)


In this paper we have studied the problem of finding the range sum of a graph G =< V,E > which is to color the vertices of a graph with ranges from a specified set in such a way that adjacent vertices are colored with non-overlapping ranges and the sum of the lengths of the ranges is the maximum possible. The problem of finding a good approximation to the range sum is often encountered in many engineering problems. We have presented an efficient parallel algorithm for computing an approximate solution to the range sum problem of a graph on CREW PRAM.


Parallel Algorithm Chromatic Number Adjacent Vertex Graph Coloring Input Graph 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. V. Kale, Ben Richards, and Terry Allen. Efficient parallel graph coloring with prioritization. Lecture Notes in Computer Science, 1996.Google Scholar
  2. 2.
    Gary Lewandowski and Anne Condon, Experiments with parallel graph coloring heuristics and applications of graph coloring, Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, pp. 309–334, 1993.Google Scholar
  3. 3.
    Gary Lewandowski. Practical Implementations and Applications of Graph Coloring. PhD thesis, University of Wisconsin-Madison, August 1994.Google Scholar
  4. 4.
    Andreas Gamst. Some lower bounds for a class of frequency assignment problems. IEEE Transactions on Vehicular Technology, 35(1):8–14, 1986.CrossRefGoogle Scholar
  5. 5.
    G. J. Chaitin, M. Auslander, A. K. Chandra, J. Cocke, M. E. Hopkins and P. Markstein. Register Allocation via coloring. Computer Languages, 6:47–57, 1981.CrossRefGoogle Scholar
  6. 6.
    S. Srivastava, S. Tripathi. Resource Optimization in CDMA based Wireless Ad Hoc Networks. BTP Report 2001-2002, Department of Computer Science and Engineering, IIT Kanpur.Google Scholar
  7. 7.
    Ewa Kubicka and A. J. Schwenk, An Introduction to Chromatic Sums, Proc. of ACM Computer Science Conference, pp. 39–45, 1989.Google Scholar
  8. 8.
    Assefaw Hadish Gebremedhin and Fredrik Manne. Scalable Parallel Graph Coloring Algorithms, Concurrency: Pract. Exper. 2000, 12:1131–1146.zbMATHCrossRefGoogle Scholar
  9. 9.
    Gjertsen, R. K., Jr., M. T. Jones, P. E. Plassmann. 1996. Parallel Heuristics for Improved, Balanced Graph Colorings. Journal of Parallel and Distributed Computing 37:171–186.Google Scholar
  10. 10.
    Magnús M. Halldórsson. Parallel and on-line graph coloring. Journal of Algorithms, 23(2):265–280, May 1997.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Saurabh Srivastava
    • 1
  • Phalguni Gupta
    • 1
  1. 1.Department of Computer Science & EngineeringIndian Institute of Technology KanpurKanpurIndia

Personalised recommendations