We study the multicoloring problem with two objective functions: minimizing the makespan and minimizing the multisum. We focus on partial k-trees and planar graphs. In particular, we give polynomial time approximation schemes (PTAS) for both classes, for both preemptive and non-preemptive multisum colorings.


Planar Graph Coloring Problem Polynomial Time Approximation Schema Outerplanar Graph Color Requirement 
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  1. [B88]
    Bodlaender, H.L.: Planar Graphs with Bounded Treewidth. Tech. Report RUU-CS-88-14, Dept. of Comp. Sci., Univ. of Utrecht (March 1988)Google Scholar
  2. [B92]
    Bell, M.: Future directions in traffic signal control. Transportation Research Part A 26, 303–313 (1992)Google Scholar
  3. [B94]
    Baker, B.S.: Approximation algorithms for NP-complete problems on planar graphs. J. ACM 41, 153–180 (1994)zbMATHCrossRefGoogle Scholar
  4. [BBH+98]
    Bar-Noy, A., Bellare, M., Halldórsson, M.M., Shachnai, H., Tamir, T.: On chromatic sums and distributed resource allocation. Information and Computation 140, 183–202 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  5. [BH94]
    Bullock, D., Hendrickson, C.: Roadway traffic control software. IEEE Transactions on Control Systems Technology 2, 255–264 (1994)zbMATHCrossRefGoogle Scholar
  6. [BK98]
    Bar-Noy, A., Kortsarz, G.: The minimum color-sum of bipartite graphs. Journal of Algorithms 28, 339–365 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  7. [BHK+98]
    Bar-Noy, A., Halldórsson, M.M., Kortsarz, G., Shachnai, H., Salman, R.: Sum Multi-Coloring of Graphs. In: Nešetřil, J. (ed.) ESA 1999. LNCS, vol. 1643, pp. 390–401. Springer, Heidelberg (1999) (To appear)CrossRefGoogle Scholar
  8. [CCO93]
    Chen, J., Cidon, I., Ofek, Y.: A local fairness algorithm for gigabit LANs/MANs with spatial reuse. IEEE Journal on Selected Areas in Communications 11, 1183–1192 (1993)CrossRefGoogle Scholar
  9. [FK98]
    Feige, U., Kilian, J.: Zero Knowledge and the Chromatic number. Journal of Computer and System Sciences 57(2), 187–199 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  10. [GJ79]
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. W. H. Freeman, New York (1979)zbMATHGoogle Scholar
  11. [HK99]
    Halldórsson, M.M., Kortsarz, G.: Multicoloring Planar Graphs and Partial k-Trees At
  12. [HK+99]
    Halldórsson, M.M., Kortsarz, G., Proskurowski, A., Salman, R., Shachnai, H., Telle, J.A.: Multi-Coloring Trees. In: Asano, T., Imai, H., Lee, D.T., Nakano, S.-i., Tokuyama, T. (eds.) COCOON 1999. LNCS, vol. 1627, p. 271. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  13. [J97]
    Jansen, K.: The Optimum Cost Chromatic Partition Problem. In: Bongiovanni, G., Bovet, D.P., Di Battista, G. (eds.) CIAC 1997. LNCS. vol. 1203, Springer, Heidelberg (1997)Google Scholar
  14. [KS89]
    Kubicka, E., Schwenk, A.J.: An Introduction to Chromatic Sums. In: Proceedings of the ACM Computer Science Conf., pp. 39–45 (1989)Google Scholar
  15. [MR97]
    McDiarmid, C., Reed, B.: Channel assignment and weighted coloring. Manuscript (1997)Google Scholar
  16. [NS97]
    Narayanan, L., Shende, S.: Static Frequency Assignment in Cellular Networks. Manuscript (1997)Google Scholar
  17. [NSS99]
    Nicoloso, S., Sarrafzadeh, M., Song, X.: On the Sum Coloring Problem on Interval Graphs. Algorithmica 23, 109–126 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  18. [SG98]
    Silberschatz, A., Galvin, P.: Operating System Concepts, 5th edn. Addison-Wesley, Reading (1998)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Magnús M. Halldórsson
    • 1
  • Guy Kortsarz
    • 2
  1. 1.Science InstituteUniversity of IcelandReykjavíkIceland
  2. 2.Dept. of Computer ScienceOpen UniversityRamat AvivIsrael

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