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Complexity of generalized graph coloring

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Mathematical Foundations of Computer Science 1986 (MFCS 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 233))

Abstract

We characterize the complexity of the class of generalized coloring problems, denoted GCP F,k , which arise in resource allocation and VLSI theory. Depending on the parameters, this complexity ranges from polynomial to ∑ p2 -complete. The latter represent apparenly the first natural graph problems to be complete for any intermediate slot of the polynomial hyerarchy. A parallelizable algorithm for the polynomial problems is presented.

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References

  1. Berge, C. Graphs and Hypergraphs, North-Holland, Amsterdam, 1973.

    Google Scholar 

  2. Bollobás, B. Extremal Graph Theory, Academic Press, London, 1978.

    Google Scholar 

  3. Chaitin, G. J. Register Allocation and Spilling via Graph Coloring, SIGPLAN Not. (1982), vol. 17, no. 6, 98–105.

    Google Scholar 

  4. Garey, M. R. and D. S. Johnson. Computers and Intractability. A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.

    Google Scholar 

  5. Garey, M. R., D. S. Johnson, L. J. Stockmeyer. “Some Simplified NP-Complete Graph Problems”, Theoretical Computer Science 1 (1976), 237–267.

    Google Scholar 

  6. Holyer, I. “The NP-Completeness of Some Edge-Paritioning Problems”, SIAM J. Comput., 10 (1981), 713–717.

    Google Scholar 

  7. Karp, R. M. “Reducibility among Combinatorial Problems”, in Complexity of Computer Computations, R. E. Miller and J. W. Thatcher, eds., Plenum, New York, 1972, 85–103.

    Google Scholar 

  8. Mansfield, A. “Topics in Computational Complexity”, Ph.D. Thesis, Univ. of Oxford., 1982.

    Google Scholar 

  9. Papadimitriou, C. H. and K. Steiglitz. Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, Englewood Cliffs, 1982.

    Google Scholar 

  10. Schaefer, T. J. “The Complexity of Satisfiability Problems”, Proceedings of the 10th ACM STOC, New York, 1978, 216–226.

    Google Scholar 

  11. Stockmeyer, L. J. “Polynomial-time Hierarchy”, Theor. Computer Science 3 (1977), 1–22.

    Google Scholar 

  12. Yannakakis, M. “Node-and Edge-Deletion NP-complete Problems”, Proceedings of the 10th ACM STOC, New York, 1978, 253–264.

    Google Scholar 

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Authors and Affiliations

  1. Operations Research Department, Stanford University, 94305, Stanford, CA

    Vladislav Rutenburg

Authors
  1. Vladislav Rutenburg
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Jozef Gruska Branislav Rovan Juraj Wiedermann

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© 1986 Springer-Verlag Berlin Heidelberg

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Rutenburg, V. (1986). Complexity of generalized graph coloring. In: Gruska, J., Rovan, B., Wiedermann, J. (eds) Mathematical Foundations of Computer Science 1986. MFCS 1986. Lecture Notes in Computer Science, vol 233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016284

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  • DOI: https://doi.org/10.1007/BFb0016284

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16783-9

  • Online ISBN: 978-3-540-39909-4

  • eBook Packages: Springer Book Archive

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