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Models and Approximation Algorithms for Channel Assignment in Radio Networks

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Abstract

We consider the frequency assignment (broadcast scheduling) problem for packet radio networks. Such networks are naturally modeled by graphs with a certain geometric structure. The problem of broadcast scheduling can be cast as a variant of the vertex coloring problem (called the distance-2 coloring problem) on the graph that models a given packet radio network. We present efficient approximation algorithms for the distance-2 coloring problem for various geometric graphs including those that naturally model a large class of packet radio networks. The class of graphs considered include (r,s)-civilized graphs, planar graphs, graphs with bounded genus, etc.

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References

  1. G. Agnarsson and M. Halldórsson, Coloring powers of planar graphs, in: Proc. Eleventh Annual ACM-SIAM Symposium on Algorithms (SODA'2000), San Francisco, CA (January 2000) pp. 654–662.

  2. S. Arnborg, Efficient algorithms for combinatorial problems on graphs with bounded decomposability, BIT 25 (1985) 2–23.

    Google Scholar 

  3. S. Arnborg, J. Lagergren and D. Seese, Easy problems for treedecomposable graphs, J. Algorithms 12 (1991) 308–340.

    Google Scholar 

  4. S. Arnborg and A. Proskurowski, Linear-time algorithms for NP-hard problems on graphs embedded in k-trees, Discrete Applied Math. 23 (1989) 11–24.

    Google Scholar 

  5. B.S. Baker, Approximation algorithms for NP-complete problems on planar graphs, J. ACM 41 (1994) 308–340.

    Google Scholar 

  6. H.L. Bodlaender, Dynamic programming on graphs of bounded treewidth, in: Proc. 15th International Colloquium on Automata Languages and Programming (ICALP'88), Lecture Notes in Computer Science, Vol. 317 (1988) pp. 105–118.

    Google Scholar 

  7. H.L. Bodlaender, Planar graphs with bounded treewidth, Technical report RUU-CS–88–14, Department of Computer Science, University of Utrecht, The Netherlands (March 1988).

    Google Scholar 

  8. B.N. Clark, C.J. Colbourn and D.S. Johnson, Unit disk graphs, Discrete Math. 86 (1990) 165–177.

    Google Scholar 

  9. P.G. Doyle and J.L. Snell, Random Walks and Electric Networks, The Carus Mathematical Monographs (The Mathematical Association of America, Providence, RI, 1984).

    Google Scholar 

  10. A. Gräf, M. Stumpf and G. Weißenfels, On coloring unit disk graphs, Algorithmica 20 (1998) 277–293.

    Google Scholar 

  11. K. Greenbaum, G.L. Miller and S.H. Teng, Moments of inertia and graph separators, in: Proc. 5th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'94), Arlington, VA (January 1994) pp. 452–461.

  12. J. van den Huevel and S. McGuinness, Coloring the square of a planar graph, Report No. LSE-CDAM–99–06, Center for Discrete and Applicable Mathematics, London School of Economics, London, UK (June 1999).

    Google Scholar 

  13. H.B. Hunt III, M.V. Marathe, V. Radhakrishnan, S.S. Ravi, D.J. Rosenkrantz and R.E. Stearns, NC-approximation schemes for NP and PSPACE-hard problems for geometric graphs, J. Algorithms 26 (1998) 238–274.

    Google Scholar 

  14. S. Irani, Coloring inductive graphs on-line, Algorithmica 11 (1994) 53–72.

    Google Scholar 

  15. K. Jansen, An approximation scheme for bin packing with conflicts, in: Proc. Scandinavian Workshop on Algorithmic Theory (SWAT'98), Stockholm, Sweden, Lecture Notes in Computer Science, Vol. 1432 (Springer-Verlag, July 1998) pp. 35–46.

    Google Scholar 

  16. D.S. Johnson, The NP-completeness column: An ongoing guide, J. Algorithms 3 (1982) 184.

    Google Scholar 

  17. X. Ma and E.L. Lloyd, Personal communication (March 1999).

  18. M.V. Marathe, H. Breu, H.B. Hunt III, S.S. Ravi and D.J. Rosenkrantz, Simple heuristics for unit disk graphs, Networks 25 (1995) 59–68.

    Google Scholar 

  19. S.T. McCormick, Optimal approximation of sparse Hessians and its equivalence to a graph coloring problem, Math. Programming 26 (1983) 153–171.

    Google Scholar 

  20. G.L. Miller, S.H. Teng, W. Thurston and S.A. Vavasis, Separators for sphere packings and nearest neighbor graphs, J. ACM 44 (1997) 1–29.

    Google Scholar 

  21. G.L. Miller, S.H. Teng and S.A. Vavasis, A unified geometric approach to graph separators, in: Proc. 32nd IEEE Symposium on Foundations of Computer Science (FOCS'91), Puerto Rico (October 1991) pp. 538–547.

  22. A. Proskurowski and M.M. Syslo, Efficient vertex and edge coloring of outerplanar graphs, SIAM J. Algebraic and Discrete Methods 7 (1986) 131–136.

    Google Scholar 

  23. S. Ramanathan, Scheduling algorithms for multi-hop radio networks, Ph.D. Thesis, Department of Computer Science, University of Delaware, Newark (1993).

    Google Scholar 

  24. S. Ramanathan, A unified framework and algorithm for (T/F/C) DMA channel assignment in wireless networks, in: Proc. IEEE INFOCOM' 97, Kobe, Japan (April 1997).

  25. S. Ramanathan and E.L. Lloyd, Scheduling algorithms for multi-hop radio networks, IEEE/ACM Transactions on Networking 1 (1993) 166–172.

    Google Scholar 

  26. N. Robertson and P. Seymour, Graph minors XIV, Wagner's conjecture, Preprint (1992).

  27. A. Sen and M.L. Huson, A new model for scheduling packet radio networks, Wireless Networks 3 (1997) 71–82.

    Google Scholar 

  28. A. Sen and E. Malesinska, On approximation algorithms for radio network scheduling, Technical report 96–008, Department of Computer Science and Engineering, Arizona State University, Tempe, AZ (1996).

    Google Scholar 

  29. D. Spielman and S.H. Teng, Spectral partitioning works: Planar graphs and finite element meshes, in: 37th Annual Symposium on Foundations of Computer Science (FOCS'96), Burlington, VT (October 1996) 96–105.

  30. S.H. Teng, Points, spheres, and separators, A unified geometric approach to graph separators, Ph.D. Thesis, School of Computer Science, Carnegie Mellon University, CMU-CS–91–184, Pittsburgh (August 1991).

  31. S.A. Vavasis, Automatic domain partitioning in three dimensions, SIAM J. Sci. Stat. Comp. 12 (1991) 950–970.

    Google Scholar 

  32. R.J. Wilson, Introduction to Graph Theory, 2nd edition (Longman Publishers, Bungay, UK, 1979).

    Google Scholar 

  33. X. Zhou, Y. Kanari and T. Nishizeki, Generalized vertex colorings of partial k-trees, IEICE Transaction Fundamentals E-A(4) (April 2000) 1–8.

    Google Scholar 

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Authors and Affiliations

  1. 14195 Berlin, Germany

    Sven O. Krumke

  2. MS M997, Los Alamos National Laboratory, Los Alamos NM 87545, USA

    Madhav V. Marathe

  3. Department of Computer Science, University at Albany–State University of New York, Albany, NY, 12222, USA

    S.S. Ravi

Authors
  1. Sven O. Krumke
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  2. Madhav V. Marathe
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  3. S.S. Ravi
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Krumke, S.O., Marathe, M.V. & Ravi, S. Models and Approximation Algorithms for Channel Assignment in Radio Networks. Wireless Networks 7, 575–584 (2001). https://doi.org/10.1023/A:1012311216333

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