Compact Forbidden-Set Routing

  • Bruno Courcelle
  • Andrew Twigg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)


We study labelling schemes for X-constrained path problems. Given a graph (V,E) and \(X\subseteq V\), a path is X-constrained if all intermediate vertices avoid X. We study the problem of assigning labels J(x) to vertices so that given {J(x):x ∈ X} for any \(X\subseteq V\), we can route on the shortest X-constrained path between x,y ∈ X. This problem is motivated by Internet routing, where the presence of routing policies means that shortest-path routing is not appropriate. For graphs of tree width k, we give a routing scheme using routing tables of size O(k 2log2 n). We introduce m-clique width, generalizing clique width, to show that graphs of m-clique width k also have a routing scheme using size O(k 2log2 n) tables.


Algorithms labelling schemes compact routing. 


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  1. 1.
    Thorup, M., Zwick, U.: Compact routing schemes. In: SPAA ’01: Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures, Crete Island, Greece, pp. 1–10. ACM Press, New York (2001), doi:10.1145/378580.378581CrossRefGoogle Scholar
  2. 2.
    Varadhan, K., Govindan, R., Estrin, D.: Persistent route oscillations in inter-domain routing. Technical report, USC/ISI (1996)Google Scholar
  3. 3.
    Griffin, T.G., Shepherd, F.B., Wilfong, G.: The stable paths problem and interdomain routing. IEEE/ACM Trans. Netw. 10(2), 232–243 (2002)CrossRefGoogle Scholar
  4. 4.
    Feigenbaum, J., et al.: Subjective-cost policy routing. In: Deng, X., Ye, Y. (eds.) WINE 2005. LNCS, vol. 3828, pp. 174–183. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Courcelle, B., Vanicat, R.: Query efficient implementation of graphs of bounded clique-width. Discrete Applied Mathematics 131(1), 129–150 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gupta, A., Kumar, A., Thorup, M.: Tree based mpls routing. In: SPAA ’03: Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures, San Diego, California, USA, pp. 193–199. ACM Press, New York (2003), doi:10.1145/777412.777443CrossRefGoogle Scholar
  7. 7.
    Courcelle, B.: Graph decompositions. Chapter of a book in preparation (2006), Available at
  8. 8.
    Arnborg, S., et al.: An algebraic theory of graph reduction. J. ACM 40(5), 1134–1164 (1993), doi:10.1145/174147.169807zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Bodlaender, H.L.: NC-algorithms for graphs with small treewidth. In: van Leeuwen, J. (ed.) WG 1988. LNCS, vol. 344, pp. 1–10. Springer, Heidelberg (1989)Google Scholar
  10. 10.
    Corneil, D.G., Rotics, U.: On the relationship between clique-width and treewidth. SIAM J. Comput. 34(4), 825–847 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Wanke, E.: k-nlc graphs and polynomial algorithms. Discrete Applied Mathematics 54(2-3), 251–266 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Courcelle, B., Olariu, S.: Upper bounds to the clique width of graphs. Discrete Appl. Math. 101(1-3), 77–114 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Kannan, S., Naor, M., Rudich, S.: Implicit representation of graphs. SIAM J. Discret. Math. 5(4), 596–603 (1992), doi:10.1137/0405049zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Fellows, M.R., et al.: Clique-width minimization is np-hard. In: STOC 2006, Proceedings of the thirty-eighth annual ACM symposium on Theory of computing, Seattle, Washington, ACM Press, New York (2006)Google Scholar
  15. 15.
    Oum, S.-i.: Approximating rank-width and clique-width quickly. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 49–58. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Bruno Courcelle
    • 1
  • Andrew Twigg
    • 2
  1. 1.LaBRI, Bordeaux 1 University and CNRS 
  2. 2.Computer Laboratory, Cambridge University 

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