Abstract
In social network theory, a simple graph G is called k-role assignable if there is a surjective mapping that assigns a number from {1,...,k} called a role to each vertex of G such that any two vertices with the same role have the same sets of roles assigned to their neighbors. The decision problem whether such a mapping exists is called the k -Role Assignment problem. This problem is known to be NP-complete for any fixed k ≥ 2. In this paper we classify the computational complexity of the k -Role Assignment problem for the class of chordal graphs. We show that for this class the problem becomes polynomially solvable for k = 2, but remains NP-complete for any k ≥ 3. This generalizes results of Sheng and answers his open problem.
This work has been supported by EPSRC (EP/D053633/1).
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References
Abello, J., Fellows, M.R., Stillwell, J.C.: On the complexity and combinatorics of covering finite complexes. Australian Journal of Combinatorics 4, 103–112 (1991)
Angluin, D.: Local and global properties in networks of processors. In: 12th ACM Symposium on Theory of Computing, pp. 82–93 (1980)
Angluin, D., Gardiner, A.: Finite common coverings of pairs of regular graphs. Journal of Combinatorial Theory B 30, 184–187 (1981)
Biggs, N.: Constructing 5-arc transitive cubic graphs. Journal of London Mathematical Society II 26, 193–200 (1982)
Bodlaender, H.L.: The classification of coverings of processor networks. Journal of Parallel Distributed Computing 6, 166–182 (1989)
Chalopin, J., Métivier, Y., Zielonka, W.: Local computations in graphs: the case of cellular edge local computations. Fundamenta Informaticae 74, 85–114 (2006)
Diestel, R.: Graph Theory, 3rd edn. Springer, Heidelberg (2005)
Everett, M.G., Borgatti, S.: Role colouring a graph. Mathematical Social Sciences 21, 183–188 (1991)
Fiala, J., Kratochvíl, J.: Complexity of partial covers of graphs. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223, pp. 537–549. Springer, Heidelberg (2001)
Fiala, J., Kratochvíl, J.: Partial covers of graphs. Discussiones Mathematicae Graph Theory 22, 89–99 (2002)
Fiala, J., Kratochvíl, J., Kloks, T.: Fixed-parameter complexity of λ-labelings. Discrete Applied Mathematics 113, 59–72 (2001)
Fiala, J., Paulusma, D.: A complete complexity classification of the role assignment problem. Theoretical Computer Science 349, 67–81 (2005)
Fiala, J., Paulusma, D.: Comparing universal covers in polynomial time. Theory of Computing Systems (to appear)
Galinier, P., Habib, M., Paul, C.: Chordal graphs and their clique graphs. In: Nagl, M. (ed.) WG 1995. LNCS, vol. 1017, pp. 358–371. Springer, Heidelberg (1995)
Garey, M.R., Johnson, D.S.: Computers and Intractability. W.H. Freeman and Co., New York (1979)
Kratochvíl, J., Proskurowski, A., Telle, J.A.: Covering regular graphs. Journal of Combinatorial Theory B 71, 1–16 (1997)
Pekeč, A., Roberts, F.S.: The role assignment model nearly fits most social networks. Mathematical Social Sciences 41, 275–293 (2001)
Rieck, Y., Yamashita, Y.: Finite planar emulators for K 4,5 − 4K 2 and Fellows’ conjecture. Manuscript (2009), arXiv:0812.3700v2
Roberts, F.S., Sheng, L.: How hard is it to determine if a graph has a 2-role assignment? Networks 37, 67–73 (2001)
Sheng, L.: 2-Role assignments on triangulated graphs. Theoretical Computer Science 304, 201–214 (2003)
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van ’t Hof, P., Paulusma, D., van Rooij, J.M.M. (2009). Computing Role Assignments of Chordal Graphs. In: Kutyłowski, M., Charatonik, W., Gębala, M. (eds) Fundamentals of Computation Theory. FCT 2009. Lecture Notes in Computer Science, vol 5699. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03409-1_18
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DOI: https://doi.org/10.1007/978-3-642-03409-1_18
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