Abstract
We present novel results on and efficient deterministic as well as randomized synchronous message-passing distributed algorithms for generalized graph alliances, a new concept incorporating and expanding previous ones. An alliance is here a group of nodes of a connected network or a population fulfilling certain thresholds for their neighbourhood. More precisely, every node outside and inside the alliance must have a minimum number of neighbours inside the alliance. A threshold function defining this number may be specific to each node. We are interested in finding minimal alliances of generalized type: the threshold function might be any. We also investigate conditions in which it is possible to have anonymity, a praised property in population protocols.
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References
Angluin, D., Aspnes, J., Eisenstat, D.: Fast computation by population protocols with a leader. Distributed Computing 21(3), 183–199 (2008)
Angluin, D., Aspnes, J., Eisenstat, D., Ruppert, E.: The computational power of population protocols. Distributed Computing 20(4), 279–304 (2007); PODC 2006, Special Issue
Beauquier, J., Datta, A.K., Gradinariu, M., Magniette, F.: Self-Stabilizing Local Mutual Exclusion and Daemon Refinement. In: Herlihy, M.P. (ed.) DISC 2000. LNCS, vol. 1914, pp. 223–237. Springer, Heidelberg (2000)
Bar-Ilan, J., Kortsarz, G., Peleg, D.: How to allocate network centers. Journal of Algorithms 15, 385–415 (1993)
Centeno, C., Dourado, M.C., Penso, L.D., Rautenbach, D., Szwarcfiter, J.L.: Irreversible Conversions on Graphs. Accepted in Theoretical Computer Science (to appear)
Dourado, M.C., Penso, L.D., Rautenbach, D., Szwarcfiter, J.L.: On Reversible and Irreversible Conversions. In: International Symposium on Distributed Computing (DISC 2010), pp. 395-397 (September 2010)
Dourado, M.C., Penso, L.D., Rautenbach, D., Szwarcfiter, J.L.: Reversible Iterative Graph Processes (under submission)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Communications of the ACM 17, 643–644 (1974)
Dolev, S.: Self-Stabilization. MIT Press, Cambridge (2000)
Dreyer Jr., P.A., Roberts, F.S.: Irreversible k-Threshold Processes: Graph-Theoretical Threshold Models of the Spread of Disease and of Opinion. Discrete Applied Mathematics 157(7), 1615–1627 (2009)
Goddard, W., Hedetniemi, S.T., Jacobs, D.D., Trevisan, V.: Distance-k Information in Self-Stabilizing Algorithms. In: Flocchini, P., Gąsieniec, L. (eds.) SIROCCO 2006. LNCS, vol. 4056, pp. 349–356. Springer, Heidelberg (2006)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman & Co., New York (1979)
Gupta, A., Maggs, B.M., Oprea, F., Reiter, M.K.: Quorum Placement in Networks to Minimize Access Delays. In: ACM Symposium on Principles of Distributed Computing, PODC 2005 (July 2005)
Golovin, D., Gupta, A., Maggs, B.M., Oprea, F., Reiter, M.K.: Quorum Placement in Networks: Minimizing Network Congestion. In: ACM Symposium on Principles of Distributed Computing, PODC 2006 (July 2006)
Herlihy, M.: Concurrency and Availability as Dual Properties of Replicated Atomic Data. Journal of the ACM 37(2), 257–278 (1990)
Hassin, Y., Peleg, D.: Average Probe Complexity in Quorum Systems. In: ACM Symposium on Principles of Distributed Computing (PODC 2001), pp. 180–189 (August 2001)
Jamieson, L.H.: Algorithms and Complexities for Alliances and Weighted Alliances of Various Types. Clemson University (May 2007)
Kuhn, F., Wattenhofer, R.: Constant-time distributed dominating set approximation. In: ACM Symposium on Principles of Distributed Computing, PODC 2003 (July 2003)
Kutten, S., Peleg, D.: Fast Distributed Construction of Small k-Dominating Sets and Applications. Journal of Algorithms 28(1), 40–66 (1998)
Lenzen, C., Wattenhofer, R.: Minimum Dominating Set Approximation in Graphs of Bounded Arboricity. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 510–524. Springer, Heidelberg (2010)
Peleg, D.: Majority Voting, Coalitions and Monopolies in Graphs. In: International Symposium in Structured Information and Communication Complexity (SIROCCO 1996), pp. 152–169 (June 1996)
Peleg, D., Upfal, E.: A tradeoff between size and efficiency for routing tables. Journal of ACM 36, 510–530 (1989)
Penso, L.D., Barbosa, V.: A Distributed Algorithm for Finding k-Dominating Sets. Discrete Applied Mathematics 141(1-3), 243–253 (2004)
Rautenbach, D., Volkmann, L.: New Bounds on the k-domination number and on the k-tuple domination number. Applied Mathematics Letters 20(1), 98–102 (2007)
Schneider, M.: Self-Stabilization. ACM Computing Surveys 25(1), 45–67 (1993)
Srimani, P.K., Xu, Z.: Distributed Protocols for Defensive and Offensive Alliances in Network Graphs Using Self-Stabilization. In: International Conference on Computing: Theory and Applications (ICCTA 2007), pp. 27–31 (2007)
Wittmann, R., Zitterbart, M.: Multicast Communication: Protocols and Applications. Morgan Kaufmann, San Francisco (2001)
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Dourado, M.C., Penso, L.D., Rautenbach, D., Szwarcfiter, J.L. (2011). The South Zone: Distributed Algorithms for Alliances. In: Défago, X., Petit, F., Villain, V. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2011. Lecture Notes in Computer Science, vol 6976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24550-3_15
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DOI: https://doi.org/10.1007/978-3-642-24550-3_15
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