Abstract
We present distributed protocols for electing a leader among k mobile agents that are dispersed among the n nodes of a graph. While previous solutions for the agent election problem were restricted to specific topologies or under specific conditions, the protocols presented in this paper face the problem in the most general case, i.e. for an arbitrary topology where the nodes of the graph may not be distinctly labelled and the agents might be all identical (and thus indistinguishable from each other). In such cases, the agent election problem is often difficult, and sometimes impossible to solve using deterministic means. We have designed protocols for solving the problem that—unlike previous solutions—are effective, meaning that they always succeed in electing a leader under any given setting if at all it is possible, and otherwise detect the fact that election is impossible in that setting. We present several election protocols, all effective. Starting with the straightforward solution, that requires an exponential amount of edge-traversals by the agents, we describe significantly more efficient algorithms; in the latter the total number of edge-traversals made by the agents is always polynomial, their difference is in the amount of bits of storage they required at the nodes.
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References
Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous. Kluwer, Dordrecht (2003)
Angluin, D.: Local and global properties in networks of processors. In: Proc. 12th ACM Symp. on Theory of Computing (STOC 1980), pp. 82–93 (1980)
Attiya, H., Snir, M., Warmuth, M.K.: Computing on an anonymous ring. Journal of ACM 35(4), 845–875 (1988)
Barrière, L., Flocchini, P., Fraigniaud, P., Santoro, N.: Can we elect if we cannot compare? In: Proc. 15th ACM Symp. on Parallel Algorithms and Architectures (SPAA 2003), pp. 200–209 (2003)
Barrière, L., Flocchini, P., Fraigniaud, P., Santoro, N.: Election and rendezvous in fully anonymous networks with sense of direction. In: Theory of Computing Systems (to appear, 2006). Preliminary version in Proc. 10th Coll. on Structural Information and Communication Complexity (SIROCCO 2003), pp. 17–32 (2003)
Beame, P.W., Bodlaender, H.L.: Distributed computing on transitive grids: The torus. In: Cori, R., Monien, B. (eds.) STACS 1989. LNCS, vol. 349, pp. 294–303. Springer, Heidelberg (1989)
Bender, M., Fernandez, A., Ron, D., Sahai, A., Vadhan, S.: The power of a pebble: Exploring and mapping directed graphs. In: Proc. 30th ACM Symp. on Theory of Computing (STOC 1998), pp. 269–287 (1998)
Boldi, P., Shammah, S., Vigna, S., Codenotti, B., Gemmell, P., Simon, J.: Symmetry breaking in anonymous networks: Characterizations. In: Proc. 4th Israel Symp. on Theory of Computing and Systems, pp. 16–26 (1996)
Das, S., Flocchini, P., Kutten, S., Nayak, A., Santoro, N.: Map construction of unknown graphs by multiple agents. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 99–114. Springer, Heidelberg (2005)
Fraigniaud, P., Ilcinkas, D.: Digraph exploration with little memory. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 246–257. Springer, Heidelberg (2004)
Gallager, R.G., Humblet, P.A., Spira, P.M.: A distributed algorithm for minimum-weight spanning trees. ACM Transactions on Programming Languages and Systems 5(1), 66–77 (1983)
Korach, E., Kutten, S., Moran, S.: A modular technique for the design of efficient distributed leader finding algorithms. ACM Transactions on Programming Languages and Systems 12(1), 84–101 (1990)
Kranakis, E.: Symmetry and computability in anonymous networks: A brief survey. In: Proc. 3rd Int. Conf. on Structural Information and Communication Complexity (SIROCCO 1997), pp. 1–16 (1997)
Kranakis, E., Krizanc, D.: Distributed computing on anonymous hypercube networks. Journal of Algorithms 23(1), 32–50 (1997)
Norris, N.: Universal covers of graphs: Isomorphism to depth n − 1 implies isomorphism to all depths. Discrete Applied Mathematics 56(1), 61–74 (1995)
Sakamoto, N.: Comparison of initial conditions for distributed algorithms on anonymous networks. In: Proc. 18th ACM Symposium on Principles of Distributed Computing (PODC 1999), pp. 173–179 (1999)
Yamashita, M., Kameda, T.: Computing on anonymous networks: Parts I and II. IEEE Trans. on Parallel and Distributed Systems 7(1), 69–96 (1996)
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Das, S., Flocchini, P., Nayak, A., Santoro, N. (2006). Effective Elections for Anonymous Mobile Agents. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_73
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DOI: https://doi.org/10.1007/11940128_73
Publisher Name: Springer, Berlin, Heidelberg
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