Abstract
In this paper we present new distributed protocols to color even rings and general bipartite graphs. Our motivation is to provide algorithmic explanation for human subject experiments that show human subjects can achieve distributed coordination in the form of 2-coloring over networks with a simple communication protocol. All our protocols use low (often constant) memory and reach a solution in feasible (polynomial rounds) and sometimes optimal time. All the protocols also have short message length and use a broadcast communication strategy. Our contributions include two simple protocols RingElect and GraphCoalescing for rings and general bipartite graphs, which can be viewed as candidates for natural human strategies. We present two other protocols RingElect and GraphElect which are optimal or nearly optimal in terms of the number of rounds (proportional to the diameter of the graph) but require somewhat more complex strategies. The question of finding simple protocols in the style of RingElect and GraphCoalescing that run in time proportional to diameter is open.
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References
Aleliunas, R., Karp, R.M., Lipton, R.J., Lovász, L., Rackoff, C.: Random Walks, Universal Traversal Sequences, and the Complexity of Maze Problems. In: FOCS 1979, pp. 218–223 (1979)
Aldous, D., Fill, J.: Reversible Markov Chains and Random Walks on Graphs, http://www.stat.berkeley.edu/~aldous/RWG/book.html
Attiya, H., Welch, J.: Distributed Computing; Fundamentals, Simulations and Advanced Topics, 2nd edn. John Wiley & Sons, Chichester (2004)
Barabási, A.L., Albert, R.: Emergence of Scaling in Random Networks. Science 286(5439), 509–512 (1999)
Bollobás, B., Riordan, O., Spencer, J., Tusnády, G.: The degree sequence of a scale-free random graph process. Random Structures & Algorithms 18(3) (May 2001)
Chaudhuri, K., Chung Graham, F., Jamall, M.S.: A network coloring game. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 522–530. Springer, Heidelberg (2008)
Cooper, C., Frieze, A., Radzik, T.: Multiple random walks in random regular graphs. SIAM Journal on Discrete Mathematics 23(4), 1738–1761 (2009)
Enemark, D., McCubbins, M., Paturi, R., Weller, N.: Good edge, bad edge: How network structure affects a group’s ability to coordinate. In: ESORICS (March 2009)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)
Israeli, A., Jalfon, M.: Token Management Schemes and Random Walks Yield Self-Stabilizing Mutual Exclusion. In: PODC 1990, pp. 119–131 (1990)
Kearns, M., Suri, S., Montfort, N.: An experimental study of the coloring problem on human subject networks. Science 313(5788), 824–827 (2006)
Kearns, M., Judd, S., Tan, J., Wortman, J.: Behavioral experiments on biased voting in networks. National Academy of Science (January 2009)
Khot, S.: Improved inapproximability results for maxclique, chromatic number and approximate graph coloring. In: FOCS 2001, pp. 600–609 (2001)
Latané, B., L’Herrou, T.: Spatial clustering in the conformity game: Dynamic social impact in electronic groups. Journal of Personality and Social Psychology 70(6), 1218–1230 (1996)
McCubbins, M.D., Paturi, R., Weller, N.: Connected Coordination: Network Structure and Group Coordination. American Politics Research 37, 899–920 (2009)
Mossel, E., Schoenebeck, G.: Reaching Consensus on Social Networks. In: Innovations in Computer Science, ICS (2009)
Peleg, D.: Distributed Computing: A Locally-Sensitive Approach. SIAM Monographs, Philadelphia (2000)
Santoro, N.: Design and Analysis of Distributed Algorithms. John Wiley & Sons, Inc., Chichester (2007)
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Israeli, A., McCubbins, M.D., Paturi, R., Vattani, A. (2010). Low Memory Distributed Protocols for 2-Coloring. In: Dolev, S., Cobb, J., Fischer, M., Yung, M. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2010. Lecture Notes in Computer Science, vol 6366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16023-3_26
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DOI: https://doi.org/10.1007/978-3-642-16023-3_26
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