Low Memory Distributed Protocols for 2-Coloring
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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- 1.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)Google Scholar
- 2.Aldous, D., Fill, J.: Reversible Markov Chains and Random Walks on Graphs, http://www.stat.berkeley.edu/~aldous/RWG/book.html
- 5.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)Google Scholar
- 8.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)Google Scholar
- 10.Israeli, A., Jalfon, M.: Token Management Schemes and Random Walks Yield Self-Stabilizing Mutual Exclusion. In: PODC 1990, pp. 119–131 (1990)Google Scholar
- 12.Kearns, M., Judd, S., Tan, J., Wortman, J.: Behavioral experiments on biased voting in networks. National Academy of Science (January 2009)Google Scholar
- 13.Khot, S.: Improved inapproximability results for maxclique, chromatic number and approximate graph coloring. In: FOCS 2001, pp. 600–609 (2001)Google Scholar
- 16.Mossel, E., Schoenebeck, G.: Reaching Consensus on Social Networks. In: Innovations in Computer Science, ICS (2009)Google Scholar