Abstract
Consider the Ants Nearby Treasure Search (ANTS) problem, where n mobile agents, initially placed at the origin of an infinite grid, collaboratively search for an adversarially hidden treasure. The agents are controlled by deterministic/randomized finite or pushdown automata and are able to communicate with each other through constant-size messages. We show that the minimum number of agents required to solve the ANTS problem crucially depends on the computational capabilities of the agents as well as the timing parameters of the execution environment. We give lower and upper bounds for different scenarios.
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References
Emek, Y., Langner, T., Uitto, J., Wattenhofer, R.: Solving the ANTS Problem with Asynchronous Finite State Machines. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014, Part II. LNCS, vol. 8573, pp. 471–482. Springer, Heidelberg (2014)
Feinerman, O., Korman, A., Lotker, Z., Sereni, J.S.: Collaborative Search on the Plane Without Communication. In: Proceedings of the 31st ACM Symposium on Principles of Distributed Computing (PODC), pp. 77–86 (2012)
Feinerman, O., Korman, A.: Memory Lower Bounds for Randomized Collaborative Search and Implications for Biology. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 61–75. Springer, Heidelberg (2012)
Fraigniaud, P., Ilcinkas, D., Peer, G., Pelc, A., Peleg, D.: Graph Exploration by a Finite Automaton. Theoretical Computer Science 345(2-3), 331–344 (2005)
Lenzen, C., Lynch, N., Newport, C., Radeva, T.: Trade-offs between Selection Complexity and Performance when Searching the Plane without Communication. In: Proceedings of the 33rd Symposium on Principles of Distributed Computing, PODC (to appear, 2014)
Albers, S., Henzinger, M.: Exploring Unknown Environments. SIAM Journal on Computing 29, 1164–1188 (2000)
Deng, X., Papadimitriou, C.: Exploring an Unknown Graph. Journal of Graph Theory 32, 265–297 (1999)
Diks, K., Fraigniaud, P., Kranakis, E., Pelc, A.: Tree Exploration with Little Memory. Journal of Algorithms 51, 38–63 (2004)
Panaite, P., Pelc, A.: Exploring Unknown Undirected Graphs. In: Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 316–322 (1998)
Reingold, O.: Undirected Connectivity in Log-Space. Journal of the ACM (JACM) 55, 17:1–17:24 (2008)
Aleliunas, R., Karp, R.M., Lipton, R.J., Lovasz, L., Rackoff, C.: Random Walks, Universal Traversal Sequences, and the Complexity of Maze Problems. In: Proceedings of the 20th Annual Symposium on Foundations of Computer Science (SFCS), pp. 218–223 (1979)
Aigner, M., Fromme, M.: A Game of Cops and Robbers. Discrete Applied Mathematics 8, 1–12 (1984)
Baeza-Yates, R.A., Culberson, J.C., Rawlins, G.J.E.: Searching in the Plane. Information and Computation 106, 234–252 (1993)
López-Ortiz, A., Sweet, G.: Parallel Searching on a Lattice. In: Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG), pp. 125–128 (2001)
Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in Networks of Passively Mobile Finite-State Sensors. Distributed Computing, 235–253 (2006)
Aspnes, J., Ruppert, E.: An Introduction to Population Protocols. In: Garbinato, B., Miranda, H., Rodrigues, L. (eds.) Middleware for Network Eccentric and Mobile Applications, pp. 97–120. Springer (2009)
Emek, Y., Wattenhofer, R.: Stone Age Distributed Computing. In: Proceedings of the 32nd ACM Symposium on Principles of Distributed Computing (PODC) (2013)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (1979)
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Emek, Y., Langner, T., Stolz, D., Uitto, J., Wattenhofer, R. (2014). How Many Ants Does It Take to Find the Food?. In: Halldórsson, M.M. (eds) Structural Information and Communication Complexity. SIROCCO 2014. Lecture Notes in Computer Science, vol 8576. Springer, Cham. https://doi.org/10.1007/978-3-319-09620-9_21
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DOI: https://doi.org/10.1007/978-3-319-09620-9_21
Publisher Name: Springer, Cham
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