Abstract
Rendezvous is concerned with enabling \(k \ge 2\) mobile agents to move within an underlying domain so that they meet, i.e., rendezvous, in the minimum amount of time. In this paper we study a generalization from \(2\) to \(k\) agents of a deterministic rendezvous model first proposed by [5] which is based on agents endowed with different speeds. Let the domain be a continuous (as opposed to discrete) ring (cycle) of length \(n\) and assume that the \(k\) agents have respective speeds \(s_1, \ldots , s_k\) normalized such that \(\min \{ s_1, \ldots , s_k \} = 1\) and \(\max \{ s_1, \ldots , s_k \} = c\). We give rendezvous algorithms and analyze and compare the rendezvous time in four models corresponding to the type of distribution of agents’ speeds, namely Not-All-Identical, One-Unique, Max-Unique, All-Unique. We propose and analyze the Herding Algorithm for rendezvous of \(k \ge 2\) agents in the Max-Unique and All-Unique models and prove that it achieves rendezvous in time at most \(\frac{1}{2}\left( \frac{c+1}{c-1}\right) n\), and that this rendezvous is strong in the All-Unique model. Further, we prove that, asymptotically in \(k\), no algorithm can do better than time \(\frac{2}{c+3}\left( \frac{c+1}{c-1}\right) n\) in either model. We also discuss and analyze additional efficient algorithms using different knowledge based on either \(n, k, c\) as well as when the mobile agents employ pedometers.
Evan Huus—A preliminary version of this work was part of the author’s undergraduate honours project [9].
Evangelos Kranakis—Research supported in part by NSERC Discovery grant.
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References
Alpern, S.: Rendezvous search: a personal perspective. Oper. Res. 50(5), 772–795 (2002)
Bampas, E., Czyzowicz, J., Gasieniec, L., Ilcinkas, D., Labourel, A.: Almost optimal asynchronous rendezvous in infinite multidimensional grids. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 297–311. Springer, Heidelberg (2010)
Czyzowicz, J., Ilcinkas, D., Labourel, A., Pelc, A.: Asynchronous deterministic rendezvous in bounded terrains. TCS 412(50), 6926–6937 (2011)
Dieudonné, Y., Pelc, A., Villain, V.: How to meet asynchronously at polynomial cost. In: Proceedings of ACM PODC, pp. 92–99. ACM (2013)
Feinerman, O., Korman, A., Kutten, S., Rodeh, Y.: Fast rendezvous on a cycle by agents with different speeds. In: Chatterjee, M., Cao, J., Kothapalli, K., Rajsbaum, S. (eds.) ICDCN 2014. LNCS, vol. 8314, pp. 1–13. Springer, Heidelberg (2014)
Flocchini, P., An, H.-C., Krizanc, D., Luccio, F.L., Santoro, N., Sawchuk, C.: Mobile agents rendezvous when tokens fail. In: Kralovic, R., Sýkora, O. (eds.) SIROCCO 2004. LNCS, vol. 3104, pp. 161–172. Springer, Heidelberg (2004)
Flocchini, P., An, H.-C., Krizanc, D., Santoro, N., Sawchuk, C.: Multiple mobile agent rendezvous in a ring. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 599–608. Springer, Heidelberg (2004)
Hegarty, P., Martinsson, A., Zhelezov, D.: A variant of the multi-agent rendezvous problem. CoRR, abs/1306.5166 (2013)
Huus, E.: Knowledge in rendezvous of agents of different speeds, Honours project, Carleton University, School of Computer Science, Spring 2014
Kranakis, E., Krizanc, D., MacQuarrie, F., Shende, S.: Randomized rendezvous on a ring for agents with different speeds. In: Proceedings of ICDCN 2015 (2015)
An, H.-C., Krizanc, D., Markou, E.: Mobile agent rendezvous in a synchronous torus. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 653–664. Springer, Heidelberg (2006)
Kranakis, E., Krizanc, D., Markou, E.: The Mobile Agent Rendezvous Problem in the Ring: An Introduction. Synthesis Lectures on Distributed Computing Theory Series. Morgan & Claypool Publishers, San Rafael (2010)
Sawchuk, C.: Mobile agent rendezvous in the ring. Ph.D. thesis. Carleton University (2004)
Schneider, J., Wattenhofer, R.: A new technique for distributed symmetry breaking. In: Proceedings of ACM PODC, pp. 257–266. ACM, New York (2010)
Yu, X., Yung, M.: Agent rendezvous: a dynamic symmetry-breaking problem. In: Meyer auf der Heide, F., Monien, B. (eds.) ICALP 1996. LNCS, vol. 1099. Springer, Heidelberg (1996)
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Huus, E., Kranakis, E. (2015). Rendezvous of Many Agents with Different Speeds in a Cycle. In: Papavassiliou, S., Ruehrup, S. (eds) Ad-hoc, Mobile, and Wireless Networks. ADHOC-NOW 2015. Lecture Notes in Computer Science(), vol 9143. Springer, Cham. https://doi.org/10.1007/978-3-319-19662-6_14
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