Abstract
The rendezvous search problem asks how two (or more) agents who are lost in a common region can optimize the process by which they meet. Usually they have restricted speed (unit speed in the continuous time context; moves allowed to adjacent nodes in discrete time). In all cases the agents are not aware of each other’s location. This chapter is concerned with the ‘operations research’ version of the problem – where optimization of the search process is interpreted as minimizing the expected time to meet, or possibly maximizing the probability of meeting within a given time. The deterministic approaches taken by the theoretical computer science community will not be considered here.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alpern, S. Hide an seek games. Seminar, Institut fur Hohere Studien, Vienna, 26 July 1976.
Alpern, S. The rendezvous search problem. LSE CDAM Research Report 1993 53, London School of Economics.
Alpern, S. The rendezvous search problem. SIAM J. Control & Optimization 1995; 33:673–683.
Alpern, S. Asymmetric rendezvous search on the circle. Dynamics and Control 2000; 10:33–45
Alpern, S. Rendezvous search: a personal perspective. Operations Research 2002; 50 (5):772–795.
Alpern, S. Rendezvous search on labelled networks. Naval Research Logistics 2002; 49:256–274.
Alpern, S. Rendezvous search with revealed information: applications to the line. Journal of Applied Probability 2007; 44 (1):1–15.
Alpern, S. Line-of-sight rendezvous. European Journal of Operational Research 2008; 188 (3): 865–883.
Alpern, S. Rendezvous Search Games, Wiley Encyclopedia of Operations Research and Management Science 2012, John Wiley & Sons, Inc.
Alpern, S, and Beck, A. Asymmetric rendezvous on the line is a double linear search problem. Mathematics of Operations Research 1999; 24 (3): 604–618.
Alpern, S and Gal, S. Rendezvous search on the line with distinguishable players. SIAM J. Control & Optimization 1995; 33:1270–1276.
Alpern, S and Gal, S. Search Games and Rendezvous Theory, Springer, 2003.
Alpern, S and Howard, JV. Alternating search at two locations. Dynamics and Control 2000; 10:319–339.
Alpern, S and Lim, WS. Rendezvous of three agents on the line. Naval Research Logistics 2002; 49:244–255. (6):2233–2252.
Anderson, EJ and Essegaier, S. Rendezvous search on the line with indistinguishable players, SIAM Journal of Control and Optimization 1995; 33:1637–1642.
Anderson, EJ. and Weber, R. The rendezvous problem on discrete locations. Journal of Applied Probability 1990; 27:839–851.
Baston, VJ. Two rendezvous search problems on the line, Naval Research Logistics 1999; 46: 335–340.
Benkoski, S, Monticino, M and Weisinger, J. . A survey of the search theory literature. Naval Research Logistics 1991; 38:469–494.
Chester, EJ and Tutuncu, RH. Rendezvous search on the labelled line Operations Research 2004; 52(2):330–334. Operations Research 1999; 47 (6):849–861.
Dessmark, A, Fraigniaud, P, Kowalski, D and Pelc, A. Deterministic rendezvous in graphs. Algorithmica 2006; 46:69–96.
Dobrev,S, Flocchini,P, Prencipe,G and Santoro, N. Multiple agents rendezvous in a ring in spite of a black hole. Lecture Notes in Computer Science 2004: Volume 3144/2004, 34–46
Howard, JV. Rendezvous search on the interval and circle. Operations Research 1999; 47 (4):550–558.
Kikuta, K and Ruckle, W. Rendezvous search on a star graph with examination costs. European Journal of Operational Research 2007; 181 (1):298–304.
Kowalski, D. and Malinoski, A. How to meet in anonymous network. Theoretical Computer Science 2008; 399:141–156.
Kranakis, E, Krizanc, D and Rajsbaum, S. Mobile agent rendezvous: a survey. Lecture Notes in Computer Science 2006, Volume 4056/2006, Springer Berlin / Heidelberg.
Lim, WS and Alpern, S. Minimax rendezvous search on the line. SIAM J. Control Optim. 1996; 34:1650–1665.
Lim, WS, Alpern, S and Beck, A. Rendezvous search on the line with more than two players. Operations Research 1997; 45 (3):357–364.
Lin, J Morse, AS and Anderson, BDO. The Multi-Agent Rendezvous Problem. Part 1: The synchronous Case. SIAM J. Control Optim 2007; 46(6):2096–2119.
Lin, J, Morse, AS and Anderson, BDO. The Multi-Agent Rendezvous Problem. Part 2: The asynchronous Case. SIAM J. Control Optim 2007; 46(6):2120–2147.
Marco,G, Gargano, Kranakis,E, Krizanc,D and Pelc, A. Asynchronous deterministic rendezvous in graphs. Theoretical Computer Science 2006; 355:315–326.
Qiaoming H, Du, D, Vera,J and Zuluaga, LF. Improved Bounds for the Symmetric Rendezvous Value on the Line Operations Research 2008; 56 (3):772–782.
Schelling, T. The Strategy of Conflict. Harvard University Press, Cambridge, 1960.
Stone, LD. Theory of Optimal Search, 2nd edition. Operations Research Society of America, Arlington, VA, 1989.
Uthaisombut, P. Symmetric rendezvous search on the line using moving patterns with different lengths. Department of Computer Science, University of Pittsburgh, 2006.
Weber, R. Optimal Symmetric Rendezvous Search on Three Locations. Mathematics of Operations Research 2012; 37 (1): 111–122.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Alpern, S. (2013). Ten Open Problems in Rendezvous Search. In: Alpern, S., Fokkink, R., Gąsieniec, L., Lindelauf, R., Subrahmanian, V. (eds) Search Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6825-7_14
Download citation
DOI: https://doi.org/10.1007/978-1-4614-6825-7_14
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-6824-0
Online ISBN: 978-1-4614-6825-7
eBook Packages: Computer ScienceComputer Science (R0)