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Optimal Symmetric Rendezvous Search on Three Locations

Richard Weber
2012 Mathematics of Operations Research  
In the symmetric rendezvous search game played on n locations two players are initially placed at two distinct locations.  ...  In this paper we prove a 20 year old conjecture that the following strategy is optimal for the game on three locations: in each block of two steps, stay where you, or search the other two locations in  ...  value for three locations.  ... 
doi:10.1287/moor.1110.0528 fatcat:uqkh42xhangy3lgxlqyi43btv4

The Anderson-Weber strategy is not optimal for symmetric rendezvous search on K4 [article]

Richard Weber
2009 arXiv   pre-print
We consider the symmetric rendezvous search game on a complete graph of n locations.  ...  Anderson and Weber suspected that their strategy might not be optimal for n>3, but they had no particular reason to believe this and no one has been able to find anything better.  ...  The Anderson-Weber strategy In the symmetric rendezvous search game on K n (the completely connected graph on n vertices) two players are initially placed at two distinct vertices (called locations).  ... 
arXiv:0912.0670v1 fatcat:hc6st3kwabeghpgw6dkge4att4

Search-and-Rescue Rendezvous

Pierre Leone, Julia Buwaya, Steve Alpern
2021 European Journal of Operational Research  
This form of rendezvous search involves both optimal movement patterns and optimal times to drop a gift.  ...  However for the symmetric problem G 2 where each player has a gift, we have already exhibited two symmetric strategies (the one in Theorem 3 and the one in Figure 14 left) which are optimal (rendezvous  ... 
doi:10.1016/j.ejor.2021.05.009 fatcat:tuavxlpzevbzhfuj3lwuvaeh5u

Rendezvous Search with Revealed Information: Applications to the Line

Steve Alpern
2007 Journal of Applied Probability  
We consider the case in which they are placed a known distance apart on the line graph Q (known as 'symmetric rendezvous on the line').  ...  The symmetric rendezvous problem on a network Q asks how two players, forced to use the same mixed strategy, can minimize their expected meeting time, starting from a known initial distribution on the  ...  Such lower bounds on rendezvous values are usually difficult to come by. We apply these notions to the symmetric rendezvous problem on the line.  ... 
doi:10.1017/s0021900200002680 fatcat:3oaehc4ygvgbrlxxabpo6cxhzu

Multi-robot Symmetric Rendezvous Search on the Line [article]

Deniz Ozsoyeller, Pratap Tokekar
2021 arXiv   pre-print
We study the Symmetric Rendezvous Search Problem for a multi-robot system. There are n>2 robots arbitrarily located on a line. Their goal is to meet somewhere on the line as quickly as possible.  ...  The symmetric version of the problem requires the robots to execute the same search strategy to achieve rendezvous. Therefore, we solve the problem in an online fashion with a randomized strategy.  ...  In this paper, we study the symmetric version of the rendezvous search problem with n > 2 robots that are arbitrarily located on a line.  ... 
arXiv:2101.05324v3 fatcat:7kj5rqszxvc7fmuv3a36a7e7gu

Symmetric Rendezvous Search on the Line With an Unknown Initial Distance

Deniz Ozsoyeller, Andrew Beveridge, Volkan Isler
2013 IEEE Transactions on robotics  
In the rendezvous search problem, two robots at unknown locations must successfully meet somewhere in the environment.  ...  We study the symmetric version of the problem in which they must use the same strategy. We provide a new algorithm for the symmetric rendezvous problem on the line.  ...  In future work, we will study symmetric rendezvous on the line for three or more robots.  ... 
doi:10.1109/tro.2013.2272252 fatcat:6mrq3wgxz5gm7bkfzesoynjvjq

Rendezvous Search with Revealed Information: Applications to the Line

Steve Alpern
2007 Journal of Applied Probability  
We consider the case in which they are placed a known distance apart on the line graph Q (known as 'symmetric rendezvous on the line').  ...  The symmetric rendezvous problem on a network Q asks how two players, forced to use the same mixed strategy, can minimize their expected meeting time, starting from a known initial distribution on the  ...  For such symmetric rendezvous problems, one could equally take the viewpoint that is chosen by a single optimizer, such as the author of a rendezvous protocol which is routinely given to people such as  ... 
doi:10.1239/jap/1175267160 fatcat:p25d7w3awbhyvjggfyamqueajq

The rendezvous problem on discrete locations

E. J. Anderson, R. R. Weber
1990 Journal of Applied Probability  
If each person searches one of the n locations at random at each step, then rendezvous will require n steps on average.  ...  Hence they must use identical strategies and must treat all locations in a symmetrical fashion. Suppose their search proceeds in discrete time.  ...  Variations on the search model.  ... 
doi:10.2307/3214827 fatcat:4pjhb43wubakrdvrb4j3426xou

The rendezvous problem on discrete locations

E. J. Anderson, R. R. Weber
1990 Journal of Applied Probability  
If each person searches one of the n locations at random at each step, then rendezvous will require n steps on average.  ...  Hence they must use identical strategies and must treat all locations in a symmetrical fashion. Suppose their search proceeds in discrete time.  ...  Variations on the search model.  ... 
doi:10.1017/s0021900200028011 fatcat:meu3dvsyhrfithy5msoymrnhue

Page 4641 of Mathematical Reviews Vol. , Issue 91H [page]

1991 Mathematical Reviews  
If each person searches one of the n locations at random at each step, then rendezvous will require n steps on average.  ...  Hence they must use identical strategies and must treat all locations in a symmetrical fashion. Suppose their search proceeds in discrete time.  ... 

Rendezvous search with markers that can be dropped at chosen times

Pierre Leone, Steve Alpern
2018 Naval Research Logistics  
The Rendezvous search problem asks how two noncomunnicating players, who move at unit-speed after a random placement in the search region (in this article, the line), can minimize their expected meeting  ...  When the players are placed facing random directions at a distance D on the line the optimal expected meeting times R are known to be as follows: With no markers, R = 13D/8; with one each dropped at the  ...  This difficult problem was later solved for three locations in Weber (2012) .  ... 
doi:10.1002/nav.21818 fatcat:ea3myivxuzgebkbv5yfzo7n7om

Computing with Mobile Agents in Distributed Networks [chapter]

Evangelos Kranakis, Danny Krizanc, Sergio Rajsbaum
2007 Handbook of Parallel Computing  
Symmetric rendezvous In the case of symmetric rendezvous, both the (generally synchronous) network and the agents are assumed to be anonymous.  ...  The problem of determining optimal search strategies under the connectivity constraint is NP-hard even on planar graphs but it has been shown that optimal connected strategies can be computed in linear  ... 
doi:10.1201/9781420011296.ch8 fatcat:eyr4zqq2qrb43b5kvcofx2jfuq

Multi-robot Symmetric Rendezvous Search on the Line with an Unknown Initial Distance [article]

Deniz Ozsoyeller
2018 arXiv   pre-print
In this paper, we study the symmetric rendezvous search problem on the line with n > 2 robots that are unaware of their locations and the initial distances between them.  ...  The multi-robot symmetric rendezvous algorithm, MSR presented in this paper is an extension our symmetric rendezvous algorithm, SR presented in [23].  ...  The rendezvous search problem on the line is studied both for the symmetric [3, 4, 6, 16, 24, 26] and asymmetric [1, 2, 7, 15] versions.  ... 
arXiv:1805.08645v1 fatcat:kwc6if4zrzdcvhsqjvzev4igiu

Search-and-Rescue Rendezvous [article]

Pierre Leone, Steve Alpern
2016 arXiv   pre-print
We find optimal agent paths and droppo? times when the search region is a line, the initial distance between the players is known and one or both of the players can leave gifts.  ...  We exhibit strategies solving these various problems and use a 'rendezvous algorithm' to establish their optimality.  ...  This difficult problem was later solved for three locations by Weber [31] .  ... 
arXiv:1611.05205v1 fatcat:56rkbzuc6nctdprja3a2skoglm

Optimal Memory Rendezvous of Anonymous Mobile Agents in a Unidirectional Ring [chapter]

L. Gąsieniec, E. Kranakis, D. Krizanc, X. Zhang
2006 Lecture Notes in Computer Science  
We study the rendezvous problem with ¾ mobile agents in a Ò-node ring. We present a new algorithm which solves the rendezvous problem for the non-symmetric distribution of agents on the ring.  ...  In this context we show an optimal algorithm that uses Ç´ÐÓ · ÐÓ ÐÓ Òµ-size internal memory and a single token available at each mobile agent which allows them to recognize the symmetric case efficiently  ...  Introduction The mobile agent rendezvous problem is a search optimization problem, whereby a number of autonomous deterministic agents starting from two (or more) given nodes of a network are required  ... 
doi:10.1007/11611257_26 fatcat:leffppjh3zevxp77dg2ixtogua
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