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Optimal Symmetric Rendezvous Search on Three Locations

2012
*
Mathematics of Operations Research
*

In the

doi:10.1287/moor.1110.0528
fatcat:uqkh42xhangy3lgxlqyi43btv4
*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*. ...##
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The Anderson-Weber strategy is not optimal for symmetric rendezvous search on K4
[article]

2009
*
arXiv
*
pre-print

We consider the

arXiv:0912.0670v1
fatcat:hc6st3kwabeghpgw6dkge4att4
*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*). ...##
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Search-and-Rescue Rendezvous

2021
*
European Journal of Operational Research
*

This form of

doi:10.1016/j.ejor.2021.05.009
fatcat:tuavxlpzevbzhfuj3lwuvaeh5u
*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*...##
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Rendezvous Search with Revealed Information: Applications to the Line

2007
*
Journal of Applied Probability
*

We consider the case in which they are placed a known distance apart

doi:10.1017/s0021900200002680
fatcat:3oaehc4ygvgbrlxxabpo6cxhzu
*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. ...##
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Multi-robot Symmetric Rendezvous Search on the Line
[article]

2021
*
arXiv
*
pre-print

We study the

arXiv:2101.05324v3
fatcat:7kj5rqszxvc7fmuv3a36a7e7gu
*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. ...##
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Symmetric Rendezvous Search on the Line With an Unknown Initial Distance

2013
*
IEEE Transactions on robotics
*

In the

doi:10.1109/tro.2013.2272252
fatcat:6mrq3wgxz5gm7bkfzesoynjvjq
*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. ...##
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Rendezvous Search with Revealed Information: Applications to the Line

2007
*
Journal of Applied Probability
*

We consider the case in which they are placed a known distance apart

doi:10.1239/jap/1175267160
fatcat:p25d7w3awbhyvjggfyamqueajq
*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 ...##
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The rendezvous problem on discrete locations

1990
*
Journal of Applied Probability
*

If each person

doi:10.2307/3214827
fatcat:4pjhb43wubakrdvrb4j3426xou
*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. ...##
###
The rendezvous problem on discrete locations

1990
*
Journal of Applied Probability
*

If each person

doi:10.1017/s0021900200028011
fatcat:meu3dvsyhrfithy5msoymrnhue
*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. ...##
###
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

2018
*
Naval Research Logistics
*

The

doi:10.1002/nav.21818
fatcat:ea3myivxuzgebkbv5yfzo7n7om
*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) . ...##
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Computing with Mobile Agents in Distributed Networks
[chapter]

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 ...

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

2018
*
arXiv
*
pre-print

In this paper, we study the

arXiv:1805.08645v1
fatcat:kwc6if4zrzdcvhsqjvzev4igiu
*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. ...##
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Search-and-Rescue Rendezvous
[article]

2016
*
arXiv
*
pre-print

We find

arXiv:1611.05205v1
fatcat:56rkbzuc6nctdprja3a2skoglm
*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] . ...##
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Optimal Memory Rendezvous of Anonymous Mobile Agents in a Unidirectional Ring
[chapter]

2006
*
Lecture Notes in Computer Science
*

We study the

doi:10.1007/11611257_26
fatcat:leffppjh3zevxp77dg2ixtogua
*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 ...
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