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Rendezvous search on the interval and the circle

By J. V. Howard

Abstract

Two people are placed randomly and independently on a street of unit length. They attempt to find each other in the shortest possible expected time. We solve this problem, assuming each searcher knows where he or she is on the street, for monotonic density functions for the initial placement (this includes the uniform pdf as a special case). This gives an example of a rendezvous search problem where there is no advantage in being allowed to use asymmetric strategies. We also solve some corresponding problems for the circle when asymmetric strategies are permitted: One of these shows that it can sometimes be optimal for one player to wait for the other to find him

Topics: QA Mathematics
Publisher: Insitute for operations research and the management sciences (INFORMS)
Year: 1999
DOI identifier: 10.1287/opre.47.4.550
OAI identifier: oai:eprints.lse.ac.uk:7021
Provided by: LSE Research Online
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