Improved Bounds for the Symmetric Rendezvous Value on the Line

A notorious open problem in the field of rendezvous search is to decide the rendezvous value of the symmetric rendezvous search problem on the line, when the initial distance between the two players is two. We show that the symmetric rendezvous value is within the interval (4.1520, 4.2574), which co...

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Bibliographic Details
Published in:Operations research Vol. 56; no. 3; pp. 772 - 782
Main Authors: Han, Qiaoming, Du, Donglei, Vera, Juan, Zuluaga, Luis F
Format: Journal Article
Language:English
Published: Linthicum, MD INFORMS 01.05.2008
Institute for Operations Research and the Management Sciences
Subjects:
Algorithms
Analysis
analysis of algorithms
Applied sciences
approximation algorithm
Asymptotic methods
Asymptotic value
Branch & bound algorithms
Business administration
Decision theory. Utility theory
Exact sciences and technology
Game theory
games/group decisions
Integers
Markov analysis
Markov chains
Markov processes
Mathematical programming
Mathematical vectors
Mixed strategy
Operational research and scientific management
Operational research. Management science
Quadratic programming
rendezvous search
search and surveillance
semidefinite programming relaxation
Studies
suboptimal algorithms
symmetric rendezvous search
Symmetry
teams
Websites
United States
Search problem
Semidefinite relaxation
symmetric rendezvous search
search and surveillance: rendezvous search
Two person game
Semi definite programming
games/group decisions: teams
Fork join problem
Approximation algorithm
Quadratic programming
Game theory
analysis of algorithms: suboptimal algorithms
semidefinite programming relaxation
Markov chain
Social decision
Surveillance
Open systems
Asymptotic approximation
Fractional programming
Rational function
Algorithm analysis
Monitoring
Mathematical programming
ISSN:0030-364X, 1526-5463
Online Access:Get full text
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Summary:A notorious open problem in the field of rendezvous search is to decide the rendezvous value of the symmetric rendezvous search problem on the line, when the initial distance between the two players is two. We show that the symmetric rendezvous value is within the interval (4.1520, 4.2574), which considerably improves the previous best-known result (3.9546, 4.3931). To achieve the improved bounds, we call upon results from absorbing Markov chain theory and mathematical programming theory-particularly fractional quadratic programming and semidefinite programming. Moreover, we also establish some important properties of this problem, which could be of independent interest and useful for resolving this problem completely. Finally, we conjecture that the symmetric rendezvous value is asymptotically equal to 4.25 based on our numerical calculations.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.1070.0439