Improved Bounds for the Symmetric Rendezvous Value on the Line

Qiaoming Han (), Donglei Du (), Juan Vera () and Luis F. Zuluaga ()
Additional contact information
Qiaoming Han: School of Engineering and Management, Nanjing University, Nanjing 210093, China
Donglei Du: Faculty of Business Administration, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3
Juan Vera: Department of Management Sciences, Faculty of Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Luis F. Zuluaga: Faculty of Business Administration, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3

Operations Research, 2008, vol. 56, issue 3, 772-782

Abstract: 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.

Keywords: search and surveillance; rendezvous search; games/group decisions; teams; analysis of algorithms; suboptimal algorithms; symmetric rendezvous search; game theory; approximation algorithm; semidefinite programming relaxation (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.1070.0439 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:56:y:2008:i:3:p:772-782

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().