Improved bounds for the symmetric rendezvous value on the line
成果类型：
Article
署名作者：
Han, Qiaoming; Du, Donglei; Vera, Juan; Zuluaga, Luis F.
署名单位：
Nanjing University; University of New Brunswick; University of Waterloo
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1070.0439
发表日期：
2008
页码：
772-782
关键词：
摘要：
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.