SIAM Journal on Control and Optimization
Rendezvous Search on the Line with Indistinguishable Players
SIAM Journal on Control and Optimization
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
Asymmetric Rendezvous on the Line is a Double Linear Search Problem
Mathematics of Operations Research
Operations Research
Pure Strategy Asymmetric Rendezvous on the Line with an Unknown Initial Distance
Operations Research
Rendezvous Search: A Personal Perspective
Operations Research
Asynchronous Deterministic Rendezvous on the Line
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
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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 apart between the two players is 2. 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 may 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.