MATHEMATICAL STUDIES ON SEARCH PROBLEMS ON GRAPHS

1.菊田和W.H.Ruckle教授一直在共同研究积累游戏，这是一类检查游戏。Ruckle教授于1999年10月至2000年5月在科比商业大学担任客座教授。在此期间，菊田和Ruckle教授共同研究了搜索博弈等问题。由于积累博弈领域存在许多问题（《积累博弈，第1部分：Noisy Search.Journal of Optimization Theory and Applications，Vol.94，1997 by Kikuta and Ruckle]，2.Baston博士于2000年9月作为访问教授在科比商业大学停留了大约10天。Kikuta和巴斯顿博士共同研究了Renaissance Search，找到了对称markstart会合搜索情况下的最优策略和最优值。3.Kikuta一直在研究有限图上的带旅行费用的搜索对策，最近解决了当底层图是循环图且参数满足一定条件时的对策。Ferguson教授对这一研究进行了评论。4.菊田、滨田和木庭一直在分析搜索博弈，与一些quorum系统的探测复杂性有关。当底层的quarak是轮形的时候，游戏已经被解决了（关于一些quorum系统的复杂性，油印。1999年4月，作者：Kikuta、Kiniwa和Hamada）。其他案件的分析仍在继续。

1.Kikuta and Prof.W.H.Ruckle have been studying jointly on Accumulation Games, which are a class of inspection games. Prof.Ruckle stayed at the Kobe University of Commerce as a visiting professor from October, 1999 to May, 2000. During his stay, Kikuta and Prof.Ruckle studied jointly on search games etc. Since there are many problems in the area of accumulation games (Table 1 at page 396 of [Accumulation Games, Part 1 : Noisy Search.Journal of Optimization Theory and Applications, Vol.94, 1997 by Kikuta and Ruckle], this joint work would continue.2.Dr.Baston stayed at the Kobe University of Commerce as a visiting professor about ten days in September, 2000. Kikuta and Dr.Baston studied jointly on Rendezvous Search, and found optimal strategies and the optimal value for the case of symmetric markstart rendezvous search. This joint work is now in continuation.3.Kikuta has been studying on search games with traveling cost on finite graphs, and recently solved the game when the underlying graph is a cyclic one and the parameters satisfy some condition. This study is still in continuation, for solving generally a game on a cyclic graph.Prof.Ferguson gave comments on this research.4.Kikuta, Hamada and Kiniwa have been analyzing search games, related to the probe complexity of some quorum systems. When the underlying netwok is wheel-shaped, the game had been already solved (On probe complexity of some quorum systems, mimeo. April, 1999, by Kikuta, Kiniwa and Hamada). Analysis in the other cases is still in continuation.