论文标题
最大的跑步者数量的下限，并应用于隔离
Lower bounds for the maximum number of runners that cause loneliness, and its application to Isolation
论文作者
论文摘要
我们考虑（n+1）跑步者，给定的持续不变的独特整数速度沿着圆形长度为一个的圆圈的圆周，所有跑步者从同一点开始。我们为每个跑步者R定义并给出了第一个查找问题的问题PMAX PMAX PMAX，可以同时将跑步者与Runner r同时分离的最大跑步者数量至少为d。对于d = 1/（2^（地板（lg（n）））），pmax的下限为（n - （（n -1）/floes（lg（n）））），这使得同时分开的跑步者的比例往往为1，因为N趋向于无限。接下来，我们定义并将上限定义为第二个问题的发现，对于每个跑步者R，隔离R所需的最小步骤数，假设可以在每个步骤中删除可以通过Reast d desteast d同时分离R的跑步者。对于d = 1/（2^（地板（lg（n）））），分离株的上限为（lg（n -1）/lg（地板（lg（n））））。
We consider (n+1) runners with given constant unique integer speeds running along the circumference of a circle whose circumferential length is one, and all runners starting from the same point. We define and give lower bounds to a first problem PMAX of finding, for every runner r, the maximum number of runners that can be simultaneously separated from runner r by a distance of atleast d. For d=1/(2^(floor(lg(n)))), a lower bound for PMAX is ( n - ((n-1)/floor(lg(n))) ), which makes the fraction of simultaneously separated runners tend to 1 as n tends to infinity. Next, we define and give upper bounds to a second problem ISOLATE of finding, for every runner r, the minimum number of steps needed to isolate r, assuming that the runners that can be simultaneously separated from r by atleast d, are removed at each step. For d=1/(2^(floor(lg(n)))), an upper bound for ISOLATE is ( lg(n - 1)/lg(floor(lg(n))) ).
