带转弯成本的在线搜索
Online Searching with Turn Cost
摘要：
我们考虑的问题，在一个未知的距离OPT的原始位置的线上搜索的对象，在存在的成本为d的每一次的方向改变的方向。这是对线性搜索问题的一个推广。我们描述了一种策略，保证找到的对象在成本最多为9*OPT + 2d，它具有最佳的竞争比9相对于OPT加上最小相应的附加项。我们的论点的上限和下限使用一个无限的线性规划，我们解决了一个无限系列的近似有限线性规划的实验解决方案，估计的限制，并解决由此产生的递归。我们认为这种技术本身就很有趣，应该有助于解决其他搜索问题。特别是，我们考虑的明星搜索或奶牛路径问题的转向成本，隐藏的对象被放置在一个m射线从原来的位置发出的射线。对于这个问题，我们给出了（1+（2（m^m）/（（m-1）^（m-1）OPT + m（（m/（m-1））^（m-1）- 1）d的一个紧界.我们还讨论了相应的系数之间的权衡，并简要地考虑随机化的战略。
英文摘要：
We consider the problem of searching for an object on a line at an unknown distance OPT from the original position of the searcher, in the presence of a cost of d for each time the searcher changes direction. This is a generalization of the well-studied linear-search problem. We describe a strategy that is guaranteed to find the object at a cost of at most 9*OPT + 2d, which has the optimal competitive ratio 9 with respect to OPT plus the minimum corresponding additive term. Our argument for upper and lower bound uses an infinite linear program, which we solve by experimental solution of an infinite series of approximating finite linear programs, estimating the limits, and solving the resulting recurrences. We feel that this technique is interesting in its own right and should help solve other searching problems. In particular, we consider the star search or cow-path problem with turn cost, where the hidden object is placed on one of m rays emanating from the original position of the searcher. For this problem we give a tight bound of (1+(2(m^m)/((m-1)^(m-1))) OPT + m ((m/(m-1))^(m-1) - 1) d. We also discuss tradeoff between the corresponding coefficients, and briefly consider randomized strategies on the line.
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