Information and Computation
Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem
Information and Computation
Optimal constructions of hybrid algorithms
Journal of Algorithms
Artificial Intelligence - special issue on computational tradeoffs under bounded resources
Lower bounds in on-line geometric searching
Computational Geometry: Theory and Applications
The ultimate strategy to search on m rays?
Theoretical Computer Science
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Operations Research
Theoretical Computer Science
Online searching with turn cost
Theoretical Computer Science - Approximation and online algorithms
Competitive Online Approximation of the Optimal Search Ratio
SIAM Journal on Computing
Contract algorithms and robots on rays: unifying two scheduling problems
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
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We consider the problem of exploring m concurrent rays using a single searcher. The rays are disjoint with the exception of a single common point, and in each ray a potential target may be located. The objective is to design efficient search strategies for locating t targets (with t ≤ m). This setting generalizes the extensively studied ray search (or star search) problem, in which the searcher seeks a single target. In addition, it is motivated by applications such as the interleaved execution of heuristic algorithms, when it is required that a certain number of heuristics have to successfully terminate. We apply two different measures for evaluating the efficiency of the search strategy. The first measure is the standard metric in the context of ray-search problems, and compares the total search cost to the cost of an optimal algorithm that has full information on the targets. We present a strategy that achieves optimal competitive ratio under this metric. The second measure is based on a weakening of the optimal cost as proposed by Kirkpatrick [ESA 2009] and McGregor et al. [ESA 2009]. For this model, we present an asymptotically optimal strategy which is within a multiplicative factor of Θ(log(m - t)) from the optimal search cost. Interestingly, our strategy incorporates three fundamental search paradigms, namely uniform search, doubling and hyperbolic dovetailing. Moreover, for both measures, our results demonstrate that the problem of locating t targets in m rays is essentially as difficult as the problem of locating a single target in m - (t - 1) rays.