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Journal Articles Theoretical Computer Science Year : 2014

Multi-target ray searching problems

Spyros Angelopoulos
Alejandro López-Ortiz
  • Function : Author
Konstantinos Panagiotou
  • Function : Author


We consider the problem of exploring m concurrent rays using a searcher. The rays are disjoint with the exception of a single common point, and in each ray at most one potential target may be located. The objective is to design search strategies for locating $t$ targets (with $t \leqslant m$) while minimizing the search distance traversed. This setting generalizes the extensively studied ray search (or star search) problem, in which the searcher seeks a single target. 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 simple strategy that achieves optimal competitive ratio under this metric. Our main result pertains to the second measure, which 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 that is within a multiplicative factor of $\Theta(\log{(m-t)})$ from the optimal search cost. Our results demonstrate that, for both problems, 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.

Dates and versions

hal-01185114 , version 1 (19-08-2015)



Spyros Angelopoulos, Alejandro López-Ortiz, Konstantinos Panagiotou. Multi-target ray searching problems. Theoretical Computer Science, 2014, 540-541, pp.2-12. ⟨10.1016/j.tcs.2014.03.028⟩. ⟨hal-01185114⟩
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