Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

Multi-target Ray Searching Problems

International audienceWe 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

Multi-target ray searching problems

International audienceWe 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