Motion planning in the presence of moving obstacles
Journal of the ACM (JACM)
Solution of David Gale's lion and man problem
Theoretical Computer Science
Escaping offline searchers and isoperimetric theorems
Computational Geometry: Theory and Applications
Maximum thick paths in static and dynamic environments
Computational Geometry: Theory and Applications
Escaping off-line searchers and a discrete isoperimetric theorem
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Cops and robber game without recharging
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
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Consider the following survival problem:Given a set of k trajectories (paths) with maximum unit speed in a boundedregion over a (long) time interval [0,T], find another trajectory (if itexists) subject to the same maximum unit speed limit, that avoids (that is, stays at a safe distance of)each of the other trajectories over the entire time interval. We call this variant the continuous model of the survival problem. The discrete model of this problem is: Given the trajectories (paths) of k point robots in a graph over a (long)time interval 0,1,2,...,T, find a trajectory (path) for anotherrobot, that avoids each of the other k at any time instance in thegiven time interval. We introduce the notions of survival number of a region,and that of a graph, respectively, as the maximum number oftrajectories which can be avoided in the region (resp. graph). We give the first estimates on the survival number of the n x n grid Gn, and also devise an efficient algorithm for the corresponding safepath planning problem in arbitrary graphs. We then show that our estimates on the survival number of Gn%on the number of paths that can be avoided in Gn can be extended for the survival number of a bounded (square) region.In the final part of our paper, we consider other related offlinequestions, such as the maximum number of men problem and the spy problem.