On a game of policemen and robber
Discrete Applied Mathematics
The complexity of searching a graph
Journal of the ACM (JACM)
An isoperimetric inequality on the discrete torus
SIAM Journal on Discrete Mathematics
Searching for a mobile intruder in a polygonal region
SIAM Journal on Computing
The complexity of pursuit on a graph
Theoretical Computer Science
Sweeping simple polygons with a chain of guards
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Solution of David Gale's lion and man problem
Theoretical Computer Science
Randomized Pursuit-Evasion in Graphs
Combinatorics, Probability and Computing
Offline variants of the "lion and man" problem
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Bounds for cops and robber pursuit
Computational Geometry: Theory and Applications
Vision-Based Pursuit-Evasion in a Grid
SIAM Journal on Discrete Mathematics
Improved bounds for cops-and-robber pursuit
Computational Geometry: Theory and Applications
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Given a set of searchers in the grid, whose search paths are known in advance, can a target that moves at the same speed as the searchers escape detection indefinitely? We study the number of searchers against which the target can still escape. This number is less than n in an nxn grid, since a row of searchers can sweep the allowed region. In an alternating-move-model where at each time searchers first move and then the target moves, we show that a target can always escape @?n2@? searchers and there is a strategy for @?n2@?+1 searchers to catch the target. This improves a recent bound @W(n) [A. Dumitrescu, I. Suzuki, P. Zylinski, Offline variants of the ''lion and man'' problem, in: SoCG 2007, Proc. 23rd Annual Symposium on Computational Geometry, ACM Press, 2007, pp. 102-111] in the simultaneous-move-model where at each time searchers and target moves simultaneously. We also prove similar bounds for the continuous analogue, as well as for searchers and targets moving with different speeds. In the proof, we use new isoperimetric theorems for subsets of the nxn grid and the nxn square, which is of independent interest.