Capture on Grids and Tori with Different Numbers of Cops

  • Fabrizio LuccioEmail author
  • Linda Pagli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11657)


This paper is a contribution to the classical cops and robber problem on a graph, directed to two-dimensional grids and tori. We apply some new concepts for solving the problem on grids and apply these concepts to give a new algorithm for the capture on tori. Then we consider using any number k of cops, give efficient algorithms for this case yielding a capture time \(t_k\), and compute the minimum value of k needed for any given capture time. We introduce the concept of work \(w_k=k\cdot t_k\) of an algorithm and study a possible speed-up using larger teams of cops.


Cops Robber Capture time Grid Tori Work Speed-up 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of PisaPisaItaly

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