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An Efficient Algorithm for Mobile Guarded Guards in Simple Grids

  • Adrian Kosowski
  • Michał Małafiejski
  • Paweł Żyliński
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3980)

Abstract

A set of mobile guards in a grid is guarded if at any point on its patrol segment every guard can be seen by at least one other guard. Herein we discuss a class of polygon-bounded grids and simple grids for which we propose a quadratic time algorithm for solving the problem of finding the minimum set of mobile guarded guards (the MinMGG problem). Recall that the MinMGG problem is NP-hard even for grids every segment of which crosses at most three other segments. We also provide an O(n log n) time algorithm for the MinMGG problem in horizontally or vertically unobstructed grids. Finally, we investigate complete rectangular grids with obstacles. We show that if both the vertical and the horizontal sizes of the grid are larger than the number of obstacles k, k+2 mobile guarded guards always suffice to cover the grid.

Keywords

Intersection Graph Domination Number Vertical Segment Horizontal Segment Minimum Total 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Adrian Kosowski
    • 1
  • Michał Małafiejski
    • 1
  • Paweł Żyliński
    • 2
  1. 1.Department of Algorithms and System ModelingGdańsk University of Technology 
  2. 2.Insitute of MathematicsUniversity of Gdańsk 

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