# How Many Lions Are Needed to Clear a Grid?

@article{Berger2009HowML, title={How Many Lions Are Needed to Clear a Grid?}, author={Florian Berger and Alexander Gilbers and Ansgar Gr{\"u}ne and Rolf Klein}, journal={Algorithms}, year={2009}, volume={2}, pages={1069-1086} }

- Published in Algorithms 2009
DOI:10.3390/a2031069

We consider a pursuit-evasion problem where some lions have the task to clear a grid graph whose nodes are initially contaminated. The contamination spreads one step per time unit in each direction not blocked by a lion. A vertex is cleared from its contamination whenever a lion moves to it. Brass et al. [5] showed that n/2 lions are not enough to clear the n x n-grid. In this paper, we consider the same problem in dimension d > 2 and prove that Θ(nd-1/√d) lions are necessary and sufficient to… CONTINUE READING

#### Citations

##### Publications citing this paper.

SHOWING 1-10 OF 10 CITATIONS

## Improved bounds for cops-and-robber pursuit

VIEW 4 EXCERPTS

CITES RESULTS & BACKGROUND

HIGHLY INFLUENCED

## Geometric Firefighting in the Half-Plane

VIEW 1 EXCERPT

CITES BACKGROUND

## SWEEPING COSTS OF JORDAN DOMAINS COLORADO STATE UNIVERSITY

VIEW 1 EXCERPT

CITES BACKGROUND

## Computational Geometry Column 63

VIEW 1 EXCERPT

## A local strategy for cleaning expanding cellular domains by simple robots

VIEW 1 EXCERPT

CITES BACKGROUND

## Ant-sweep: a decentral strategy for cooperative cleaning in expanding domains

VIEW 1 EXCERPT

CITES BACKGROUND

## Path planning with spatial and temporal constraints

VIEW 2 EXCERPTS

## Vision-Based Pursuit-Evasion in a Grid

VIEW 2 EXCERPTS

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 15 REFERENCES

## Compressions and isoperimetric inequalities

VIEW 9 EXCERPTS

HIGHLY INFLUENTIAL

## Lower Bounds for g-Cuts on Multi-Dimensional Rectangular Grids

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## A Mathematician's Miscellany

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Escaping offline searchers and isoperimetric theorems

VIEW 2 EXCERPTS

## Die Graphensuchvariante des Löwenproblems

VIEW 2 EXCERPTS

## How Many Lions Can One Man Avoid ?

VIEW 2 EXCERPTS

## Offline variants of the "lion and man" problem

VIEW 2 EXCERPTS

## The On-Line Encyclopedia of Integer Sequences

VIEW 1 EXCERPT

## Recontamination Does Not Help to Search a Graph

VIEW 1 EXCERPT