On a pursuit game played on graphs for which a minor is excluded
Journal of Combinatorial Theory Series B
Easy problems for tree-decomposable graphs
Journal of Algorithms
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Regular Article: On the Cop Number of a Graph
Advances in Applied Mathematics
The complexity of pursuit on a graph
Theoretical Computer Science
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Subgraph isomorphism in planar graphs and related problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Coverage for robotics – A survey of recent results
Annals of Mathematics and Artificial Intelligence
The complexity of pursuit on a graph
The complexity of pursuit on a graph
Equivalence of local treewidth and linear local treewidth and its algorithmic applications
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
A refined search tree technique for Dominating Set on planar graphs
Journal of Computer and System Sciences
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Algorithmica - Parameterized and Exact Algorithms
Cop-Robber Guarding Game with Cycle Robber Region
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
The Guarding Problem --- Complexity and Approximation
Combinatorial Algorithms
Pursuing a fast robber on a graph
Theoretical Computer Science
Capacitated domination and covering: a parameterized perspective
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Algorithmica
Guard games on graphs: keep the intruder out!
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Multi-robot learning for continuous area sweeping
LAMAS'05 Proceedings of the First international conference on Learning and Adaption in Multi-Agent Systems
Parameterized Complexity
The guarding game is E-complete
Theoretical Computer Science
| Hi-index | 5.23 |
A team of mobile agents, called guards, tries to keep an intruder out of an assigned area by blocking all possible attacks. In a graph model for this setting, the guards and the intruder are located on the vertices of a graph, and they move from node to node via connecting edges. The area protected by the guards is an induced subgraph of the given graph. We investigate the algorithmic aspects of the guarding problem, which is to find the minimum number of guards sufficient to patrol the area. We show that the guarding problem is PSPACE-hard and provide a set of approximation algorithms. All approximation algorithms are based on the study of a variant of the game where the intruder must reach the guarded area in a single step in order to win. This variant of the game appears to be a 2-approximation for the guarding problem, and for graphs without cycles of length 5 the minimum number of required guards in both games coincides. We give a polynomial time algorithm for solving the one-step guarding problem in graphs of bounded treewidth, and complement this result by showing that the problem is W[1]-hard parameterized by the treewidth of the input graph. We also show that the problem is fixed parameter tractable (FPT) parameterized by the treewidth and maximum degree of the input graph. Finally, we turn our attention to a large class of sparse graphs, including planar graphs and graphs of bounded genus, namely apex-minor-free graphs. We prove that the one-step guarding problem is FPT and possess a PTAS on apex-minor-free graphs.