Parameterized Algorithms for Generalized Domination
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
The parameterized complexity of the induced matching problem
Discrete Applied Mathematics
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Theoretical Computer Science
Capacitated domination and covering: a parameterized perspective
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Parameterized algorithm for eternal vertex cover
Information Processing Letters
On the small cycle transversal of planar graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
On the small cycle transversal of planar graphs
Theoretical Computer Science
Guard games on graphs: Keep the intruder out!
Theoretical Computer Science
Guard games on graphs: keep the intruder out!
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Irredundant set faster than O(2n)
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Vertex cover, dominating set and my encounters with parameterized complexity and mike fellows
The Multivariate Algorithmic Revolution and Beyond
Polynomial kernels for dominating set in graphs of bounded degeneracy and beyond
ACM Transactions on Algorithms (TALG)
FPT algorithms for domination in biclique-free graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We show that several problems that are hard for various parameterized complexity classes on general graphs, become fixed parameter tractable on graphs with no small cycles. More specifically, we give fixed parameter tractable algorithms for Dominating Set, t -Vertex Cover (where we need to cover at least t edges) and several of their variants on graphs with girth at least five. These problems are known to be W[i]-hard for some i≥1 in general graphs. We also show that the Dominating Set problem is W[2]-hard for bipartite graphs and hence for triangle free graphs. In the case of Independent Set and several of its variants, we show these problems to be fixed parameter tractable even in triangle free graphs. In contrast, we show that the Dense Subgraph problem where one is interested in finding an induced subgraph on k vertices having at least l edges, parameterized by k, is W[1]-hard even on graphs with girth at least six. Finally, we give an O(log p) ratio approximation algorithm for the Dominating Set problem for graphs with girth at least 5, where p is the size of an optimum dominating set of the graph. This improves the previous O(log n) factor approximation algorithm for the problem, where n is the number of vertices of the input graph.