Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
On interval routing schemes and treewidth
Information and Computation
An improved fixed-parameter algorithm for vertex cover
Information Processing Letters
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
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Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
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Approximation algorithms and hardness results for cycle packing problems
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An O(2O(k)n3) FPT Algorithm for the Undirected Feedback Vertex Set Problem
Theory of Computing Systems
Tight lower bounds for certain parameterized NP-hard problems
Information and Computation
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Improved upper bounds for vertex cover
Theoretical Computer Science
Algorithmic meta-theorems for restrictions of treewidth
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
European Journal of Combinatorics
Parameterized Complexity
A single-exponential FPT algorithm for the K4- minor cover problem
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Linear kernels and single-exponential algorithms via protrusion decompositions
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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The c-pumpkin is the graph with two vertices linked by c ≥ 1 parallel edges. A c-pumpkin-model in a graph G is a pair {A,B} of disjoint subsets of vertices of G, each inducing a connected subgraph of G, such that there are at least c edges in G between A and B. We focus on hitting and packing c-pumpkin-models in a given graph: On the one hand, we provide an FPT algorithm running in time 2O(k)nO(1) deciding, for any fixed c ≥ 1, whether all c-pumpkin-models can be hit by at most k vertices. This generalizes the single-exponential FPT algorithms for VERTEX COVER AND FEEDBACK VERTEX SET, which correspond to the cases c = 1, 2 respectively. For this, we use a combination of iterative compression and a kernelization-like technique. On the other hand, we present an O(log n)-approximation algorithm for both the problems of hitting all c-pumpkin-models with a smallest number of vertices, and packing a maximum number of vertex-disjoint c-pumpkin-models. Our main ingredient here is a combinatorial lemma saying that any properly reduced n-vertex graph has a c-pumpkin-model of size at most f(c) log n, for a function f depending only on c.