Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
A characterization of weakly bipartite graphs
Journal of Combinatorial Theory Series B
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Bidimensionality: new connections between FPT algorithms and PTASs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Invitation to data reduction and problem kernelization
ACM SIGACT News
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Catalan structures and dynamic programming in H-minor-free graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A Linear-Time Approximation Scheme for TSP in Undirected Planar Graphs with Edge-Weights
SIAM Journal on Computing
Improved Approximation Algorithms for Minimum Weight Vertex Separators
SIAM Journal on Computing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Decomposition, approximation, and coloring of odd-minor-free graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Parameterized Complexity
Contraction decomposition in h-minor-free graphs and algorithmic applications
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fast sub-exponential algorithms and compactness in planar graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
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We improve the running time of the general algorithmic technique known as Baker's approach (1994) on H-minor-free graphs from O(nf(|H|)) to O(f(|H|)nO(1)). The numerous applications include, e.g. a 2-approximation for coloring and PTASes for various problems such as dominating set and max-cut, where we obtain similar improvements. On classes of odd-minor-free graphs, which have gained significant attention in recent time, we obtain a similar acceleration for a variant of the structural decomposition theorem proved by Demaine et al. (2010). We use these algorithms to derive faster 2-approximations; furthermore, we present the first PTASes and subexponential FPT-algorithms for independent set and vertex cover on these graph classes using a novel dynamic programming technique. We also introduce a technique to derive (nearly) subexponential parameterized algorithms on H-minor-free graphs. Our technique applies, in particular, to problems such as Steiner tree, (directed) subgraph with a property, (directed) longest path, and (connected/independent) dominating set, on some or all proper minor-closed graph classes. We obtain as a corollary that all problems with a minor-monotone subexponential kernel and amenable to our technique can be solved in subexponential FPT-time on H-minor free graphs. This results in a general methodology for subexponential parameterized algorithms outside the framework of bidimensionality.