Short Regular Expressions from Finite Automata: Empirical Results
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Rank-width and tree-width of H-minor-free graphs
European Journal of Combinatorics
On brambles, grid-like minors, and parameterized intractability of monadic second-order logic
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Faster approximation schemes and parameterized algorithms on H-minor-free and odd-minor-free graphs
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Approximation algorithms for domination search
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Contraction obstructions for treewidth
Journal of Combinatorial Theory Series B
Sparse spanners vs. compact routing
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Proceedings of the forty-third annual ACM symposium on Theory of computing
Theoretical Computer Science
Linear kernels for (connected) dominating set on H-minor-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximate tree decompositions of planar graphs in linear time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Faster approximation schemes and parameterized algorithms on (odd-)H-minor-free graphs
Theoretical Computer Science
Local search: Is brute-force avoidable?
Journal of Computer and System Sciences
Algorithmic aspects of dominator colorings in graphs
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Shortest-path queries for complex networks: exploiting low tree-width outside the core
Proceedings of the 15th International Conference on Extending Database Technology
Fixed-Parameter tractability of treewidth and pathwidth
The Multivariate Algorithmic Revolution and Beyond
Completely inapproximable monotone and antimonotone parameterized problems
Journal of Computer and System Sciences
Large-treewidth graph decompositions and applications
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
A node-capacitated okamura-seymour theorem
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On the 2-sum embedding conjecture
Proceedings of the twenty-ninth annual symposium on Computational geometry
Decomposing combinatorial auctions and set packing problems
Journal of the ACM (JACM)
Lower bounds for treewidth of product graphs
Discrete Applied Mathematics
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We develop the algorithmic theory of vertex separators and its relation to the embeddings of certain metric spaces. Unlike in the edge case, we show that embeddings into $L_1$ (and even Euclidean embeddings) are insufficient but that the additional structure provided by many embedding theorems does suffice for our purposes. We obtain an $O(\sqrt{\log n})$ approximation for minimum ratio vertex cuts in general graphs, based on a new semidefinite relaxation of the problem, and a tight analysis of the integrality gap which is shown to be $\Theta(\sqrt{\log n})$. We also prove an optimal $O(\log k)$-approximate max-flow/min-vertex-cut theorem for arbitrary vertex-capacitated multicommodity flow instances on $k$ terminals. For uniform instances on any excluded-minor family of graphs, we improve this to $O(1)$, and this yields a constant-factor approximation for minimum ratio vertex cuts in such graphs. Previously, this was known only for planar graphs, and for general excluded-minor families the best known ratio was $O(\log n)$. These results have a number of applications. We exhibit an $O(\sqrt{\log n})$ pseudoapproximation for finding balanced vertex separators in general graphs. In fact, we achieve an approximation ratio of $O(\sqrt{\log {opt}})$, where ${opt}$ is the size of an optimal separator, improving over the previous best bound of $O(\log {opt})$. Likewise, we obtain improved approximation ratios for treewidth: in any graph of treewidth $k$, we show how to find a tree decomposition of width at most $O(k \sqrt{\log k})$, whereas previous algorithms yielded $O(k \log k)$. For graphs excluding a fixed graph as a minor (which includes, e.g., bounded genus graphs), we give a constant-factor approximation for the treewidth. This in turn can be used to obtain polynomial-time approximation schemes for several problems in such graphs.