Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
Graph minors. XII: distance on a surface
Journal of Combinatorial Theory Series B
Analytic combinatorics of non-crossing configurations
Discrete Mathematics - Special issue on selected papers in honor of Henry W. Gould
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Dynamic Programming on Graphs with Bounded Treewidth
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Efficient Approximation for Triangulation of Minimum Treewidth
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
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WG '88 Proceedings of the 14th International Workshop on Graph-Theoretic Concepts in Computer Science
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Journal of the ACM (JACM)
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SIAM Journal on Discrete Mathematics
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Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Analytic Combinatorics
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SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Efficient exact algorithms on planar graphs: exploiting sphere cut branch decompositions
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Faster parameterized algorithms for minor containment
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
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ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Fast minor testing in planar graphs
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Faster parameterized algorithms for minor containment
Theoretical Computer Science
Faster parameterized algorithms for minor containment
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Catalan structures and dynamic programming in H-minor-free graphs
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The Multivariate Algorithmic Revolution and Beyond
On approximating the d-girth of a graph
Discrete Applied Mathematics
Parameterized Domination in Circle Graphs
Theory of Computing Systems
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We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic programming runs in 2O(kċlog k)ċ n steps. Our approach combines tools from topological graph theory and analytic combinatorics. In particular, we introduce a new type of branch decomposition called surface cut decomposition, capturing how partial solutions can be arranged on a surface. Then we use singularity analysis over expressions obtained by the symbolic method to prove that partial solutions can be represented by a single-exponential (in the branchwidth k) number of configurations. This proves that, when applied on surface cut decompositions, dynamic programming runs in 2O(k) ċ n steps. That way, we considerably extend the class of problems that can be solved in running times with a single-exponential dependence on branchwidth and unify/improve all previous results in this direction.