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Conference Papers Year : 2010

Dynamic programming for graphs on surfaces

Abstract

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.
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Dates and versions

lirmm-00736703 , version 1 (28-09-2012)

Identifiers

  • HAL Id : lirmm-00736703 , version 1

Cite

Juanjo Rué, Ignasi Sau, Dimitrios M. Thilikos. Dynamic programming for graphs on surfaces. ICALP: International Colloquium on Automata, Languages and Programming, 2010, Bordeaux, France. pp.372-383. ⟨lirmm-00736703⟩
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