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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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Conference papers
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00736703
Contributor : Ignasi Sau <>
Submitted on : Friday, September 28, 2012 - 6:09:10 PM
Last modification on : Thursday, August 27, 2020 - 3:40:04 PM

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  • HAL Id : lirmm-00736703, version 1

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Juanjo Rué, Ignasi Sau Valls, 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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