Dynamic Programming for Graphs on Surfaces - Archive ouverte HAL Access content directly
Reports (Research Report) Year : 2009

Dynamic Programming for Graphs on Surfaces

(1) , (2, 3) , (4)
1
2
3
4

Abstract

We provide a framework for the design of $2^{\mathcal{O}(k)}\cdot n$ step dynamic programming algorithms for surface-embedded graphs on $n$ vertices of branchwidth at most $k$. Our technique applies to graph problems for which dynamic programming uses tables encoding set partitions. For general graphs, the best known algorithms for such problems run in $2^{\mathcal{O}(k\cdot \log k)}\cdot n$ steps. That way, we considerably extend the class of problems that can be solved by algorithms whose running times have a {\em single exponential dependence} on branchwidth, and improve the running time of several existing algorithms. Our approach is based on a new type of branch decomposition called {\em surface cut decomposition}, which generalizes sphere cut decompositions for planar graphs, and where dynamic programming should be applied for each particular problem. The construction of such a decomposition uses a new graph-topological tool called {\em polyhedral decomposition}. The main result is that if dynamic programming is applied on surface cut decompositions, then the time dependence on branchwidth is {\sl single exponential}. This fact is proved by a detailed analysis of how non-crossing partitions are arranged on surfaces with boundary and uses diverse techniques from topological graph theory and analytic combinatorics.
Fichier principal
Vignette du fichier
RR-7166.pdf (619.17 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

inria-00443582 , version 1 (30-12-2009)

Identifiers

  • HAL Id : inria-00443582 , version 1

Cite

Juanjo Rué, Ignasi Sau Valls, Dimitrios M. Thilikos. Dynamic Programming for Graphs on Surfaces. [Research Report] RR-7166, INRIA. 2009, pp.39. ⟨inria-00443582⟩
224 View
174 Download

Share

Gmail Facebook Twitter LinkedIn More