Dynamic programming and planarity: Improved tree-decomposition based algorithms

Authors:
Frederic Dorn
Affiliations:
Department of Informatics, University of Bergen, N-5020 Bergen, Norway
Venue:
Discrete Applied Mathematics
Year:
2010

Citing 19
Cited 1

Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs

SIAM Journal on Computing
Finding small simple cycle separators for 2-connected planar graphs

Journal of Computer and System Sciences
Counting clique trees and computing perfect elimination schemes in parallel

Information Processing Letters
Graph minors: X. obstructions to tree-decomposition

Journal of Combinatorial Theory Series B
The pathwidth and treewidth of cographs

SIAM Journal on Discrete Mathematics
Characterizations and algorithmic applications of chordal graph embeddings

Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
A polynomial-time approximation scheme for weighted planar graph TSP

Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for Vertex Partitioning Problems on Partial k-Trees

SIAM Journal on Discrete Mathematics
Dominating sets in planar graphs: branch-width and exponential speed-up

SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Treewidth: Algorithmoc Techniques and Results

MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Improved Tree Decomposition Based Algorithms for Domination-like Problems

LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Tour Merging via Branch-Decomposition

INFORMS Journal on Computing
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs

Journal of the ACM (JACM)
Dynamic programming and fast matrix multiplication

ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Catalan structures and dynamic programming in H-minor-free graphs

Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
How to use planarity efficiently: new tree-decomposition based algorithms

WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Fast subexponential algorithm for non-local problems on graphs of bounded genus

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
Two birds with one stone: the best of branchwidth and treewidth with one algorithm

LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics

Fixed-Parameter tractability of treewidth and pathwidth

The Multivariate Algorithmic Revolution and Beyond

Quantified Score

Hi-index	0.04

Visualization

Abstract

We study some structural properties for tree-decompositions of 2-connected planar graphs that we use to improve upon the runtime of tree-decomposition based dynamic programming approaches for several NP-hard planar graph problems. E.g., we derive the fastest algorithm for Planar Dominating Set of runtime 3^t^w@?n^O^(^1^), when we take the width tw of a given tree-decomposition as the measure for the exponential worst case behavior. We also introduce a tree-decomposition based approach to solve non-local problems efficiently, such as Planar Hamiltonian Cycle in runtime 6^t^w@?n^O^(^1^). From any input tree-decomposition of a 2-connected planar graph, one computes in time O(nm) a tree-decomposition with geometric properties, which decomposes the plane into disks, and where the graph separators form Jordan curves in the plane.