Characterizing minimal interval completions towards better understanding of profile and pathwidth

Authors:
Pinar Heggernes;Karol Suchan;Ioan Todinca;Yngve Villanger
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway;LIFO, Université d'Orleans, Orleans Cedex 2, France and Faculty of Applied Mathematics, AGH - University of Science and Technology, Krakow, Poland;LIFO, Université d'Orleans, Orleans Cedex 2, France;Department of Informatics, University of Bergen, Bergen, Norway
Venue:
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Year:
2007

Citing 12
Cited 11

On the pathwidth of chordal graphs

Discrete Applied Mathematics - ARIDAM IV and V
A partial k-arboretum of graphs with bounded treewidth

Theoretical Computer Science
Tractability of Parameterized Completion Problems on Chordal, Strongly Chordal, and Proper Interval Graphs

SIAM Journal on Computing
A survey of graph layout problems

ACM Computing Surveys (CSUR)
Computer Solution of Large Sparse Positive Definite

Computer Solution of Large Sparse Positive Definite
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Treewidth and Minimum Fill-in: Grouping the Minimal Separators

SIAM Journal on Computing
A Polynomial Approximation Algorithm for the Minimum Fill-In Problem

SIAM Journal on Computing
Minimal Orderings Revisited

SIAM Journal on Matrix Analysis and Applications
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
A Combinatorial Characterization of Higher-Dimensional Orthogonal Packing

Mathematics of Operations Research
Minimal interval completions

ESA'05 Proceedings of the 13th annual European conference on Algorithms

Characterizing and Computing Minimal Cograph Completions

FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
On Listing, Sampling, and Counting the Chordal Graphs with Edge Constraints

COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Single-edge monotonic sequences of graphs and linear-time algorithms for minimal completions and deletions

Theoretical Computer Science
Minimal split completions

Discrete Applied Mathematics
Pathwidth is NP-Hard for Weighted Trees

FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Strongly Chordal and Chordal Bipartite Graphs Are Sandwich Monotone

COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Characterizing and computing minimal cograph completions

Discrete Applied Mathematics
Pathwidth of circular-arc graphs

WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
On listing, sampling, and counting the chordal graphs with edge constraints

Theoretical Computer Science
Strongly chordal and chordal bipartite graphs are sandwich monotone

Journal of Combinatorial Optimization
Single-edge monotonic sequences of graphs and linear-time algorithms for minimal completions and deletions

COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Minimal interval completions of graphs are central in understanding two important and widely studied graph parameters: profile and pathwidth. Such understanding seems necessary to be able to attack the problem of computing these parameters. An interval completion of a given graph is an interval supergraph of it on the same vertex set, obtained by adding edges. If no subset of the added edges can be removed without destroying the interval property, we call it a minimal interval completion. In this paper, we give the first characterization of minimal interval completions. We present a polynomial time algorithm, for deciding whether a given interval completion of an arbitrary graph is minimal. If the interval completion is not minimal the algorithm can be used to extract a minimal interval completion that is a subgraph of the given interval completion.