Computing minimum distortion embeddings into a path for bipartite permutation graphs and threshold graphs

Authors:
Pinar Heggernes;Daniel Meister;Andrzej Proskurowski
Affiliations:
Department of Informatics, University of Bergen, Norway;Department of Informatics, University of Bergen, Norway;Department of Information and Computer Science, University of Oregon, USA
Venue:
Theoretical Computer Science
Year:
2011

Citing 14
Cited 0

The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete

SIAM Journal on Algebraic and Discrete Methods
Bipartite permutation graphs

Discrete Applied Mathematics
Computing the bandwidth of interval graphs

SIAM Journal on Discrete Mathematics
An $0(n \log n)$ Algorithm for Bandwidth of Interval Graphs

SIAM Journal on Discrete Mathematics
Algorithmic Applications of Low-Distortion Geometric Embeddings

FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On Approximation Intractability of the Bandwidth Problem

On Approximation Intractability of the Bandwidth Problem
Low distortion maps between point sets

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Low-distortion embeddings of general metrics into the line

Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The complexity of low-distortion embeddings between point sets

SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for low-distortion embeddings into low-dimensional spaces

SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for embedding general metrics into trees

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Distortion Is Fixed Parameter Tractable

ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Bandwidth of bipartite permutation graphs in polynomial time

Journal of Discrete Algorithms
Hardness and approximation of minimum distortion embeddings

Information Processing Letters

Quantified Score

Hi-index	5.23

Visualization

Abstract

The problem of computing minimum distortion embeddings of a given graph into a line (path) was introduced in 2004 and has quickly attracted significant attention with subsequent results appearing at recent stoc and soda conferences. So far, all such results concern approximation algorithms or exponential-time exact algorithms. We give the first polynomial-time algorithms for computing minimum distortion embeddings of graphs into a path when the input graphs belong to specific graph classes. In particular, we solve this problem in polynomial time for bipartite permutation graphs and threshold graphs. For both graph classes, the distortion can be arbitrarily large. The graphs that we consider are unweighted.