The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete
SIAM Journal on Algebraic and Discrete Methods
Finding the minimum bandwidth of an interval graph
Information and Computation
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
$O(M.N)$ Algorithms for the Recognition and Isomorphism Problems on Circular-Arc Graphs
SIAM Journal on Computing
Matching 2D patterns of protein spots
Proceedings of the fourteenth annual symposium on Computational geometry
`` Strong '' NP-Completeness Results: Motivation, Examples, and Implications
Journal of the ACM (JACM)
Approximating the bandwidth via volume respecting embeddings
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems
Theoretical Computer Science - Selected papers in honor of Manuel Blum
Improved bandwidth approximation for trees and chordal graphs
Journal of Algorithms
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Lectures on Discrete Geometry
Comparing Images Using the Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Point matching under non-uniform distortions
Discrete Applied Mathematics - Special issue: Computational molecular biology series issue IV
Sublinear geometric algorithms
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The Complexity of the Approximation of the Bandwidth Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Isomorphism of graphs with bounded eigenvalue multiplicity
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Isomorphism testing for graphs of bounded genus
STOC '80 Proceedings of the twelfth 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
Embedding ultrametrics into low-dimensional spaces
Proceedings of the twenty-second annual symposium on Computational geometry
Approximation algorithms for embedding general metrics into trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Metric clustering via consistent labeling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Circular partitions with applications to visualization and embeddings
Proceedings of the twenty-fourth annual symposium on Computational geometry
Testing embeddability between metric spaces
CATS '08 Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77
Improved algorithms for optimal embeddings
ACM Transactions on Algorithms (TALG)
Two-Dimensional Pattern Matching with Combined Scaling and Rotation
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Minimum Distortion Embeddings into a Path of Bipartite Permutation and Threshold Graphs
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Hardness of Embedding Metric Spaces of Equal Size
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
New Complexity Bounds for Image Matching under Rotation and Scaling
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Distortion Is Fixed Parameter Tractable
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Theoretical Computer Science
Hardness and approximation of minimum distortion embeddings
Information Processing Letters
On the complexity of affine image matching
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Inapproximability for planar embedding problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
New complexity bounds for image matching under rotation and scaling
Journal of Discrete Algorithms
Theoretical Computer Science
Low Distortion Maps Between Point Sets
SIAM Journal on Computing
An exact algorithm for minimum distortion embedding
Theoretical Computer Science
On the hardness of embeddings between two finite metrics
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
An efficient approximation algorithm for point pattern matching under noise
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Distortion is Fixed Parameter Tractable
ACM Transactions on Computation Theory (TOCT)
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We initiate the study of the minimum distortion problem: given as input two n-point metric spaces, find a bijection between them with minimum distortion. This is an abstraction of certain geometric problems in shape and image matching, and is also a natural variation and extension of the fundamental problems of graph isomorphism and bandwidth. Our focus is on algorithms that find an optimal (or near-optimal) bijection when the distortion is fairly small. We present a polynomial time algorithm that finds an optimal bijection between two line metrics, provided the distortion is less than 3+2√2. We also give a parameterized polynomial time algorithm that finds an optimal bijection between an arbitrary unweighted graph metric and a bounded-degree tree metric.