A Lex-BFS-based recognition algorithm for Robinsonian matrices

@inproceedings{Laurent2015ALR,
  title={A Lex-BFS-based recognition algorithm for Robinsonian matrices},
  author={Monique Laurent and Matteo Seminaroti},
  booktitle={Discret. Appl. Math.},
  year={2015}
}
Similarity-First Search: A New Algorithm with Application to Robinsonian Matrix Recognition
TLDR
A new algorithm is introduced, named Similarity-First-Search (SFS), which extends Lexicographic Breadth-First Search (Lex-BFS) to weighted graphs and which is used in a multisweep algorithm to recognize Robinsonian matrices.
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TLDR
The interval graph recognition problem is accurately reviewed and the intimate connection between cocomparability graph and dense Robinsonian similarity is established and the current trend in recognizing special graph structures is examined in regard to multiple lexicographic search sweeps.
A Structural Characterization for Certifying Robinsonian Matrices
TLDR
A structural characterization for Robinsonian matrices in terms of forbidden substructures is provided, extending the notion of asteroidal triples to weighted graphs and leading to an efficient algorithm for certifying that a matrix is not Robinsonian.
A simple and optimal algorithm for strict circular seriation
TLDR
It is proved that the circular Robinson dissimilarities are exactly the pre-circular Robinson Dissimilarities (which are defined by the existence of compatible orders on one of the two arcs between each pair of points).
PQser: a Matlab package for spectral seriation
TLDR
This paper presents a Matlab implementation of an algorithm for spectral seriation by Atkins et al., based on the use of the Fiedler vector of the Laplacian matrix associated to the problem, which encodes the set of admissible solutions into a PQ-tree.
On the Recognition of Strong-Robinsonian Incomplete Matrices
TLDR
This document shows that there is an incomplete Robinson matrix which is not Strong-Robinsonian, and presents an O(|w|n) recognition algorithm for Strong- Robinsonian matrices, where b is the number of missing entries, n is the size of the matrix, and |w| is thenumber of different values in the matrix.
Uniform Embeddings for Robinson Similarity Matrices
TLDR
A necessary and sufficient condition for the existence of a uniform embedding, derived from paths in an associated graph, is given and an efficient combinatorial algorithm is given to find a uniformembedding or give proof that it does not exist.
The Weighted Sitting Closer to Friends than Enemies Problem in the Line
TLDR
This work provides a characterization of the set of weighted graphs with an injection in $\mathbb{R}$ that satisfies the restrictions of the weighted SCFE problem, and concludes that deciding the existence of, and constructing such an injection for a given complete weighted graph can be done in polynomial time.
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