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}
}
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15 Citations
Background Citations
6
Methods Citations
8

15 Citations

Citation Type

Citation Type

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.
Combinatorial algorithms for the seriation problem
In this thesis we study the seriation problem, a combinatorial problem arising in data analysis, which asks to sequence a set of objects in such a way that similar objects are ordered close to each…
Robinsonian Matrices: Recognition Challenges
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.
The quadratic assignment problem is easy for Robinsonian matrices with Toeplitz structure
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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References

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Combinatorial algorithms for the seriation problem
In this thesis we study the seriation problem, a combinatorial problem arising in data analysis, which asks to sequence a set of objects in such a way that similar objects are ordered close to each…
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  • Klaus Simon
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    Workshop on Computational Geometry
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TLDR
A new solution of the second phase of this algorithm is shown by repeated use of lexBFS, which produces a linear arrangement of the maximal cliques A1,..., A s, if there is one.
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TLDR
It follows from an earlier paper that the class of proper interval bigraphs is equal to the better known class of bipartite permutation graphs, and so there is a certifying algorithm for that class as well.
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TLDR
This paper presents an optimal O (n2) algorithm to recognize Robinsonian dissimilarities, where n is the cardinal of S and improves the already known algorithms.
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The ultimate interval graph recognition algorithm?
TLDR
This work exhibits a very simple, lineartime, recognition algorithm for interval graphs involving four sweeps of the the authors&known Lexicographic Breadth First Search based on a less well-known characterization by a linear order of the vertices.
Recognizing and representing proper interval graphs in parallel using merging and sorting
A Fully Dynamic Algorithm for Recognizing and Representing Proper Interval Graphs
TLDR
A near-optimal fully dynamic algorithm for the problem of recognizing and representing dynamically changing proper interval graphs that operates in time O(log n) per edge insertion or deletion is given.
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