# An Optimal Algorithm for Strict Circular Seriation

@article{Armstrong2021AnOA, title={An Optimal Algorithm for Strict Circular Seriation}, author={Santiago Armstrong and Crist'obal Guzm'an and C. Sing-Long}, journal={ArXiv}, year={2021}, volume={abs/2106.05944} }

We study the problem of circular seriation, where we are given a matrix of pairwise dissimilarities between n objects, and the goal is to find a circular order of the objects in a manner that is consistent with their dissimilarity. This problem is a generalization of the classical linear seriation problem where the goal is to find a linear order, and for which optimal O(n) algorithms are known. Our contributions can be summarized as follows. First, we introduce circular Robinson matrices as the… Expand

#### References

SHOWING 1-10 OF 30 REFERENCES

Seriation in the Presence of Errors: A Factor 16 Approximation Algorithm for l∞-Fitting Robinson Structures to Distances

- Mathematics, Computer Science
- Algorithmica
- 2009

A factor 16 approximation algorithm for the following NP-hard fitting problem: given a finite set X and a dissimilarity d on X, the aim is to find a Robinsonian dissimilarities dR on X minimizing the l∞-error between d and dR. Expand

A Spectral Algorithm for Seriation and the Consecutive Ones Problem

- Mathematics, Computer Science
- SIAM J. Comput.
- 1998

Whereas most previous applications of spectral techniques provide only bounds or heuristics, this work presents an algorithm that correctly solves a nontrivial combinatorial problem and helps explain and justify these applications. Expand

An Optimal Algorithm To Recognize Robinsonian Dissimilarities

- Computer Science, Mathematics
- J. Classif.
- 2014

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. Expand

Seriation in the Presence of Errors: NP-Hardness of l∞ -Fitting Robinson Structures to Dissimilarity Matrices

- Mathematics, Computer Science
- J. Classif.
- 2009

In this paper, we establish that the following fitting problem is NP-hard: given a finite set X and a dissimilarity measure d on X (d is a symmetric function from X2 to the nonnegative real numbers… Expand

Similarity-First Search: A New Algorithm with Application to Robinsonian Matrix Recognition

- Mathematics, Computer Science
- SIAM J. Discret. Math.
- 2017

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. Expand

Circular representation problem on hypergraphs

- Computer Science, Mathematics
- Discret. Math.
- 1984

A connection between circular graphs and circular representable hypergraphs of the type of the Fulkerson-Gross connection between interval graphs and matrices having the consecutive one's property is established, in some special cases. Expand

Circular object arrangement using spherical embeddings

- Computer Science
- Pattern Recognit.
- 2020

This work proposes a bilevel optimization framework where it employs a spherical embedding approach together with a spectral method for circular ordering in order to recover circular arrangements of the embedded data. Expand

Recognition of Robinsonian dissimilarities

- Mathematics
- 1997

We present an O(n3)-time, O(n2)-space algorithm to test whether a dissimilarity d on an n-object set X is Robinsonian, i.e., X admits an ordering such that i≤j≤k implies that d(xi,xk)≥max… Expand

Seriation and matrix reordering methods: An historical overview

- Computer Science
- Stat. Anal. Data Min.
- 2010

An historical overview of seriation and matrix reordering methods is presented, several applications from the following disciplines are included in the retrospective review: archaeology and anthropology; cartography, graphics, and information visualization; sociology and sociometry; psychology and psychometry; ecology and bioinformatics; cellular manufacturing; and operations research. Expand

Incidence matrices and interval graphs

- Mathematics
- 1965

Abstract : According to present genetic theory, the fine structure of genes consists of linearly ordered elements. A mutant gene is obtained by alteration of some connected portion of this structure.… Expand