Numerical Algorithms

, Volume 80, Issue 3, pp 879–902 | Cite as

PQser: a Matlab package for spectral seriation

  • Anna ConcasEmail author
  • Caterina Fenu
  • Giuseppe Rodriguez
Original Paper


Seriation is an important ordering problem which consists of finding the best ordering of a set of units whose interrelationship is defined by a bipartite graph. It has important applications in, e.g., archaeology, anthropology, psychology, and biology. 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. We introduce some numerical technicalities in the original algorithm to improve its performance, and point out that the presence of a multiple Fiedler value may have a substantial influence on the computation of an approximated solution, in the presence of inconsistent data sets. Practical examples and numerical experiments show how to use the toolbox to process data sets deriving from real-world applications.


Seriation Fiedler value Bipartite graphs PQ-trees Bandwidth reduction 

Mathematics Subject Classification (2010)

65F15 65F50 05C82 91D30 


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We would like to thank Matteo Sommacal for pointing our attention to the problem of seriation and to its application in archaeology. The paper [37], which he coauthored, was our principal source of information when the research which led to this paper started. We are indebted to the reviewers for their comments and suggestions, which contributed to improve both the form and the content of the paper.

Funding information

The authors are members of the INdAM Research group GNCS, which partially supported the research. Anna Concas gratefully acknowledges Sardinia Regional Government for the financial support of her Ph.D. scholarship (P.O.R. Sardegna F.S.E. Operational Programme of the Autonomous Region of Sardinia, European Social Fund 2014-2020 - Axis III Education and Formation, Objective 10.5, Line of Activity 10.5.12).


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Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di CagliariCagliariItaly
  2. 2.AICES Graduate SchoolRWTH Aachen UniversityAachenGermany

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