Nearest constrained circular words

Authors Guillaume Blin, Alexandre Blondin Massé, Marie Gasparoux, Sylvie Hamel, Élise Vandomme

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Author Details

Guillaume Blin
  • LaBRI, Université de Bordeaux, CNRS UMR 5800, Talence, France
Alexandre Blondin Massé
  • Dép. d'informatique, Université du Québec à Montréal, QC, Canada
Marie Gasparoux
  • LaBRI, Université de Bordeaux, CNRS UMR 5800, Talence, France, Dép. d'informatique et de recherche opérationnelle, Université de Montréal, QC, Canada
Sylvie Hamel
  • Dép. d'informatique et de recherche opérationnelle, Université de Montréal, QC, Canada
Élise Vandomme
  • LaCIM, Université du Québec à Montréal, QC, Canada

Cite AsGet BibTex

Guillaume Blin, Alexandre Blondin Massé, Marie Gasparoux, Sylvie Hamel, and Élise Vandomme. Nearest constrained circular words. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


In this paper, we study circular words arising in the development of equipment using shields in brachytherapy. This equipment has physical constraints that have to be taken into consideration. From an algorithmic point of view, the problem can be formulated as follows: Given a circular word, find a constrained circular word of the same length such that the Manhattan distance between these two words is minimal. We show that we can solve this problem in pseudo polynomial time (polynomial time in practice) using dynamic programming.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic programming
  • Mathematics of computing → Combinatorics on words
  • Applied computing → Bioinformatics
  • Circular constrained alignments
  • Manhattan distance
  • Application to brachytherapy


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