An introduction to periodical discrete sets from a tomographical perspective

Authors:
Andrea Frosini;Maurice Nivat;Laurent Vuillon
Affiliations:
Dipartimento di Scienze Matematiche ed Informatiche Roberto Magari Università degli Studi di Siena, Siena, Italy;Laboratoire d'Informatique, Algorithmique, Fondements et Applications(LIAFA), Université Denis Diderot, Paris Cedex, France;Laboratoire de Mathématiques, Université de Savoie, Le Bourget du Lac, France
Venue:
Theoretical Computer Science
Year:
2005

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Abstract

In this paper we introduce a new class of binary matrices whose entries show periodical configurations, and we furnish a first approach to their analysis from a tomographical point of view. In particular we propose a polynomial-time algorithm for reconstructing matrices with a special periodical behavior from their horizontal and vertical projections. We succeeded in our aim by using a reduction involving polyominoes which can be characterized by means of 2 - SAT formulas.