The NP-completeness of a tomographical problem on bicolored domino tilings

Authors:
A. Frosini;G. Simi
Affiliations:
Dipartimento di Scienze Matematiche ed Informatiche "Roberto Magari", Università degli Studi di Siena, Pian dei Mantellini 44, Siena 53100, Italy;Dipartimento di Scienze Matematiche ed Informatiche "Roberto Magari", Università degli Studi di Siena, Pian dei Mantellini 44, Siena 53100, Italy
Venue:
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Year:
2004

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Abstract

In this paper we study the problem of reconstructing a bicolored domino tiling of a rectangular surface from its horizontal and vertical projections. We use a reduction from the NP-complete problem NUMERICAL MATCHING WITH TARGET SUMS in order to prove that, unless P = NP, this task cannot be performed in polynomial time. The reconstruction of monochromatic domino tilings is still open.