A note on tiling under tomographic constraints

Marek Chrobak; Peter Couperus; Christoph Dürr; Gerhard Woeginger

doi:10.1016/S0304-3975(02)00542-X

A note on tiling under tomographic constraints

Marek Chrobak, Peter Couperus, Christoph Dürr, Gerhard Woeginger

Discrete Mathematics and Mathematical Programming

Research output: Contribution to journal › Article › Academic › peer-review

15 Citations (Scopus)

29 Downloads (Pure)

Abstract

Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the projections. We are interested in the problem of reconstructing a tiling which has given projections. Some simple variants of this problem, involving tiles that are 1×1 or 1×2 rectangles, have been studied in the past, and were proved to be either solvable in polynomial time or NP-complete. In this note, we make progress toward a comprehensive classification of various tiling reconstruction problems, by proving NP-completeness results for several sets of tiles.

Original language	English
Pages (from-to)	2125-2136
Journal	Theoretical computer science
Volume	290
Issue number	3
DOIs	https://doi.org/10.1016/S0304-3975(02)00542-X
Publication status	Published - 2003

Keywords

Discrete tomography
METIS-213200
IR-75176
Tiling

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T1 - A note on tiling under tomographic constraints

AU - Chrobak, Marek

AU - Couperus, Peter

AU - Dürr, Christoph

AU - Woeginger, Gerhard

PY - 2003

Y1 - 2003

N2 - Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the projections. We are interested in the problem of reconstructing a tiling which has given projections. Some simple variants of this problem, involving tiles that are 1×1 or 1×2 rectangles, have been studied in the past, and were proved to be either solvable in polynomial time or NP-complete. In this note, we make progress toward a comprehensive classification of various tiling reconstruction problems, by proving NP-completeness results for several sets of tiles.

AB - Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the projections. We are interested in the problem of reconstructing a tiling which has given projections. Some simple variants of this problem, involving tiles that are 1×1 or 1×2 rectangles, have been studied in the past, and were proved to be either solvable in polynomial time or NP-complete. In this note, we make progress toward a comprehensive classification of various tiling reconstruction problems, by proving NP-completeness results for several sets of tiles.

KW - Discrete tomography

KW - METIS-213200

KW - IR-75176

KW - Tiling

U2 - 10.1016/S0304-3975(02)00542-X

DO - 10.1016/S0304-3975(02)00542-X

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SP - 2125

EP - 2136

JO - Theoretical computer science

JF - Theoretical computer science

SN - 0304-3975

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ER -