Tile Packing Tomography is NP-hard
Computational Complexity
2010-12-22 v2 Data Structures and Algorithms
Abstract
Discrete tomography deals with reconstructing finite spatial objects from lower dimensional projections and has applications for example in timetable design. In this paper we consider the problem of reconstructing a tile packing from its row and column projections. It consists of disjoint copies of a fixed tile, all contained in some rectangular grid. The projections tell how many cells are covered by a tile in each row and column. How difficult is it to construct a tile packing satisfying given projections? It was known to be solvable by a greedy algorithm for bars (tiles of width or height 1), and NP-hardness results were known for some specific tiles. This paper shows that the problem is NP-hard whenever the tile is not a bar.
Keywords
Cite
@article{arxiv.0911.2567,
title = {Tile Packing Tomography is NP-hard},
author = {Marek Chrobak and Christoph Durr and Flavio Guinez and Antoni Lozano and Nguyen Kim Thang},
journal= {arXiv preprint arXiv:0911.2567},
year = {2010}
}