Reconstructing hv-convex polyominoes from orthogonal projections
Marek Chrobak,Christoph Dürr +1 more
TLDR
In this paper, the problem of reconstructing a discrete 2D object, represented by a set of grid cells, from its orthogonal projections is addressed, and a simple O(mn min(m2,n2))-time algorithm for reconstructing hv-convex polyominoes is presented.About:
This article is published in Information Processing Letters.The article was published on 1999-03-26 and is currently open access. It has received 134 citations till now. The article focuses on the topics: Discrete tomography.read more
Citations
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Journal ArticleDOI
The reconstruction of polyominoes from their orthogonal projections
TL;DR: It will be proved that it is NP-complete to reconstruct a two-dimensional pattern from its two orthogonal projections H and V, if (1) the pattern has to be connected (and hence forms a so-called polyomino), or if (2) the patterns have to be horizontally and vertically convex.
Journal ArticleDOI
Reconstruction of 4- and 8-connected convex discrete sets from row and column projections
TL;DR: The problem of reconstructing a discrete two-dimensional set from its two orthogonal projection (H,V) when the set satisfies some convexity conditions can be solved in polynomial time also in a class of discrete sets which is larger than the class of convex polyominoes, namely, in theclass of 8-connected convex sets.
Book ChapterDOI
Discrete Tomography: A Historical Overview
Attila Kuba,Gabor T. Herman +1 more
TL;DR: This chapter gives the details of the classical special case (namely, two-dimensional discrete sets — i.e.,binary matrices — and two orthogonal projections) including a polynomial time reconstruction algorithm.
Journal ArticleDOI
An algorithm reconstructing convex lattice sets
Sara Brunetti,Alain Daurat +1 more
TL;DR: The main result of this paper is a polynomial-time algorithm solving the reconstruction problem for the “Q-convex” sets, a new class of subsets of Z2 having a certain kind of weak connectedness.
Journal ArticleDOI
Comparison of algorithms for reconstructing hv-convex discrete sets
TL;DR: Three reconstruction algorithms to be used for reconstructing hv-convex discrete sets from their row and column sums are compared and it is shown that the algorithm which was better from the viewpoint of worst time complexity was the worse from the viewpoints of average time complexity and memory requirements.
References
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On the Complexity of Timetable and Multicommodity Flow Problems
Shimon Even,Alon Itai,Adi Shamir +2 more
TL;DR: A very primitive version of Gotlieb’s timetable problem is shown to be NP-complete, and therefore all the common timetable problems areNP-complete.
Journal ArticleDOI
A linear-time algorithm for testing the truth of certain quantified boolean formulas☆
TL;DR: A simple constructive algorithm for the evaluation of formulas having two literals per clause, which runs in linear time on a random access machine.
Journal ArticleDOI
Reconstructing convex polyominoes from horizontal and vertical projections
TL;DR: Some operations for recontructing convex polyominoes by means of vectors H's and V's partial sums allows a new algorithm to be defined whose complexity is less than O(n2m2).
Journal ArticleDOI
Matrices of zeros and ones with fixed row and column sum vectors
TL;DR: In this paper, the combinational properties of all m × n matrices of 0's and 1's having r i 1's in row i and s i 1s in column j were studied.
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On the computational complexity of reconstructing lattice sets from their x-rays
TL;DR: It turns out that for all d ⩾ 2 and for a prescribed but arbitrary set of m ⩽ 2 pairwise nonparallel lattice directions, the problems are solvable in polynomial time if m = 2 and are NP-complete (or NP-equivalent) otherwise.