Book ChapterDOI
An Optimal Algorithm for One-Separation of a Set of Isothetic Polygons
Amitava Datta,Kamala Krithivasan,Thomas Ottmann +2 more
- pp 110-121
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TLDR
This paper considers the problem of separating a collection of isothetic polygons in the plane by translating one polygon at a time to infinity by detecting whether a set is separable in this sense and computes a translational ordering of the polygons.Abstract:
We consider the problem of separating a collection of isothetic polygons in the plane by translating one polygon at a time to infinity. The directions of translation are the four isothetic (parallel to the axes) directions, but a particular polygon can be translated only in one of these four directions. Our algorithm detects whether a set is separable in this sense and computes a translational ordering of the polygons. The time and space complexities of our algorithm is Θ(n log n) and Θ(n) respectively, where n is the total number of edges of the polygons in the set. The best previous algorithm in the plane for this problem had complexities of O(n log2n) time and O(n log n) space.read more
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Complexity of Interlocking Polyominoes
Sidharth Dhawan,Zachary Abel +1 more
TL;DR: In this article, it was shown that polyominoes with five or fewer squares cannot interlock, and that determining interlockedness of a polyomial system with six or more squares is PSPACE hard.
References
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Computational geometry. an introduction
TL;DR: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.
Proceedings Article
Complexity of the Mover's Problem and Generalizations Extended Abstract
TL;DR: This paper concerns the problem of moving a polyhedron through Euclidean space while avoiding polyhedral obstacles.
Proceedings ArticleDOI
Complexity of the mover's problem and generalizations
TL;DR: In this article, the problem of moving a polyhedron through Euclidean space while avoiding polyhedral obstacles is addressed, and the authors propose a solution to the problem by moving the polyhedra through the polygonal space.
Proceedings ArticleDOI
On translating a set of rectangles
TL;DR: In this paper, the authors study the nature of these constraints and exhibit optimal algorithms for finding valid motion ordering for several different classes of objects in the plane for disjoint objects.
Book ChapterDOI
The Complexity and Decidability of Separation
TL;DR: The difficulty of solving instances of a new family of sliding block puzzles called SEPARATIONTM, where each puzzle in the family consists of an arrangement in the plane of n rectilinear wooden blocks, is studied.