Polygon containment under translation
Journal of Algorithms
Sorting Jordan sequences in linear time using level-linked search trees
Information and Control
Binary partitions with applications to hidden surface removal and solid modelling
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
On the area of overlap of translated polygons
Computer Vision and Image Understanding
Finding the largest area axis-parallel rectangle in a polygon
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
On fat partitioning, fat covering and the union size of polygons
Computational Geometry: Theory and Applications
State of the art in shape matching
Principles of visual information retrieval
An Interactive System for Drawing Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
Elastic Labels: the Two-Axis Case
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Elastic labels around the perimeter of a map
Journal of Algorithms
Algorithms for the placement of diagrams on maps
Proceedings of the 12th annual ACM international workshop on Geographic information systems
On labeling in graph visualization
Information Sciences: an International Journal
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
IEEE Computer Graphics and Applications
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In this paper we consider the problem of placing a unit square on a face of a drawn graph bounded by n vertices such that the area of overlap is maximized. Exact algorithms are known that solve this problem in O(n 2) time. We present an approximation algorithm that—for any given ε 0—places a (1 + ε)-square on the face such that the area of overlap is at least the area of overlap of a unit square in an optimal placement. The algorithm runs in $O(\frac{1}{\epsilon}\, n\log^2 n)$ time. Extensions of the algorithm solve the problem for unit discs, using $O(\frac{\log (1/\epsilon)}{\epsilon\sqrt{\epsilon}}\, n\log ^2n)$ time, and for bounded aspect ratio rectangles of unit area, using $O(\frac{1}{\epsilon^2}\, n\log^2 n)$ time.