Topic
Dissection problem
About: Dissection problem is a research topic. Over the lifetime, 7 publications have been published within this topic receiving 89 citations.
Papers
TL;DR: The problem of dissecting a plane rectilinear polygon with arbitrary (possibly, degenerate) holes into a minimum number of rectangles is shown to be solvable inO(n3/2 logn) time, disproves a famous assertion about the NP-hardness of the minimum rectangular dissection problem for rectiline polygons with point holes.
Abstract: In this paper, the problem of dissecting a plane rectilinear polygon with arbitrary (possibly, degenerate) holes into a minimum number of rectangles is shown to be solvable inO(n3/2 logn) time. This fact disproves a famous assertion about the NP-hardness of the minimum rectangular dissection problem for rectilinear polygons with point holes.
37 citations
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28 citations
1 Jul 1992
TL;DR: The problem of dissecting a plane rectilinear polygon with arbitrary (possibly, degenerate) holes into a minimum number of rectangles is shown to be solvable inO(n3/2 logn) time, disproves a famous assertion about the NP-hardness of the minimum rectangular dissection problem for rectiline polygons with point holes.
Abstract: In this paper, the problem of dissecting a plane rectilinear polygon with arbitrary (possibly, degenerate) holes into a minimum number of rectangles is shown to be solvable inO(n3/2 logn) time. This fact disproves a famous assertion about the NP-hardness of the minimum rectangular dissection problem for rectilinear polygons with point holes.
25 citations
1 Oct 2006
TL;DR: Novel algorithms based on two new dissections are presented for encoding and decoding binary block codes of length n and constant Hamming weight w by working with a w-dimensional Euclidean space representation for the information and code vectors.
Abstract: The problem of encoding and decoding binary block codes of length n and constant Hamming weight w is formulated as a polytope dissection problem. This is done by working with a w-dimensional Euclidean space representation for the information and code vectors. Novel algorithms based on two new dissections are presented. The first is a dissection of a subset of the codebook, and has time-complexity o(w). The second is a dissection of the entire codebook, and has time-complexity o(w log w). Implementation issues associated with the second algorithm are discussed in detail.
4 citations
4 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2013 | 1 |
| 2006 | 1 |
| 2005 | 1 |
| 1993 | 1 |
| 1992 | 1 |
| 1968 | 1 |