Fekete, S. and Pulleybank, W. (1993). Area Optimization of Simple Polygons, In: Ninth Annual Symposium on Computational Geometry, San Diego, California, May19-21,ACM Press, New York, pp. 173-182. Home/Search Document Details and Download
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New Solutions For Surface Reconstruction From.. - Weinert, Mehnen.. (1 citation) (Correct)
.... (6) fl = a Theta b k a k Deltakb k : 7) The total sum of the triangle areas 4 k of each triangulation T i (P)is SURF i (P) X k 4 k : 8) The optimal surface with the smallest surface area is defined by SURF = min i fSURF i (P )g : 9) Complexity of SURF Following the proof of Fekete and Pulleyblank (1993), one can show that the problem of finding a minimum surface polyhedron can be described by a reduction of Hamiltonian Cycles in Grid Graphs (HCGG) Thus, the problem of SURF is NP hard. The authors show more generally that in any fixed dimension 1 k dand 2 d it is NP hard to minimize the volume ....
Fekete, S. and Pulleybank, W. (1993). Area Optimization of Simple Polygons, In: Ninth Annual Symposium on Computational Geometry, San Diego, California, May19-21,ACM Press, New York, pp. 173-182.
Geometric Shortest Paths and Network Optimization - Mitchell (1998) (39 citations) (Correct)
....a set of points in the Euclidean plane Area Optimization Problems In the min area TSP (resp. max area TSP) the goal is to determine a cycle on a given set S of points such that the cycle defines a simple polygon of minimum (resp. maximum) area. Fekete [153] in part together with Pulleyblank [155]) has studied these problems extensively. He has shown that both the min area and max area TSP problems are NP complete. For the max area TSP, Fekete gives a (1=2) approximation algorithm, showing how, in O(n log n) time, one can obtain a cycle surrounding area that is at least half that of the ....
S. P. Fekete and W. R. Pulleyblank. Area optimization of simple polygons. In Proc. 9th Annu. ACM Sympos. Comput. Geom., pages 173--182, 1993.
Geometric Shortest Paths and Network Optimization - Mitchell (1998) (39 citations) (Correct)
....PTAS for the minimum latency problem on a set of points in the Euclidean plane Area Optimization Problems In the min area TSP (resp. max area TSP) the goal is to determine a cycle on a given set S of points such that the cycle defines a simple polygon of minimum (resp. maximum) area. Fekete [153] (in part together with Pulleyblank [155] has studied these problems extensively. He has shown that both the min area and max area TSP problems are NP complete. For the max area TSP, Fekete gives a (1=2) approximation algorithm, showing how, in O(n log n) time, one can obtain a cycle surrounding ....
S. P. Fekete. Area optimization of simple polygons. Technical Report 97-256, Mathematisches Institut, Universitat zu Koln, 1997.
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