论文信息 - Largest Subsets of Triangles in a Triangulation

Largest Subsets of Triangles in a Triangulation

Given a triangulation of n points, with some triangles marked \good", this paper discusses the problems of computing the largest-area connected set of good triangles that (i) is convex, (ii) is monotone, (iii) has a bounded total angular change, or (iv) has a bounded negative turning angle. The flrst, second, and fourth problems are solved in polynomial time, the third problem is NP-hard.

Maarten Löffler | Boris Aronov | Marc J. van Kreveld | Rodrigo I. Silveira

[1] Sivan Toledo,et al. Extremal polygon containment problems , 1991, SCG '91.

[2] Gerhard J. Woeginger,et al. Angle-Restricted Tours in the Plane , 1997, Comput. Geom..

[3] Alok Aggarwal,et al. The angular-metric traveling salesman problem , 1997, SODA '97.

[4] Esther M. Arkin,et al. An efficiently computable metric for comparing polygonal shapes , 1991, SODA '90.

[5] Gill Barequet,et al. Maximizing the area of an axis-symmetric polygon inscribed by a convex polygon , 2004, CCCG.

[6] Dan Roth,et al. Finding the Largest Area Axis-parallel Rectangle in a Polygon , 1997, Comput. Geom..

[7] Dan Roth,et al. Finding the Maximum Area Axis-parallel Rectangle in a Polygon , 1993, CCCG.

[8] Jorge Urrutia,et al. Finding the largest axis aligned rectangle in a polygon in o(n log n) time , 2001, CCCG.

[9] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[10] Chee-Keng Yap,et al. A polynomial solution for the potato-peeling problem , 1986, Discret. Comput. Geom..