ISSN:
1432-2315
Keywords:
Computational geometry
;
Locality
;
Monotonicity
;
Polygon distances
;
Polygon intersection
;
Unimodality
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract A generalized problem is defined in terms of functions on sets and illustrated in terms of the computational geometry of simple planar polygons. Although its apparent time complexity is O(n 2), the problem is shown to be solvable for several cases of interest (maximum and minimum distance, intersection detection and rerporting) in O(n logn), O(n) or O(logn) time, depending on the nature of a specialized “selection” function. (Some of the cases can also be solved by the Voronoi diagram method; but time complexity increases with that approach.) A new use of monotonicity and a new concept of “locality” in set mappings contribute significantly to the derivation of the results.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01898356
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