Average Case Analysis of an Adjacency Map Searching Technique.
Abstract
The adjacency map is a data structure (a tree) used to solve the following problem: given a set of parallel segments in the plane and a point p, find the segments closest to p among those intersected by the straight line through p, perpendicular to the common direction of the segments. The search is performed in the repetitive mode, so that preprocessing is convenient. The problem considered is a particular case of planar point location for which algorithms are known (Lipton-Tarjan, Kirkpatrick), which make use of data structures constructed in time 0(nlogn), searched in time 0(logn), and stored in space 0(n). Though asymptotically optimal, the previous algorithms are not very practical. More practical algorithms have been proposed (Preparata, Preparata-Lipski), which use 0(nlogn) space. In this thesis a modification of these algorithm is presented for the adjacency map, and the worst case analysis is performed. The technique is easily extensible to general planar graphs. It is conjectured that, under reasonable assumptions on the input distribution, the new algorithm takes expected linear storage. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1981
- Accession Number
- ADA124473
Entities
People
- Gianfranco Bilardi
Organizations
- University of Illinois Urbana–Champaign