Unit disk graphs are the intersection graphs of unit diameter closed disks in the plane. This paper reduces SATISFIABILITY to the problem of recognizing unit disk graphs. Equivalently, it shows thatâ€¦ (More)

ACKNOWLEDGMENT The authors express their appreciation for numerous constructive suggestions, which led to improvements on various phases of the manuscript, to Dr. A high performance multiple dataâ€¦ (More)

We present a new planar convex hull algorithm with worst case time complexity O(n log H) where n is the size of the input set and H is the size of the output set, i.e. the number of vertices found toâ€¦ (More)

We show how (now familiar) hierarchical representations of (convex) polyhedra can be used to answer various separation queries e ciently (in a number of cases, optimally). Our emphasis is i) theâ€¦ (More)

Methods are given for unifyin:: and extending previous work on detecting intersections of suitably preprocessed polyhedra. New upper bounds of O(log n) and O\log* IZ I are given on plane-polyhedronâ€¦ (More)

Given two intersecting polyhedraP, Q and a directiond, find the smallest translation ofQ alongd that renders the interiors ofP andQ disjoint. The same problem can also be posed without specifying theâ€¦ (More)

20th Annual Symposium on Foundations of Computerâ€¦

1979

An O(n lgn) algorithm is presented for the construction of skeletons of arbitrary n-line polygonal figures. This algorithm is based on an O(n lgn) algorithm for the construction of generalizedâ€¦ (More)