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Verification and Sensitivity Analysis Of Minimum Spanning Trees In Linear Time
 SIAM J. COMPUT
, 1992
"... Komlos has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree. The total computational work required by his method is much larger than linear, however. We describe a lineartime algorithm for verifyi ..."
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Komlos has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree. The total computational work required by his method is much larger than linear, however. We describe a lineartime algorithm for verifying a minimum spanning tree. Our algorithm combines the result of Komlos with a preprocessing and table lookup method for small subproblems and with a previously known almostlineartime algorithm. Additionally, we present an optimal deterministic algorithm and a lineartime randomized algorithm for sensitivity analysis of minimum spanning trees.
Computing the IntersectionDepth of Polyhedra
 Algorithmica
, 1993
"... Given two intersecting polyhedra P , Q and a direction d, find the smallest translation of Q along d that renders the interiors of P and Q disjoint. The same problem can also be posed without specifying the direction, in which case the minimum translation over all directions is sought. These are fun ..."
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Cited by 56 (2 self)
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Given two intersecting polyhedra P , Q and a direction d, find the smallest translation of Q along d that renders the interiors of P and Q disjoint. The same problem can also be posed without specifying the direction, in which case the minimum translation over all directions is sought. These are fundamental problems that arise in robotics and computer vision. We develop techniques for implicitly building and searching convolutions and apply them to derive efficient algorithms for these problems. 1 Introduction The computation of spatial relationships among geometric objects is a fundamental problem in such areas as robotics, computeraided design, VLSI layout, and computer graphics. In a dynamic environment where objects are mobile, intersection or proximity among objects has obvious applications. Consider, for instance, the problem of collision detection in robot motion planning. The Euclidean distance is a commonly used measure in these areas. Numerous efficient algorithms are known...
Walking an unknown street with bounded detour. Computational geometry: theory and applications
 in The 32nd Symposium on Foundations of Computer Science
, 1992
"... A polygon with two distinguished vertices, s and g, is called a street iff the two boundary chains from s to g are mutually weakly visible. For a mobile robot with onboard vision system we describe a strategy for finding a short path from s to g in a street not known in advance, and prove that the ..."
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Cited by 49 (7 self)
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A polygon with two distinguished vertices, s and g, is called a street iff the two boundary chains from s to g are mutually weakly visible. For a mobile robot with onboard vision system we describe a strategy for finding a short path from s to g in a street not known in advance, and prove that the length of the path created does not exceed 1 + 2. times the length of the shortest path from s to g. Experiments suggest that our strategy is much better than this, as no ratio bigger than 1.8 has yet been observed. This is complemented by a lower bound of 1.41 for the relative detour each strategy can be forced to generate. 1