Michael A. Soss

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The maximum detour and spanning ratio of an embedded graph G are values that measure how well G approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe O(n logn) time algorithms for computing the maximum detour and spanning ratio of a planar polygonal path. These algorithms solve open problems posed in at least(More)
The detour and spanning ratio of a graph embedded in measure how well approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe time algorithms for computing the detour and spanning ratio of a planar polygonal path. By generalizing these algorithms, we obtain -time algorithms for computing the detour or spanning(More)
It is widely accepted that (1) the natural or folded state of proteins is a global energy minimum, and (2) in most cases proteins fold to a unique state determined by their amino acid sequence. The H-P (hydrophobic-hydrophilic) model is a simple combinatorial model designed to answer qualitative questions about the protein folding process. In this paper we(More)
Given a set S of n points in R 2 , the Oja depth of a point is the sum of the areas of all triangles formed by and two elements of S. A point in R 2 with minimum depth is an Oja median. We show how an Oja median may be computed in O(n log 3 n) time. In addition, we present an algorithm for computing the Fermat-Torricelli points of n lines in O(n) time.(More)
We examine a computational geometric problem concerning the structure of polymers. We model a polymer as a polygonal chain in three dimensions. Each edge splits the polymer into two subchains, and a dihedral rotation rotates one of these subchains rigidly about the edge. The problem is to determine, given a chain, an edge, and an angle of rotation, if the(More)
This paper considers reconngurations of polygons, where each polygon edge is a rigid link, no two of which can cross during the motion. We prove that one can reconngure any monotone polygon into a convex polygon; a polygon is monotone if any vertical line intersects the interior at a (possibly empty) interval. Our algorithm computes in O(n 2) time a(More)
Let V be a set of distinct points in the Euclidean plane. For each point x 2 V , let sx be the ball centered at x with radius equal to the distance from x to its nearest neighbour. We refer to these balls as the spheres of in uence of the set V . The sphere of in uence graph on V is de ned as the graph where (x; y) is an edge if and only if sx and sy(More)
Given a simple polygon in the plane, a deflation is defined as the inverse of a flip in the Erdős-Nagy sense. In 1993 Bernd Wegner conjectured that every simple polygon admits only a finite number of deflations. In this note we describe a counterexample to this conjecture by exhibiting a family of polygons on which deflations go on forever.
We explore which classes of linkages have the property that each pair of their flat states—that is, their embeddings in R without self-intersection—can be connected by a continuous dihedral motion that avoids self-intersection throughout. Dihedral motions preserve all angles between pairs of incident edges, which is most natural for protein models. Our(More)