Esther M. Arkin

Learn More
Model-based recognition is concerned with comparing a shape A, which is stored as a model for some particular object, with a shape B, which is found to exist in an image. If A and B are close to being the same shape, then a vision system should report a match and return a measure of how good that match is. To be useful this measure should satisfy a number(More)
We introduce a geometric version of the Covering Salesman Problem: Each of the n salesman's clients speciies a neighborhood in which they are willing to meet the salesman. Identifying a tour of minimum length that visits all neighborhoods is an NP-hard problem, since it is a generalization of the Traveling Salesman Problem. We present simple heuristic(More)
We study the problem of finding shortest tours/paths for “lawn mowing” and “milling” problems: Given a region in the plane, and given the shape of a “cutter” (typically, a circle or a square), find a shortest tour/path for the cutter such that every point within the region is covered by the cutter at some position along the tour/path. In the milling version(More)
We study the class of problems associated with the detection and computation of monotone paths among a set of disjoint obstacles. We give an <italic>&Ogr;</italic>(<italic>nE</italic>) algorithm for finding a monotone path (if one exists) between two points in the plane in the presence of polygonal obstacles. (Here, <italic>E</italic> is the size of the(More)
The tree and tour cover problems on an edge-weighted graph are to compute a minimum weight tree and closed walk, respectively, whose vertices form a vertex cover. Both problems are NP-hard. In this note we give strongly polynomial time, constant factor approximation algorithms for both problems. An interesting feature of our algorithms is how they combine(More)
Given a collection of sets of cardinality at most k, with weights for each set, the maximum weighted packing problem is that of nding a collection of disjoint sets of maximum total weight. We study the worst case behavior of the t-local search heuristic for this problem proving a tight bound of k ? 1 + 1 t. As a consequence, for any given r < 1 k?1 we can(More)
High-performance rendering engines are often pipelined; their speed is bounded by the rate at which triangulation data can be sent into the machine. An ordering such that consecutive triangles share a face, which reduces the data rate, exists if and only if the dual graph of the triangulation contains a Hamiltonian path. We (1) show thatany set ofn points(More)
We consider a variety of vehicle routing problems. The input to a problem consists of a graph G = (N, E) and edge lengths l(e) e ∈ E. Customers located at the vertices have to be visited by a set of vehicles. Two important parameters are k the number of vehicles, and λ the longest distance traveled by a vehicle. We consider two types of problems: (1) Given(More)