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This paper studies the point location problem in Delau-nay triangulations without preprocessing and additional storage. The proposed procedure finds the query point simply by " walking through " the triangulation, after selecting a " good starting point " by random sampling. The analysis generalizes and extends a recent result for d = 2 dimensions by… (More)

This short note considers the problem of point location in a Delaunay triangulation of n random points, using no additional preprocessing or storage other than a standard data structure representing the triangulation. A simple and easy-to-implement (but, of course, worst-case suboptimal) heuristic is shown to take expected time O(n 1/3). 1. Introduction and… (More)

Matching two geometric objects in two-dimensional (2D) and three-dimensional (3D) spaces is a central problem in computer vision, pattern recognition, and protein structure prediction. In particular, the problem of aligning two polygonal chains under translation and rotation to minimize their distance has been studied using various distance measures. It is… (More)

The paper " The Approximability of the Exemplar Break-point Distance Problem " [1], which appeared in AAIM 2006, contained several negative results and one positive result — a claimed O(log n)-factor greedy approximation for the One-sided Exemplar Breakpoint Distance Problem. Here, we show that the analysis was incorrect and the approximation factor of the… (More)

A genomic map is represented by a sequence of gene markers, and a gene marker can appear in several different genomic maps, in either positive or negative form. A strip (syntenic block) is a sequence of distinct markers that appears as subsequences in two or more maps, either directly or in reversed and negated form. Given two genomic maps G and H, the… (More)

Given a label shape L and a set of n points in the plane, the 2-label point-labeling problem consists of placing 2n non-intersecting translated copies of L of maximum size such that each point touches two unique copies—its labels. In this paper we give new and simple approximation algorithms for L an axis-parallel square or a circle. For squares we improve… (More)

In this paper, we present an ¥ § ¦ © ¨ ¨ time solution for the following multi-label map labeling problem: Given a set of¨distinct sites in the plane, place at each site a triple of uniform squares of maximum possible size such that all the squares are axis-parallel and a site is on the boundaries of its three labeling squares. We also study the problem… (More)

Given two genomic maps G and H represented by a sequence of n gene markers, a strip (syntenic block) is a sequence of distinct markers of length at least two which appear as subsequences in the input maps, either directly or in reversed and negated form. The problem Maximal Strip Recovery (MSR) is to find two subsequences G' and H' of G and H, respectively,… (More)