arXiv subjects

Ovidiu Daescu

Publications and source records attributed to Ovidiu Daescu.

21 records · Page 2Linked to original sources

arXiv2010

Fréchet Distance Problems in Weighted Regions

We discuss two versions of the Fréchet distance problem in weighted planar subdivisions. In the first one, the distance between two points is the weighted length of the line segment joining the points. In the second one, the distance between two points is the length of the shortest path between the points. In both cases, we give algorithms for finding a (1+epsilon)-factor approximation of the Fréchet distance between two polygonal curves. We also consider the Fréchet distance between two polygonal curves among polyhedral obstacles in R^3 and present a (1+epsilon)-factor approximation algorithm.

cs.CG↗

arXiv2010

Approximate Point-to-Face Shortest Paths in R^3

We address the point-to-face approximate shortest path problem in R: Given a set of polyhedral obstacles with a total of n vertices, a source point s, an obstacle face f, and a real positive parameter epsilon, compute a path from s to f that avoids the interior of the obstacles and has length at most (1+epsilon) times the length of the shortest obstacle avoiding path from s to f. We present three approximation algorithms that take by extending three well-known "point-to-point" shortest path algorithms.

cs.CG↗

arXiv2008

Towards an optimal algorithm for recognizing Laman graphs

Laman graphs are fundamental to rigidity theory. A graph G with n vertices and m edges is a generic minimally rigid graph (Laman graph), if m=2n-3 and every induced subset of k vertices spans at most 2k-3 edges. We consider the verification problem: Given a graph G with n vertices, decide if it is Laman. We present an algorithm that takes O(T(n)+n log n) time, where T(n) is the best time to extract two edge disjoint spanning trees from G or decide no such trees exist. Our algorithm exploits a known construction called red-black hierarchy (RBH), that is a certificate for Laman graphs. First, we show how to verify if G admits an RBH and argue this is enough to conclude whether G is Laman or not. Second, we show how to construct the RBH using a two steps procedure that is simple and easy to implement. Finally, we point out some difficulties in using red-black hierarchies to compute a Henneberg construction, which seem to imply super-quadratic time algorithms when used for embedding a planar Laman graph as a pointed pseudo-triangulation.

math.CO↗