arXiv subjects

Sariel Har-Peled

Publications and source records attributed to Sariel Har-Peled.

130 records · Page 8Linked to original sources

arXiv2005

Fast Construction of Nets in Low Dimensional Metrics, and Their Applications

We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain improved algorithms for the following problems: Approximate nearest neighbor search, well-separated pair decomposition, compact representation scheme, doubling measure, and computation of the (approximate) Lipschitz constant of a function. In all cases, the running (preprocessing) time is near-linear and the space being used is linear.

cs.DS↗

arXiv2005

A Time-Optimal Delaunay Refinement Algorithm in Two Dimensions

We propose a new refinement algorithm to generate size-optimal quality-guaranteed Delaunay triangulations in the plane. The algorithm takes $O(n \log n + m)$ time, where $n$ is the input size and $m$ is the output size. This is the first time-optimal Delaunay refinement algorithm.

cs.CG↗

arXiv2003

When Crossings Count - Approximating the Minimum Spanning Tree

In the first part of the paper, we present an (1+μ)-approximation algorithm to the minimum-spanning tree of points in a planar arrangement of lines, where the metric is the number of crossings between the spanning tree and the lines. The expected running time is O((n/μ^5) alpha^3(n) log^5 n), where μ> 0 is a prescribed constant. In the second part of our paper, we show how to embed such a crossing metric, into high-dimensions, so that the distances are preserved. As a result, we can deploy a large collection of subquadratic approximations algorithms \cite im-anntr-98,giv-rahdg-99 for problems involving points with the crossing metric as a distance function. Applications include matching, clustering, nearest-neighbor, and furthest-neighbor.

cs.CG↗

arXiv2002

Optimally cutting a surface into a disk

We consider the problem of cutting a set of edges on a polyhedral manifold surface, possibly with boundary, to obtain a single topological disk, minimizing either the total number of cut edges or their total length. We show that this problem is NP-hard, even for manifolds without boundary and for punctured spheres. We also describe an algorithm with running time n^{O(g+k)}, where n is the combinatorial complexity, g is the genus, and k is the number of boundary components of the input surface. Finally, we describe a greedy algorithm that outputs a O(log^2 g)-approximation of the minimum cut graph in O(g^2 n log n) time.

cs.CG↗