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- Alon Efrat, Alon Itai, Matthew J. Katz
- Algorithmica
- 2001

Let A and B be two sets of n objects in \reals d , and let Match be a (one-to-one) matching between A and B . Let min(Match ), max(Match ), and Σ(Match) denote the length of the shortest edge, the length of the longest edge, and the sum of the lengths of the edges of Match , respectively. Bottleneck matching— a matching that minimizes max(Match )— is… (More)

- Moshe Dror, Alon Efrat, Anna Lubiw, Joseph S. B. Mitchell
- STOC
- 2003

Given a sequence of <i>k</i> polygons in the plane, a start point <i>s</i>, and a target point, <i>t</i>, we seek a shortest path that starts at <i>s</i>, visits in order each of the polygons, and ends at <i>t</i>. If the polygons are disjoint and convex, we give an algorithm running in time <i>O(kn log (n/k))</i>, where <i>n</i> is the total number of… (More)

- Helmut Alt, Alon Efrat, Günter Rote, Carola Wenk
- J. Algorithms
- 2003

The subject of this paper are algorithms for measuring the similarity of patterns of line segments in the plane, a standard problem in, e.g. computer vision, geographic information systems, etc. More precisely, we will define feasible distance measures that reflect how close a given pattern <i>H</i> is to some part of a larger pattern <i>G</i>. These… (More)

- Peter Braß, Eowyn Cenek, +6 authors Joseph S. B. Mitchell
- Comput. Geom.
- 2003

We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another in which the mapping is not given. We present positive and negative results for the two versions of the problem. Among the positive results with given mapping, we… (More)

- Alon Efrat
- 2000

An (α, β)-covered object is a simply connected planar region c with the property that for each point p ∈ ∂c there exists a triangle contained in c and having p as a vertex, such that all its angles are at least α and all its edges are at least β · diam(c)long. This notion extends that of fat convex objects. We show that the combinatorial complexity of the… (More)

- Otfried Cheong, Alon Efrat, Sariel Har-Peled
- SODA
- 2004

We present a near-quadratic time algorithm that computes a point inside a simple polygon <i>P</i> having approximately the largest visibility polygon inside <i>P</i>, and near-linear time algorithm for finding the point that will have approximately the largest Voronoi region when added to an <i>n</i>-point set. We apply the same technique to find the… (More)

- Alon Efrat, Sariel Har-Peled
- Inf. Process. Lett.
- 2002

Let P be a polygon with n vertices. We say that two points of P see each other if the line segment connecting them lies inside (the closure of) P . In this paper we present efficient approximation algorithms for finding the smallest set G of points of P so that each point of P is seen by at least one point of G, and the points of G are constrained to be… (More)

This paper studies two problems that arise in optimization of sensor networks: First, we devise provable approximation schemes for locating a base station and constructing a network among a set of sensors each of which has a data stream to get to the base station. Subject to power constraints at the sensors, our goal is to locate the base station and… (More)

- Alon Efrat, Micha Sharir
- Symposium on Computational Geometry
- 1997

On the Complexity of the Union of Fat Objects in the Plane* Alon Efratt Micha Sharir$ We prove a near-linear bound on the combutorial complexity of the union of n fat convex objects in the plane, each pair of whose boundaries cross at most a constant number of times.

- Alon Efrat, Arnon Amir
- INFOCOM
- 2004

Global positioning systems (GPS) and mobile phone networks are making it possible to track individual users with an increasing accuracy. It is natural to ask whether this information can be used to maintain social networks. In such a network each user wishes to be informed whenever one of a list of other users, called the user’s friends, appears in the… (More)