We present an extensive experimental study comparing the performance of four algorithms for the following orthogonal segment intersection problem: given a set of horizontal and vertical line segments in the plane, report all intersecting horizontal-vertical pairs. The problem has important applications in VLSI layout and graphics, which are large-scale in nature. The algorithms under evaluation...

It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We study the planar slope number, i.e., the minimum number of distinct edge-slopes in such a drawing of a planar graph with maximum degree Δ. We show that the planar slope number of every series-parallel graph of maximum degree three is three. We also show that the plan...

Given a set of points, we define a minimum Steiner point tree to be a tree interconnecting these points and possibly some additional points such that the length of every edge is at most 1 and the number of additional points is minimized. We propose using Steiner minimal trees to approximate minimum Steiner point trees. It is shown that in arbitrary metric spaces this gives a performance differe...

The relative neighbourhood graph (RNG) of a set of n points on the plane is defined. The ability of the RNG to extract a perceptually meaningful structure from the set of points is briefly discussed and compared to that of two other graph structures: the minimal spanning tree (MST) and the Delaunay (Voronoi) triangulation (DT). It is shown that the RNG is a superset of the MST and a subset of t...

| We nd a large number of \geometric separator theorems" such as: I: Given N disjoint iso-oriented squares in the plane, there exists a rectangle with 2N=3 squares inside, 2N=3 squares outside, and (4 + o(1)) p N partly in & out. II: There exists a rectangle that is crossed by the minimal spanning tree of N sites in the plane at (4 3 1=4 + o(1)) p N points, having 2N=3 sites inside and outside....

The Domain Name System (DNS) [7] provides vital mapping services for the Internet. It maps domain names such as ucla.edu to values ranging from IP addresses to email servers to geographic locations and more. Virtually every Internet application relies on looking up some form of DNS data. This article first describes a dichotomy that exists between DNS’ well structured and ordered data plane (th...

Hyper-spectral images consist of huge amount of data. This paper presents a compression technique developed specifically for these images. This technique explores unique characteristics of the hyper-spectral images and incorporates them into the compression. It also exploits the wavelet transformation and bit plane entropy coding used in general image compression. In this technique, predicting ...

In this paper, we deal with the problem of generating all triangulations of plane graphs. We give an algorithm for generating all triangulations of a triconnected plane graph G of n vertices. Our algorithm establishes a tree structure among the triangulations of G, called the “tree of triangulations,” and generates each triangulation of G in O(1) time. The algorithm uses O(n) space and generate...

In this paper, we design and evaluate algorithms for fast recovery from link failures in a smart grid communication network, addressing all three aspects of link failure recovery: (a) link failure detection, (b) algorithms for computing backup multicast trees, and (c) fast backup tree installation. To address (a), we design link-failure detection and reporting mechanisms that use OpenFlow to de...

Let X be a set of multicolored points in the plane such that no three points are collinear and each color appears on at most ⌈|X|/2⌉ points. We show the existence of a non-crossing properly colored geometric perfect matching on X (if |X| is even), and the existence of a non-crossing properly colored geometric spanning tree with maximum degree at most 3 on X. Moreover, we show the existence of a...