• Publications
  • Influence
Fractals and the analysis of waveforms.
  • M. J. Katz
  • Mathematics, Medicine
  • Computers in biology and medicine
  • 1988
Waveforms are planar curves--ordered collections of (x, y) point pairs--where the x values increase monotonically. One technique for numerically classifying waveforms assesses their fractalExpand
Geometry Helps in Bottleneck Matching and Related Problems
TLDR
We propose a semidynamic data structure for answering containment problems for a set of congruent disks in the plane is developed. Expand
Fractals and the analysis of growth paths
A simple practical method exists for classifying and comparing planar curves composed of connected line segments. This method assigns, a single numberD, the fractal dimension, to eachExpand
On guarding the vertices of rectilinear domains
TLDR
We establish an interesting connection between this problem and the problem of computing a minimum clique cover in chordal graphs. Expand
Realistic input models for geometric algorithms
TLDR
The traditional worst-case analysis often fails to predict the actual behavior of the running time of geometric algorithms in practical situations. Expand
Covering Points by Unit Disks of Fixed Location
TLDR
We significantly improve the constant of approximation of the discrete unit disk cover problem from 72 to 38, using a novel approach. Expand
Power Assignment in Radio Networks with Two Power Levels
TLDR
We study the power-assignment problem in radio networks, where each radio station can transmit in one of two possible power levels, corresponding to two ranges—short and long. Expand
TSP with neighborhoods of varying size
TLDR
In TSP with neighborhoods we are given a set of objects in the plane, called neighborhoods, and we seek the shortest tour that visits all neighborhoods. Expand
An Expander-Based Approach to Geometric Optimization
TLDR
We present a new approach to problems in geometric optimization that are traditionally solved using the parametric-searching technique of Megiddo [J. ACM, 30 (1983), pp. 852--865]. Expand
A Constant-Factor Approximation Algorithm for Optimal 1.5D Terrain Guarding
TLDR
We present the first constant-factor approximation algorithm for a nontrivial instance of the optimal guarding (coverage) problem in polygons. Expand
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