Space-Efficient Algorithms for Klee's Measure Problem

An Efficient Transformation for the Klee's Measure Problem in the Streaming Model

Given a stream of rectangles over a discrete space, we consider the problem of computing the total number of distinct points covered by the rectangles. This can be seen as the discrete version of the two-dimensional Klee’s measure problem for streaming inputs. We provide an ( , δ)-approximation for fat rectangles. For the case of arbitrary rectangles, we provide an O( √ logU)approximation, wher...

A Streaming Approximation Algorithm for Klee's Measure Problem

The efficient estimation of frequency moments of a data stream in one-pass using limited space and time per item is one of the most fundamental problem in data stream processing. An especially important estimation is to find the number of distinct elements in a data stream, which is generally referred to as the zeroth frequency moment and denoted by F0. In this paper, we consider streams of rec...

Solving Geometric Problems in Space-Conscious Models

When dealing with massive data sets, standard algorithms may easily “run out of memory”. In this thesis, we design efficient algorithms in space-conscious models. In particular, in-place algorithms, multi-pass algorithms, read-only algorithms, and stream-sort algorithms are studied, and the focus is on fundamental geometric problems, such as 2D convex hulls, 3D convex hulls, Voronoi diagrams an...

Conjugate Gradients and Related KMP Algorithms

Faster s-metric calculation by considering dominated hypervolume as klee's measure problem

The dominated hypervolume (or S-metric) is a commonly accepted quality measure for comparing approximations of Pareto fronts generated by multi-objective optimizers. Since optimizers exist, namely evolutionary algorithms, that use the S-metric internally several times per iteration, a fast determination of the S-metric value is of essential importance. This work describes how to consider the S-...