Date of Award

2022

Document Type

Open Access Master's Thesis

Degree Name

Master of Science in Computer Science (MS)

Administrative Home Department

Department of Computer Science

Advisor 1

Yakov Nekrich

Committee Member 1

Zhenlin Wang

Committee Member 2

Ali Ebnenasir

Abstract

Given a set of points P, we often need to report the ones that lie within a certain query range Q. This is referred to as orthogonal range reporting. We can also go further, reporting only the dominant points within that query. In 2 dimensions, a point p1 = (x1, y1) dominates a point p2 = (x2, y2) iff x1 ≥ x2 and y1 > y2 or x1 > x2 and y1 ≥ y2. The set of all dominant points within a query range is called the skyline of that query. There are several different variants of skyline queries. For example, we can consider each point in P to be colored. Given a query range Q, can we efficiently count the number of points of each color in the skyline? In this thesis, we will present a new O( log n log log n + D log log n) method for doing so. The method is possible thanks to a new reduction from skyline queries to orthogonal range queries. We will also explore novel algorithms for answering skyline query variants in the I/O model of computation, making use of techniques such as Ganguly et al.’s [2] double-chaining method and Alstrup et al.’s [14] grid approach. By applying these existing techniques in new ways, we can not only derive our own efficient algorithms for skyline queries, but also explore potential avenues for future research

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