UWSpace is currently experiencing technical difficulties resulting from its recent migration to a new version of its software. These technical issues are not affecting the submission and browse features of the site. UWaterloo community members may continue submitting items to UWSpace. We apologize for the inconvenience, and are actively working to resolve these technical issues.
 

A Las Vegas Algorithm for the Ordered Majority Problem

Thumbnail Image

Files

Baral_Ben.pdf (341.57 KB)

Date

2022-09-29

Authors

Baral, Ben

Journal Title

Journal ISSN

Volume Title

Publisher

University of Waterloo

Abstract

In this thesis, we study the majority problem using ordered comparisons under the Las Vegas randomized algorithm model. The majority problem asks whether a given set of n elements, each with some colour, has a colour which appears on more than half of the elements. We focus on algorithms for this problem whose fundamental operation is to compare two elements, and in particular the comparison returns one of {<, =, >}. Additionally, we are interested specifically in Las Vegas randomized algorithms for this problem, which solve the problem correctly in all cases but whose running time is a random variable. Interestingly, most previous work studying this problem considers a different model where comparisons return just whether two elements are equal or not, instead of providing ordered information. Our contribution is a novel Las Vegas algorithm that uses only n + o(n) comparisons in the expectation, compared to 7n/6 + o(n) comparisons required in the expectation by the previous best algorithm for this problem.

Description

Keywords

theoretical computer science, algorithm, comparison-based problems, majority, randomized algorithms

LC Keywords

Citation

URI

http://hdl.handle.net/10012/18852

Collections

Theses
Computer Science