A New Study of Applying Complexity Theoretical Tools in Algorithm Design

Authors

Shuai XuFollow

Document Type

Dissertation

Degree

Doctor of Philosophy (PhD)

Major/Program

Computer Science

First Advisor's Name

Ning Xie

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

S.S.Iyengar

Second Advisor's Committee Title

Committee Member

Third Advisor's Name

Wei Zeng

Third Advisor's Committee Title

Committee Member

Fourth Advisor's Name

Leonardo Bobadilla

Fourth Advisor's Committee Title

Committee Member

Fifth Advisor's Name

Xiaosheng Li

Fifth Advisor's Committee Title

Committee Member

Keywords

Algorithm Design, Randomized Algorithm, Combinatorial Search, Error Correction Code, Fast Matrix Multiplication

Date of Defense

6-26-2019

Abstract

Given n vectors with dimension m in Boolean domain, how to find two vectors whose pairwise Hamming distance is minimum? This problem is known as the Closest Pair Problem. If these vectors are generated uniformly at random except two of them are correlated with Pearson-correlation coefficient, then the problem is called the Light Bulb Problem. In this work, we propose a novel coding-based scheme for the Closest Pair Problem. We design both randomized and deterministic algorithms, which achieve the best-known running time when the length of input vectors m is small and the minimum distance is very small compared to m. When applied to the Light Bulb Problem, our result yields state-of-the-art deterministic running time when the Pearson-correlation coefficient is very large. Specifically, when it is greater than 0.9933, our deterministic algorithm runs faster than the previously best deterministic algorithm (Alman, SOSA 2019).

Identifier

FIDC007791

Recommended Citation

Xu, Shuai, "A New Study of Applying Complexity Theoretical Tools in Algorithm Design" (2019). FIU Electronic Theses and Dissertations. 4242.
https://digitalcommons.fiu.edu/etd/4242