Now showing items 1-6 of 6

• #### The Complexity of Finding Dense Subgraphs in Graphs with Large Cliques ﻿

(University of Waterloo, 2021-08-25)
The GapDensest-k-Subgraph(d) problem (GapDkS(d)) is defined as follows: given a graph G and parameters k,d, distinguish between the case that G contains a k-clique, and the case that every k-subgraph of G has density at ...
• #### Domain Ordering and Box Cover Problems for Beyond Worst-Case Join Processing ﻿

(University of Waterloo, 2019-09-17)
Join queries are a fundamental computational task in relational database management systems. For decades, complex joins were most often computed by decomposing the query into a query plan made of a sequence of binary joins. ...
• #### Halfway to Halfspace Testing ﻿

(University of Waterloo, 2017-10-18)
In this thesis I study the problem of testing halfspaces under arbitrary probability distributions, using only random samples. A halfspace, or linear threshold function, is a boolean function f : Rⁿ → {±1} defined as the ...
• #### Monotonicity Testing for Boolean Functions over Graph Products ﻿

(University of Waterloo, 2020-09-09)
We establish a directed analogue of Chung and Tetali's isoperimetric inequality for graph products. We use this inequality to obtain new bounds on the query complexity for testing monotonicity of Boolean-valued functions ...
• #### On Tolerant Testing and Tolerant Junta Testing ﻿

(University of Waterloo, 2020-07-08)
Over the past few decades property testing has became an active field of study in theoretical computer science. The algorithmic task is to determine, given access to an unknown large object (e.g., function, graph, probability ...
• #### Testing Submodularity ﻿

(University of Waterloo, 2017-09-28)
We show that for any constants $\epsilon > 0$ and $p \ge 1$, given oracle access to an unknown function $f : \{0,1\}^n \to [0,1]$ it is possible to determine if the function is submodular or is $\epsilon$-far from every ...

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