## Search

Now showing items 1-10 of 13

#### Packing Unit Disks

(University of Waterloo, 2008-08-27)

Given a set of unit disks in the plane with union area A, what fraction of A can be covered by selecting a pairwise disjoint subset of the disks? Richard Rado conjectured 1/4 and proved 1/4.41. In this thesis, we consider ...

#### Space-Efficient Data Structures for Information Retrieval

(University of Waterloo, 2013-04-30)

The amount of data that people and companies store has grown exponentially over the last few years. Storing this information alone is not enough, because in order to make it useful we need to be able to efficiently search ...

#### Performance of the Ultra-Wide Word Model

(University of Waterloo, 2017-09-08)

The Ultra-wide word model of computation (UWRAM) is an extension of the Word-RAM model which has an ALU that can operate on w^2 bits at a time, where w is the size in bits of a cell in memory. The purpose of this thesis ...

#### Three Approaches to Building Time-Windowed Geometric Data Structures

(University of Waterloo, 2016-08-18)

Given a set of geometric objects (points or line segments) each associated with a time value, we wish to determine whether a given property is true for a subset of those objects whose time values fall within a query time ...

#### A Parameterized Algorithm for Upward Planarity Testing of Biconnected Graphs

(University of Waterloo, 2003)

We can visualize a graph by producing a geometric representation of the graph in which each node is represented by a single point on the plane, and each edge is represented by a curve that connects its two ...

#### Folding and Unfolding

(University of Waterloo, 2001)

The results of this thesis concern folding of one-dimensional objects in two dimensions: planar linkages. More precisely, a planar linkage consists of a collection of rigid bars (line segments) connected at their ...

#### RNA Homology Searches Using Pair Seeding

(University of Waterloo, 2005)

Due to increasing numbers of non-coding RNA (ncRNA) being discovered recently, there is interest in identifying homologs of a given structured RNA sequence. Exhaustive homology searching for structured RNA molecules using covariance models is infeasible on genome-length sequences. Hence, heuristic methods are employed, but they largely ignore structural information in the query. We present a novel method, which uses secondary structure information, to perform homology searches for a structured RNA molecule. We define the concept of a

**pair seed**and theoretically model alignments of random and related paired regions to compute expected sensitivity and specificity. We show that our method gives theoretical gains in sensitivity and specificity compared to a BLAST-based heuristic approach. We provide experimental verification of this gain. <br /><br /> We also show that pair seeds can be effectively combined with the spaced seeds approach to nucleotide homology search. The hybrid search method has theoretical specificity superior to that of the BLAST seed. We provide experimental evaluation of our hypotheses. Finally, we note that our method is easily modified to process pseudo-knotted regions in the query, something outside the scope of covariance model based methods....#### A Geometric Approach to Pattern Matching in Polyphonic Music

(University of Waterloo, 2005)

The music pattern matching problem involves finding matches of a small fragment of music called the "pattern" into a larger body of music called the "score". We represent music as a series of horizontal line segments in the plane, and reformulate the problem as finding the best translation of a small set of horizontal line segments into a larger set of horizontal line segments. We present an efficient algorithm that can handle general weight models that measure the musical quality of a match of the pattern into the score, allowing for approximate pattern matching.
We give an algorithm with running time

**O**(**nm**(**d**+ log**m**)), where**n**is the size of the score,**m**is the size of the pattern, and**d**is the size of the discrete set of musical pitches used. Our algorithm compares favourably to previous approaches to the music pattern matching problem. We also demonstrate that this geometric formulation of the music pattern matching problem is unlikely to have a significantly faster algorithm since it is at least as hard as 3SUM, a basic problem that is conjectured to have no subquadratic algorithm. Lastly, we present experiments to show how our algorithm can find musically sensible variations of a theme, as well as polyphonic musical patterns in a polyphonic score....#### Models for Parallel Computation in Multi-Core, Heterogeneous, and Ultra Wide-Word Architectures

(University of Waterloo, 2013-04-26)

Multi-core processors have become the dominant processor architecture with 2, 4, and 8 cores on a chip being widely available and an increasing number of cores predicted for the future. In addition, the decreasing costs ...

#### The Incremental Constraint of k-Server

(University of Waterloo, 2012-05-19)

Online algorithms are characterized by operating on an input sequence revealed over time versus a single static input. Instead of generating a single solution, they produce a sequence of incremental solutions corresponding ...