## 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 ...

#### Combinatorial and Probabilistic Approaches to Motif Recognition

(University of Waterloo, 2010-11-10)

Short substrings of genomic data that are responsible for biological processes, such as gene expression, are referred to as motifs. Motifs with the same function may not entirely match, due to mutation events at a few of ...

#### 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 ...

#### 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 ...

#### Adaptive Comparison-Based Algorithms for Evaluating Set Queries

(University of Waterloo, 2004)

In this thesis we study a problem that arises in answering boolean queries submitted to a search engine. Usually a search engine stores the set of IDs of documents containing each word in a pre-computed sorted order and ...

#### 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 ...

#### 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....#### Algorithms for fast linear system solving and rank profile computation

(University of Waterloo, 2014-07-16)

We give randomized algorithms for linear algebra problems concerning an n*m input matrix A over a field K. We give an algorithm that simultaneously computes the row and column rank profiles of A in 2r^3 + (r^2+n+m+|A|)^{1+o(1)} ...

#### 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 ...