## Search

Now showing items 1-7 of 7

#### 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 ...

#### 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....#### 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 ...

#### 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)} ...

#### 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 ...

#### 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 ...