Browsing Mathematics (Faculty of) by Supervisor "Munro, J. Ian"
Now showing items 113 of 13

Approximately Optimum Search Trees in External Memory Models
(University of Waterloo, 20160516)We examine optimal and near optimal solutions to the classic binary search tree problem of Knuth. We are given a set of n keys (originally known as words), B_1, B_2, ..., B_n and 2n+1 frequencies. {p_1, p_2, ..., p_n} ... 
Compact Routing on Planar Graphs
(University of Waterloo, 20240104)This thesis delves into the exploration of shortest path queries in planar graphs, with an emphasis on the utilization of spaceefficient data structures. Our investigation primarily targets connected, undirected, static ... 
Efficient Data Structures for Partial Orders, Range Modes, and Graph Cuts
(University of Waterloo, 20210430)This thesis considers the study of data structures from the perspective of the theoretician, with a focus on simplicity and practicality. We consider both the time complexity as well as space usage of proposed solutions. ... 
Efficient Representation and Encoding of Distributive Lattices
(University of Waterloo, 20180820)This thesis presents two new representations of distributive lattices with an eye towards efficiency in both time and space. Distributive lattices are a wellknown class of partiallyordered sets having two natural operations ... 
InMemory Storage for Labeled TreeStructured Data
(University of Waterloo, 20170316)In this thesis, we design inmemory data structures for labeled and weights trees, so that various types of path queries or operations can be supported with efficient query time. We assume the word RAM model with word size ... 
A Las Vegas Algorithm for the Ordered Majority Problem
(University of Waterloo, 20220929)In this thesis, we study the majority problem using ordered comparisons under the Las Vegas randomized algorithm model. The majority problem asks whether a given set of n elements, each with some colour, has a colour which ... 
Majority in the ThreeWay Comparison Model
(University of Waterloo, 20190828)In this thesis, we study comparison based problems in a new comparison model called threeway, where a comparison can result in { >, =, < }. We consider a set of n balls with fixed ordered coloring. Particularly, we are ... 
Optimal PathDecomposition of Tries
(University of Waterloo, 20160516)In this thesis, we consider the pathdecomposition representation of prefix trees. We show that given query probabilities for every word in the prefix tree, the heavypath strategy produces the optimal trie with respect ... 
Performance of the UltraWide Word Model
(University of Waterloo, 20170908)The Ultrawide word model of computation (UWRAM) is an extension of the WordRAM 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 ... 
Space Efficient Data Structures and Algorithms in the WordRAM Model
(University of Waterloo, 20180430)In modern computation the volume of datasets has increased dramatically. Since the majority of these datasets are stored in internal memory, reducing their storage requirement is an important research topic. One way ... 
Succinct and Compact Data Structures for Intersection Graphs
(University of Waterloo, 20230814)This thesis designs space efficient data structures for several classes of intersection graphs, including interval graphs, path graphs and chordal graphs. Our goal is to support navigational operations such as adjacent and ... 
Succinct Data Structures for Chordal Graphs
(University of Waterloo, 20190410)We study the problem of approximate shortest path queries in chordal graphs and give a n log n + o(n log n) bit data structure to answer the approximate distance query to within an additive constant of 1 in O(1) time. We ... 
Towards the Efficient Generation of Gray Codes in the Bitprobe Model
(University of Waterloo, 20160513)We examine the problem of representing integers modulo L so that both increment and decrement operations can be performed efficiently. This problem is studied in the bitprobe model, where the complexity of the underlying ...