Daniel R. PageUniversity of Regina · Department of Computer Sciences
Daniel R. Page
PhD
Studying hard scheduling and graph problems, approximation algorithms.
Creating accessible Computer Science education!
About
15
Publications
75,335
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40
Citations
Introduction
My main interests are Theoretical Computer Science, Algorithms (Approximation Algorithms), Combinatorial Optimization (Scheduling and Graph Algorithms).
I am a Lecturer for the Dept. of CS at U of Regina. In the past, I was an Asst. Professor at StFX, an Instructor for Uni. of Western Ontario, a Sessional Instr. for the U of Manitoba, a Science Educator/Museum Interpreter for the Royal Aviation Museum of Western Canada, an ex-"Mad Scientist" for Mad Science, and have worked with all ages.
Additional affiliations
July 2021 - present
Position
- Lecturer
Description
- Courses Taught (Fall 2021): CS 340 Advanced Data Structures and Algorithm Design CS 411 Computability and Formal Languages CS 811 Theory of Computing
October 2020 - present
PageWizard Games Learning & Entertainment
Position
- Owner
Description
- My goal is to continue doing my research in theoretical computer science. I create free or accessible Computer Science educational content, and in addition I make games. To support my work: https://www.patreon.com/PageWizard
January 2020 - September 2020
Position
- Professor (Assistant)
Description
- Assistant Professor and Alley Heaps Associate (2020-2022, resigned late 2020). Area: Theoretical Computer Science. Proposed new courses, voted on, approved: -CSCI 435: Algorithms and Complexity -CSCI 550: Approximation Algorithms. Was on the hiring committee.
Education
January 2015 - June 2019
September 2012 - October 2014
September 2007 - October 2011
Publications
Publications (15)
![Figure 3.4: The flow network N of Kolliopoulos and Moysoglou [66]. The...](profile/Daniel-Page-7/publication/332865046/figure/fig3/AS:756643516121089@1557409280297/The-flow-network-N-of-Kolliopoulos-and-Moysoglou-66-The-shaded-edge-nodes-represent_Q320.jpg)
A fundamental problem in scheduling is makespan minimization on unrelated parallel machines (R||Cmax). Let there be a set J of jobs and a set M of parallel machines, where every job Jj ∈ J has processing time or length pi,j ∈ ℚ+ on machine Mi ∈ M. The goal in R||Cmax is to schedule the jobs non-preemptively on the machines so as to minimize the len...
Let there be a set M of m parallel machines and a set J of n jobs, where each job j takes p_{i,j} time units on machine M_i. In makespan minimization the goal is to schedule each job non-preemptively on a machine such that the length of the schedule, the makespan, is minimum. We investigate a generalization of makespan minimization on unrelated par...
Let there be a set J of n jobs and a set M of m parallel machines, where each job j takes p_{i,j} ∈ ℤ^+ time units on machine i and assume p_{i,j}=∞ implies job j cannot be scheduled on machine i. In makespan minimization on unrelated parallel machines (R||C_{max}), the goal is to schedule each job non-preemptively on a machine so as to minimize th...
Let there be m parallel machines and n jobs, where a job j can be scheduled on machine i to take pi, j ∈ Z+ time units. The makespan Cmax is the completion time of a machine that finishes last. The goal is to produce a schedule with all n jobs that has minimum makespan. This is the makespan problem on unrelated parallel machines, denoted as R||Cmax...
Image processing has been applied for aesthetic or artistic purposes to produce a range of visual effects including abstracted images, painterly renderings, and comic-book, or cartoon effects. In this paper we examine the problem of transforming standard RGB images to having an appearance reminiscent of older console games. This is achieved by way...
In this paper we present a linear-time algorithm for drawing String Graphs in the plane for a restricted type of outerplanar grid drawing called an 8-Grid Outerplanar Grid Drawing. If a Grid Drawing has edges that only intersect integer coordinates and every vertex has at most eight neighbours, then a Grid Drawing is 8-Grid. If an 8-Grid Outerplana...
URL: http://hdl.handle.net/1993/23825
Let there be m parallel machines and n jobs to be scheduled non-preemptively. A job j scheduled on machine i takes p_{i,j} time units to complete, where 1 ≤ i ≤ m and 1 ≤ j ≤ n. For a given schedule, the makespan is the completion time of a machine that finishes last. The goal is to produce a schedule of all n...
In 2012, Page presented a sequential combinatorial generation algorithm for generalized types of restricted weak integer compositions called second–order restricted weak integer compositions. Second–order restricted weak integer compositions cover various types of restricted weak integer compositions of n parts such as integer compositions, bounded...
This paper presents a new algorithm that arrives at a generalized solution for the generation of restricted weak compositions of n-parts. In particular, this generalized algorithm covers many commonly sought compositions such as bounded compositions, restricted compositions, weak compositions, and restricted part compositions. Introduced is an algo...
In this thesis I present two new algorithms that arrive at a generalized solution for the enumeration (generation) of restricted weak compositions of n-parts. In particular, these generalized algorithms cover many common sought compositions such as bounded compositions, restricted compositions, weak compositions, and restricted part compo-sitions....
Questions
Questions (9)
Projects
Projects (2)
In this project we consider parallel machine scheduling problems where bag constraints are imposed: the set of jobs is partitioned into sets called bags, and no two jobs from the same bag can be scheduled on the same machine. The goal in this project is to design exact, parameterized, and approximation algorithms for hard scheduling problems when the bag constraints must be satisfied. In addition, we are considering scheduling problems that currently may not have any established complexity results, so another aspect of this project is to determine the existence of certain kinds of algorithms under fundamental assumptions.
Let there be m parallel machines and n jobs, where each job j takes p_{i,j} time units on machine i. Consider the following problem: given n jobs and m unrelated parallel machines, schedule non-preemptively the n jobs to the machines so as to minimize the length of the schedule, the makespan. This is the makespan minimization problem on unrelated parallel machines, and is commonly denoted as R||C_{max}. Lenstra, Shmoys, and Tardos (1990) gave a 2-approximation algorithm for R||C_{max}, and proved there is no p-approximation algorithm with p<3/2, unless P=NP. This 3/2-to-2 inapproximability-to-approximation gap still remains open and reconciling this gap is often regarded as one of the most challenging open problems in approximation algorithms today.
In this project we study special cases of R||C_{max} to determine the existence of approximation algorithms with approximation ratio strictly less than 2. An emphasis is placed on a special case known as the graph balancing problem, which recently was shown to have a 7/4-approximation algorithm. In addition, we also focus on structured instances that have nice properties and the restricted assignment problem.
Another aspect of this project is the study of generalizations of R||C_{max} and studying it with respect to the special cases above in the hopes to gain further insights into the classic problem or to find better approximation algorithms where none currently have been discovered.
