## Search

Now showing items 1-10 of 62

#### On 2-crossing-critical graphs with a V8-minor

(University of Waterloo, 2014-05-22)

The crossing number of a graph is the minimum number of pairwise edge crossings in a drawing of a graph. A graph $G$ is $k$-crossing-critical if it has crossing number at least $k$, and any subgraph of $G$ has crossing ...

#### Implementing the Schoof-Elkies-Atkin Algorithm with NTL

(University of Waterloo, 2013-04-30)

In elliptic curve cryptography, cryptosystems are based on an additive subgroup of an elliptic curve defined over a finite field, and the hardness of the Elliptic Curve Discrete Logarithm Problem is dependent on the order ...

#### Highly Non-Convex Crossing Sequences

(University of Waterloo, 2012-05-18)

For a given graph, G, the crossing number crₐ(G) denotes the minimum number of edge crossings when a graph is drawn on an orientable surface of genus a. The sequence cr₀(G), cr₁(G), ... is said to be the crossing sequence ...

#### Evaluating Large Degree Isogenies between Elliptic Curves

(University of Waterloo, 2010-12-20)

An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between elliptic curves efficiently. For ordinary curves ...

#### Dynamic Programming: Salesman to Surgeon

(University of Waterloo, 2013-05-15)

Dynamic Programming is an optimization technique used in computer science and mathematics. Introduced in the 1950s, it has been applied to many classic combinatorial optimization problems, such as the Shortest Path Problem, ...

#### Cops and Robber Game with a Fast Robber

(University of Waterloo, 2011-03-24)

Graph searching problems are described as games played on graphs, between a set of searchers and a fugitive. Variants of the game restrict the abilities of the searchers and the fugitive and the corresponding search number ...

#### Iterative Rounding Approximation Algorithms in Network Design

(University of Waterloo, 2010-05-21)

Iterative rounding has been an increasingly popular approach to solving network design optimization problems ever since Jain introduced the concept in his revolutionary 2-approximation for the Survivable Network Design ...

#### A New Class of Cycle Inequality for the Time-Dependent Traveling Salesman Problem

(University of Waterloo, 2010-09-29)

The Time-Dependent Traveling Salesman Problem is a generalization of the well-known Traveling Salesman Problem, where the cost for travel between two nodes is dependent on the nodes and their position in the tour. Inequalities ...

#### Ehrhart Theory and Unimodular Decompositions of Lattice Polytopes

(University of Waterloo, 2015-01-20)

Ehrhart theory studies the behaviour of lattice points contained in dilates of lattice polytopes. We provide an introduction to Ehrhart theory. In particular, we prove Ehrhart's Theorem, Stanley Non-negativity, and ...

#### A Quick-and-Dirty Approach to Robustness in Linear Optimization

(University of Waterloo, 2013-01-07)

We introduce methods for dealing with linear programming (LP) problems
with uncertain data, using the notion of weighted analytic centers.
Our methods are based on high interaction with the decision maker (DM) and try ...