Hoffman and Schwartz [13] developed the Lattice Polyhedron model and proved that it is totally dual integral (TDI), and so has integral optimal solutions. The model generalizes many important combinatorial optimization problems such as polymatroid intersection, cut covering polyhedra, min cost aborescences, etc., but has lacked a combinatorial algorithm. The problem can be seen as the blocking ...

For a proper cone K ⊂ R and its dual cone K∗ the complementary slackness condition x s = 0 defines an n-dimensional manifold C(K) in the space { (x, s) | x ∈ K, s ∈ K∗ }. When K is a symmetric cone, this fact translates to a set of n bilinear optimality conditions satisfied by every (x, s) ∈ C(K). This proves to be very useful when optimizing over such cones, therefore it is natural to look for...

We consider the problem of covering and packing subsets of δ-hyperbolic metric spaces and graphs by balls. These spaces, defined via a combinatorial Gromov condition, have recently become of interest in several domains of computer science. Specifically, given a subset S of a δhyperbolic graph G and a positive number R, let γ(S, R) be the minimum number of balls of radius R covering S. It is kno...

The Goodwin growth model is a particular dynamical system exhibiting limit cycle behaviour. I wish to add a measure of search and selection into the basic model by adapting one of the parameters of the model to be affected by an operator, such that the search process itself is a function of the relative slackness of the labour market summarised by the Phillips curve relationship modelled within...

Skin aging includes intrinsic aging, a universal and inevitable process attributable to the passage of the time alone; and photoaging, changes attributable to chronic sun exposure, which are neither universal nor inevitable. The major clinical features of aging skin include xerosis, laxity, wrinkles, slackness, and the occurrence of benign neoplasms such as seborrheic keratoses and cherry angio...

In process control, many automated applications with high degree of safety require the human operator’s permanent presence. The operators have to control the system’s evolution and to react to unexpected events. Graphical user interfaces inform the operators about the process evolution and assist them in their complex task of problem solving. Several researchers are interested in the improvemen...

A bisection of an n-vertex graph is a partition of its vertices into two sets S and T , each of size n/2. The bisection cost is the number of edges connecting the two sets. In directed graphs, the cost is the number of arcs going from S to T . Finding a minimum cost bisection is NP-hard for both undirected and directed graphs. For the undirected case, an approximation of ratio O(log n) is known...

The field of constrained nonlinear programming (NLP) has been principally challenging to various gradient based optimization techniques. The Sequential quadratic programming algorithm (SQP) that uses active set strategy in solving quadratic programming (QP) subproblems proves to be efficient in locating the points of local optima. However, its efficient determination of the optimal active set h...

Highly targeted spear phishing attacks are increasingly common, and have been implicated in many major security breeches. Email filtering systems are the first line of defense against such attacks. These filters are typically configured with uniform thresholds for deciding whether or not to allow a message to be delivered to a user. However, users have very significant differences in both their...

The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. This thesis presents a systematic approach to the design and analysis of BSP algorithms. We introduce an extension of the BSP model, called BSPRAM, which reconciles shared-memory style programming with e cient exploitation of data locality. The BSPRAM model can be optimally si...