The paper is concerned with the problem of binary classification of data records, given an already classified training set of records. Among the various approaches to the problem, the methodology of the logical analysis of data (LAD) is considered. Such approach is based on discrete mathematics, with special emphasis on Boolean functions. With respect to the standard LAD procedure, enhancements...

A clutter (V;E) packs if the smallest number of vertices needed to intersect all the edges (i.e. a transversal) is equal to the maximum number of pairwise disjoint edges (i.e. a matching). This terminology is due to Seymour 1977. A clutter is minimally nonpacking if it does not pack but all its minors pack. A 0,1 matrix is minimally nonpacking if it is the edge-vertex incidence matrix of a mini...

Inspired by problems in data center scheduling, we study the submodularity of certain scheduling problems as a function of the set of machine capacities and the corresponding implications. In particular, we • give a short proof that, as a function of the excess vector, maximum generalized flow is submodular and minimum cost generalized flow is supermodular; • extend Wolsey’s approximation guara...

In this paper we establish some bounds on the complexity of disjunctive normal forms of boolean function from narrow subclasses (e.g. functions takes value 0 in a limited number of points). The bounds are obtained by reduction the initial problem to a simple set covering problem. The nature of the complexity bounds provided is tightly connected with Shannon effect and semi-effect for this classes.

We study simultaneous learning and covering problems: submodular set cover problems that depend on the solution to an active (query) learning problem. The goal is to jointly minimize the cost of both learning and covering. We extend recent work in this setting to allow for a limited amount of adversarial noise. Certain noisy query learning problems are a special case of our problem. Crucial to ...