One important result in secret sharing is the Brickell-Davenport Theorem: every ideal perfect secret sharing scheme defines a matroid that is uniquely determined by the access structure. Even though a few attempts have been made, there is no satisfactory definition of ideal secret sharing scheme for the general case, in which non-perfect schemes are considered as well. Without providing another...

In this paper we propose a heuristic approach for the problem of packing equal rectangles within a convex region. The approach is based on an Iterated Local Search scheme (or, using a terminology employed for continuous problems, a Monotonic Basin Hopping), in which the key step is the perturbation move. Different perturbation moves, both combinatorial and continuous ones, are proposed and comp...

Michael Zillich University of Birmingham, [email protected] Abstract: The detection of closed convex contours in edge segmented images quickly leads to a large number of hypotheses. Typically two methods are used to limit the combinatorial explosion inherent in such perceptual grouping tasks: indexing and early thresholding of less salient hypotheses. We show that the adoption of an incremental...

We show that any family of sets uniformly definable in an ominimal structure has an extended compression scheme of size equal to the number of parameters in the defining formula. As a consequence, the combinatorial complexity (or density) of any definable family in a structure with a o-minimal theory is bounded by the number of parameters in the defining formula. ∗Partially supported by NSF gra...

Medial is an inference rule scheme that appears in various deductive systems based on deep inference. In this paper we investigate the properties of medial as rewriting rule independently from logic. We present a graph theoretical criterion for checking whether there exists a medial rewriting path between two formulas. Finally, we return to logic and apply our criterion for giving a combinatori...

The NumericalHilbert package for Macaulay2 includes algorithms for computing local dual spaces of polynomial ideals, and related local combinatorial data about its scheme structure. These techniques are numerically stable, and can be used with floating point arithmetic over the complex numbers. They provide a viable alternative in this setting to purely symbolic methods such as standard bases. ...

The problem considered is the estimation of the evolutionary history of a collection of organisms in terms of a phylogenetic tree using genetic algorithm. This paper presents a new chromosome representation scheme for individuals in the population. A new stack based fitness evaluation method has been proposed to handle the populations generated in genetic algorithms. The problem of phylogenetic...

This paper presents a new parametric learning scheme, namely, Reformulated Parametric Learning (RPL). Instead of learning the parameters directly by using the original model, this scheme reformulates the model into a simpler yet equivalent one, and all parameters are estimated on the reformulated model. While a set of simpler equivalent models can be obtained from deriving Equivalent Decomposit...

We discuss how a new pricing scheme can be integrated within a communication network. The pricing scheme is based on the availability of end-to-end communications, and is an alternative to congestion pricing, which is not applicable when communication capacity is higher than demand (as happens in most communication backbone networks). We also investigate how, based on this scheme, an optimizati...

In recent years, the size of combinatorial applications and the need to produce high-quality solutions quickly have increased steadily, providing significant challenges for optimization algorithms. This paper addresses this issue for large-scale vehicle routing problems with time windows, a class of very difficult optimization problems involving complex spatial and temporal dependencies. It pro...