This paper presents a method of calculating an interval including a bifurcation point. Turning points, simple bifurcation points, symmetry breaking bifurcation points and hysteresis points are calculated with guaranteed accuracy by the extended systems for them and by the Krawczyk-based interval validation method. Taking several examples, the results of validation are also presented. key words:...

We consider one-dimensional and multi-dimensional vector covering with variable sized bins. In the one-dimensional case, we consider variable sized bin covering with bounded item sizes. For every finite set of bins B, and upper bound 1/m on the size of items for some integer m, we define a ratio r(B, m). We prove this is the best possible competitive ratio for the set of bins B and the paramete...

We consider the offline and online versions of a bin packing problem called bin packing with conflicts. Given a set of items V = {1, 2, . . . , n} with sizes s1, s2 . . . , sn ∈ [0, 1] and a conflict graph G = (V, E), the goal is to find a partition of the items into independent sets of G, where the total size of each independent set is at most one, so that the number of independent sets in the...

In this paper, we consider the Generalized Bin Covering problem: We are given m bin types, where each bin of type i has profit pi and demand di. Furthermore, there are n items, where item j has size sj . A bin of type i is covered if the set of items assigned to it has total size at least the demand di. In that case, the profit of pi is earned and the objective is to maximize the total profit. ...

We propose an approach using optimal quantization and smoothing to generate adaptive histograms for multi-class one dimensional data. The discretization of data is optimal in maximizing a quantizer performance measure, defined by a combination of average log likelihood, entropy and correct classification probability. The optimal partition is found by dynamic programming. The density of each bin...

This paper investigates a method of reconstructing images from energy-resolved CT data with negligible beam-hardening artifacts and improved contrast-to-nosie ratio (CNR) compared to conventional energy-weighting methods. Conceptually, the investigated method first reconstructs separate images from each energy bin. The final image is a linear combination of the energy-bin images, with the weigh...

In the bin packing problem we are given an instance consisting of a sequence of items with sizes between 0 and 1. The objective is to pack these items into the smallest possible number of bins of unit size. BestFit algorithm packs each item into the most full bin where it fits, possibly opening a new bin if the item cannot fit into any currently open bin. In early seventies it was shown that th...

We deal with developing a Decision Support System (DSS) to promote the ridesharing among both students and staff of a big organization. The DSS includes a set of functions that allow the management of the riders’ requests and drivers’ availability and embeds a novel two-phase optimization approach that helps in defining the optimal riders-drivers matching. The first phase consists o...