In this paper we develop a new upper bound for the mean square estimation error of a parameter that takes values on a bounded interval. The bound is based on the discretization of the region into a finite number of points, and the determination of the estimate by a maximum likelihood procedure. It is assumed that inaccurate versions of the true spectra are utilized in the implementation of the ...

The linear discrepancy of a poset P , denoted ld(P ), is the minimum, over all linear extensions L, of the maximum distance in L between two elements incomparable in P . With r denoting the maximum vertex degree in the incomparability graph of P , we prove that ld(P ) ≤ ⌊(3r − 1)/2⌋ when P has width 2. Tanenbaum, Trenk, and Fishburn asked whether this upper bound holds for all posets. We give a...

A planar point set is in convex position precisely when it has a convex polygonization, that is, a polygonization with maximum interior angle measure at most π. We can thus talk about the convexity of a set of points in terms of the minimum, taken over all polygonizations, of the maximum interior angle. The main result presented here is a nontrivial combinatorial upper bound of this min-max val...

We investigate the enumerative geometry aspects of algorithmic line problems when the admissible bodies are balls or polytopes. For this purpose, we study the common tangent lines/transversals to k balls of arbitrary radii and 4− k lines in R3. In particular, we compute tight upper bounds for the maximum number of real common tangents/transversals in these cases. Our results extend the results ...

In 15], Keliher et al. present a new method for upper bounding the maximum average linear hull probability (MALHP) for SPNs, a value which is required to make claims about provable security against linear cryptanalysis. Application of this method to Rijndael (AES) yields an upper bound of UB = 2 ?75 when 7 or more rounds are approximated, corresponding to a lower bound on the data complexity of...

We consider the maximization version of the edge disjoint path problem (EDP). In undirected graphs and directed acyclic graphs, we obtain anO( √ n) upper bound on the approximation ratio where n is the number of nodes in the graph. We show this by establishing the upper bound on the integrality gap of the natural multicommodity flow based relaxation. Our upper bound matches to within a constant...

Abstract. Let G be a simple undirected connected graph on n vertices. Suppose that the vertices of G are labelled 1,2, . . . ,n. Let di be the degree of the vertex i. The Randić matrix of G , denoted by R, is the n× n matrix whose (i, j)−entry is 1 √ did j if the vertices i and j are adjacent and 0 otherwise. The normalized Laplacian matrix of G is L = I−R, where I is the n× n identity matrix. ...

In this paper a two-dimensional non-oriented guillotine bin packing problem is studied when items have different priorities. Our objective is to maximize the total profit which is total revenues minus costs of used bins and wasted area. A genetic algorithm is developed to solve this problem where a new coding scheme is introduced. To evaluate the performance of the proposed GA, first an upper b...