We continue, and in a sense complete, our study the motion of a rod (line segment) in the plane in the presence of polygonal obstacles, under an optimality criterion based on minimizing the trace length of a fixed but arbitrary point (called the focus) on the rod. In an earlier paper, we showed that this problem is NP-hard when the focus is in the relative interior of the rod. Our proof did not...

The problem of asymptotically optimum watermark detection and embedding has been addressed in a recent paper by Merhav and Sabbag where the optimality criterion corresponds to the maximization of the false negative error exponent for a fixed false positive error exponent. In particular Merhav and Sabbag derive the optimum detection rule under the assumption that the detector relies on the secon...

In this paper we consider the problem of constructing T -optimal discriminating designs for Fourier regression models. We provide explicit solutions of the optimal design problem for discriminating between two Fourier regression models, which differ by at most three trigonometric functions. In general, the T -optimal discriminating design depends in a complicated way on the parameters of the la...

Determination of Cramer-Rao lower bound (CRLB) as an optimality criterion for the problem of localization in wireless sensor networks (WSNs) is a very important issue. Currently, CRLBs have been derived for line-of-sight (LOS) situation in WSNs. However, one of major problems for accurate localization in WSNs is non-line-of-sight (NLOS) propagation. This article proposes two CRLBs for WSNs loca...

Consider an undirected graph G = (V,E) with a set of nodes V and a set of weighted edges E. The weight of an edge e ∈ E is denoted by ce ≥ 0. The degree constrained minimum spanning tree (DCMST) problem consists in finding a minimum spanning tree of G subject to maximum degree constraints dv ∈ N on the number of edges connected to each node v ∈ V . We propose a Variable Neighborhood Search (VNS...

An h-layer drawing of a graph G is a planar drawing of G in which each vertex is placed on one of h parallel lines and each edge is drawn as a straight line between its end-vertices. In such a drawing, we say that an edge is proper if its endpoints lie on adjacent layers, flat if they lie on the same layer and long otherwise. Thus, a proper h-layer drawing contains only proper edges, a short h-...

We consider planning of freight train classification at hump yards using integer programming. The problem involves the formation of departing freight trains from arriving trains subject to scheduling and capacity constraints. To increase yard capacity, we allow the temporary storage of early freight cars on specific mixed-usage tracks. The problem has previously been modeled using a direct inte...