Approximation Algorithms for Generalized MST and TSP in Grid Clusters

We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell is $1 \times 1$. In the MST version of the problem, the goal is to find a minimum tree that contains exactly one point from each non-empty grid cell (cluster). Similarly, in the TSP version of the problem, the goal is to find a minimum weight cycle containing one point from each non-empty grid cell. We give a $(1+4\sqrt{2}+\epsilon)$ and $(1.5+8\sqrt{2}+\epsilon)$-approximation algorithm for these two problems in the described setting, respectively. Our motivation is based on the problem posed in [7] for a constant approximation algorithm. The authors designed a PTAS for the more special case of the GMST where non-empty cells are connected end dense enough. However, their algorithm heavily relies on this connectivity restriction and is unpractical. Our results develop the topic further

Towards an universal memory based on self-organized quantum dots

A concept of a memory device based on self-organized quantum dots (QDs) is presented, which has the potential to fulfill the requirements of an universal memory. We demonstrate here a hole storage time of 1.6 s at room temperature in InAs/GaAs QDs with an additional Al0.9Ga0.1As barrier. This value is already three orders of magnitude longer than the typical DRAM refresh time. The connection between localization energy and storage time for different QD/matrix material combinations enables us to predict a retention time of more than 10 years in In(Ga)Sb/AlAs QDs, like in a Flash memory. Furthermore, we demonstrate a very fast write time below 20 ns for our memory concept in GaSb/GaAs QDs around 100 K. The write time is at the moment only limited by the parasitic cut off frequency of the RC low pass. Hence, an universal QD-based Flash memory-having a storage time in the order of years in combination with a fast write access time below 20 ns-seems feasible. (c) 2007 Elsevier B.V. All rights reserved