Multilayer grid embeddings for VLSI

In this paper we propose two new multilayer grid models for VLSI layout, both of which take into account the number of contact cuts used. For the first model in which nodes “exist” only on one layer, we prove a tight area × (number of contact cuts) = Θ(n ²) tradeoff for embeddingn-node planar graphs of bounded degree in two layers. For the second model in which nodes “exist” simultaneously on all layers, we give a number of upper bounds on the area needed to embed groups using no contact cuts. We show that anyn-node graph of thickness 2 can be embedded on two layers inO(n ²) area. This bound is tight even if more layers and any number of contact cuts are allowed. We also show that planar graphs of bounded degree can be embedded on two layers inO(n ^3/2(logn)²) area. Some of our embedding algorithms have the additional property that they can respect prespecified grid placements of the nodes of the graph to be embedded. We give an algorithm for embeddingn-node graphs of thicknessk ink layers usingO(n ³) area, using no contact cuts, and respecting prespecified node placements. This area is asymptotically optimal for placement-respecting algorithms, even if more layers are allowed, as long as a fixed fraction of the edges do not use contact cuts. Our results use a new result on embedding graphs in a single-layer grid, namely an embedding ofn-node planar graphs such that each edge makes at most four turns, and all nodes are embedded on the same line.     

库里南钻石百年纪念——库啦南Ⅰ，Ⅱ的历史和宝石学分析

库里南原石发现于100年前，当时的大英帝国正处于最鼎盛时期，库里南的发现通过电报迅速传遍了世界，同时它的发现地——南非比勒陀利亚附近的新矿山——Premier矿也名声鹊起。     

Nonsmooth-optimization methods in problems of stochastic programming

Nonsmooth-optimization methods with space expansion are considered as applied to decomposition schemes realized in solving two-stage problems of stochastic programming in the SLP—IOR simulation systems. This work has been carried out with support from the Federal Foreign Administration and the National Scientific Fund of Switzerland within the framework of the program of scientific cooperation between states of Western Europe and newly independent states. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 33–47, September–October, 1999.     

Desorption kinetics for field-aged polycyclic aromatic hydrocarbons from sediments

This study considers desorption kinetics for 12 field-aged polycyclic aromatic hydrocarbons (PAHs) desorbing from size- and density-fractionated sediments collected from two locations in the New York/New Jersey Harbor Estuary. Desorption kinetics for PAHs with a log octanol-water partition coefficient greater than 6 were well-described by a one-domain diffusion model that assumes that PAHs are initially uniformly distributed throughout spherical sediment aggregates. PAH hydrophobicity and sediment specific surface area were the parameters most strongly correlated with the magnitude of the observed diffusivity for the one-domain model. For less hydrophobic PAHs, a two-domain desorption model was used also, and the results suggest that a substantial fraction of these field-aged PAHs desorb via a relatively fast macro-mesopore diffusion mechanism. The model-predicted fraction of PAHs in the fast-diffusion regime by compound and sediment was highly correlated with the measured percent PAH desorption in 24 h. The fast-domain diffusivity was 100 times greater than the slow-domain diffusivity, was correlated with both PAH properties and sediment physical and chemical properties, and could be estimated by readily obtainable physical and chemical parameters. In contrast, the slow-domain diffusivity was not significantly correlated with PAH properties. Our results suggest that macro-mesopore diffusion may control mass transport of less-hydrophobic PAHs in estuarine sediments.     

The rectilinear steiner arborescence problem

The Rectilinear Steiner Arborescence (RSA) problem is “Given a setN ofn nodes lying in the first quadrant of E², find the shortest directed tree rooted at the origin, containing all nodes inN, and composed solely of horizontal and vertical arcs oriented only from left to right or from bottom to top.” In this paper we investigate many fundamental properties of the RSA problem, propose anO(n logn)-time heuristic algorithm giving an RSA whose length has an upper bound of twice that of the minimum length RSA, and show that a polynomial-time algorithm that was earlier reported in the literature for this problem is incorrect.