Center for Discrete Mathematics and Theoretical Computer Science

About: Center for Discrete Mathematics and Theoretical Computer Science is a facility organization based out in Piscataway, New Jersey, United States. It is known for research contribution in the topics: Local search (optimization) & Optimization problem. The organization has 140 authors who have published 175 publications receiving 2345 citations.

A Latent Source Model to Detect Multiple Spatial Clusters With Application in a Mobile Sensor Network for Surveillance of Nuclear Materials

Abstract: Potential nuclear attacks are among the most devastating terrorist attacks, with severe loss of human lives as well as damage to infrastructure. To deter such threats, it becomes increasingly vital to have sophisticated nuclear surveillance and detection systems deployed in major cities in the United States, such as New York City. In this article, we design a mobile sensor network and develop statistical algorithms and models to provide consistent and pervasive surveillance of nuclear materials in major cities. The network consists of a large number of vehicles on which nuclear sensors and Global Position System (GPS) tracking devices are installed. Real time sensor readings and GPS information are transmitted to and processed at a central surveillance center. Mathematical and statistical analyses are performed, in which we mimic a signal-generating process and develop a latent source modeling framework to detect multiple spatial clusters. A Monte Carlo expectation-maximization algorithm is developed to e...

Nonsmooth Optimization Method for VLSI Global Placement

Abstract: The common objective of very large-scale integration (VLSI) placement problem is to minimize the total wirelength, which is calculated by the total half-perimeter wirelength (HPWL). Since the HPWL is not differentiable, various differentiable wirelength approximation functions have been proposed in analytical placement methods. In this paper, we reformulate the HPWL as an $l_{1}$ -norm model of the wirelength function, which is exact but nonsmooth. Based on the $l_{1}$ -norm wirelength model and exact calculation of overlapping areas between cells and bins, a nonsmooth optimization model is proposed for the VLSI global placement problem, and a subgradient method is proposed for solving the nonsmooth optimization problem. Moreover, local convergence of the subgradient method is proved under some suitable conditions. In addition, two enhanced techniques, i.e., an adaptive parameter to control the step size and a cautious strategy for increasing the penalty parameter, are also used in the nonsmooth optimization method. In order to make the placement method scalable, a multilevel framework is adopted. In the clustering stage, the best choice clustering algorithm is modified according to the $l_{1}$ -norm wirelength model to cluster the cells, and the nonsmooth optimization method is recursively used in the declustering stage. Comparisons of experimental results on the International Symposium on Physical Design (ISPD) 2005 and 2006 benchmarks show that the global placement method is promising.

Lagrange Dual Method for Sparsity Constrained Optimization

Abstract: In this paper, we investigate the $l_{0}$ quasi-norm constrained optimization problem in the Lagrange dual framework and show that the strong duality property holds. Motivated by the property, we propose a Lagrange dual method for the sparsity constrained optimization problem. The method adopts the bisection search technique to maximize the Lagrange dual function. For each Lagrange multiplier, we adopt the iterative hard thresholding method to minimize the Lagrange function. We show that the proposed method converges to an $L$ -stationary point of the primal problem. Computational experiments and comparisons on a number of test instances (including random compressed sensing instances and random and real sparse logistic regression instances) demonstrate the effectiveness of the proposed method in generating sparse solution accurately.