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.

The robust constant and its applications in random global search for unconstrained global optimization

Abstract: Robust analysis is important for designing and analyzing algorithms for global optimization. In this paper, we introduce a new concept, robust constant, to quantitatively characterize the robustness of measurable sets and functions. The new concept is consistent to the theoretical robustness presented in literatures. This paper shows that, from the respects of convergence theory and numerical computational cost, robust constant is valuable significantly for analyzing random global search methods for unconstrained global optimization.

Weighted thresholding homotopy method for sparsity constrained optimization

Abstract: We propose in this paper a novel weighted thresholding method for the sparsity-constrained optimization problem. By reformulating the problem equivalently as a mixed-integer programming, we investigate the Lagrange duality with respect to an $$l_1$$-norm constraint and show the strong duality property. Then we derive a weighted thresholding method for the inner Lagrangian problem, and analyze its convergence. In addition, we give an error bound of the solution under some assumptions. Further, based on the proposed method, we develop a homotopy algorithm with varying sparsity level and Lagrange multiplier, and prove that the algorithm converges to an L-stationary point of the primal problem under some conditions. Computational experiments show that the proposed algorithm is competitive with state-of-the-art methods for the sparsity-constrained optimization problem.

Nesterov’s Smoothing and Excessive Gap Methods for an Optimization Problem in VLSI Placement

Abstract: In this paper, we propose an algorithm for a nonsmooth convex optimization problem arising in very large-scale integrated circuit placement. The objective function is the sum of a large number of Half-Perimeter Wire Length (HPWL) functions and a strongly convex function. The algorithm is based on Nesterov’s smoothing and excessive gap techniques. The main advantage of the algorithm is that it can capture the HPWL information in the process of optimization, and every subproblem has an explicit solution in the process of optimization. The convergence rate of the algorithm is $$O(1/k^{2}),$$ where k is the iteration counter, which is optimal. We also present preliminary experiments on nine placement contest benchmarks. Numerical examples confirm the theoretical results.

Multispectral imaging for improved liquid classification in security sensor systems

Abstract: Multispectral imaging can be used as a multimodal source to increase prediction accuracy of many machine learning algorithms by introducing additional spectral bands in data samples. This paper introduces a newly curated Multispectral Liquid 12-band (MeL12) dataset, consisting of 12 classes: eleven liquids and an "empty container" class. Multispectral images in this dataset have been captured using the PCO Ultraviolet, Grasshopper3 12.3 MP Color USB3 Vision, Mil-Rugged-High Resolution Snapshot Short Wave Infrared 1280JS, FLIR Medium Wave Infrared A6750sc and FLIR Long Wave Infrared T650sc cameras. Each of the classes initially results in a 640 × 480 × 12 data cube, where the 12 × 1 vector for each spectral pixel spans the spectral bands observed using the above-mentioned cameras and seven add-on bandpass optical filters. The usefulness of multispectral imaging in classification of liquids is demonstrated through the use of a support vector machine on MeL12 for classification of the 12 classes. The reported results are both encouraging and point to the need for additional work to improve liquid classification of harmless and dangerous liquids in high-risk environments, such as airports, concert halls, and political arenas, using multispectral imaging.

Complex Placement Region Handling Based on Electrostatic System Modeling

Abstract: With the additional fence region constraints in modern circuit designs, the VLSI placement problem has become more complex and challenging. A placement solution without considering fence region constraints may cause many problems in the legalization stage and result in an inferior placement. In this paper, we present an effective placement region handling method based on the two-dimensional electrostatic system modeling. Under the fence region constrains, we first generate multiple density maps for assigning cells to their respective fence regions. Then, we further add proper fence filler nodes to each density map, which is able to squeeze fence cells to be placed closer. The placement performance is validated through experiments on ISPD 2015 benchmarks. Experimental results show that, compared with the state-of-the-art placer NTUplace4dr, our proposed method not only reduces the wirelength by 9.9% but also achieves 5x faster runtime.