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.

Necessary and sufficient conditions for hyperplane transversals

Abstract: We prove that a finite family ℬ={B 1,B 2, ...,B n } of connected compact sets in ℝ d has a hyperplane transversal if and only if for somek there exists a set of pointsP={p 1,p 2, ...,p n } (i.e., ak-dimensional labeling of the family) which spans ℝ k and everyk+2 sets of ℬ are met by ak-flat consistent with the order type ofP. This is a common generalization of theorems of Hadwiger, Katchalski, Goodman-Pollack and Wenger.

Mixed-cell-height legalization considering technology and region constraints

Abstract: Mixed-cell-height circuits have become popular in advanced technologies for better power, area, routability, and performance tradeoffs. With technology and region constraints imposed by modern circuit designs, the mixed-cell-height legalization problem has become even more challenging. Additionally, an ideal legalization method should minimize both the average and maximum cell movements to preserve the quality of a given placement as much as possible. In this article, we present an effective and efficient mixed-cell-height legalization algorithm to consider technology and region constraints while minimizing the average and maximum cell movements. We first present a fence region handling technique to unify the fence regions and the default region. To obtain a desired cell assignment, we then propose a movement-aware cell reassignment method by iteratively reassigning cells in locally dense areas to their desired rows. After cell reassignment, a technology-aware legalization is presented to remove cell overlaps while satisfying the technology constraints. Finally, we propose a technology-aware refinement to further reduce the average and maximum cell movements without increasing the technology constraints violations. Compared with the champion of the 2017 CAD Contest at ICCAD and the state-of-the-art work, experimental results based on the 2017 CAD Contest at ICCAD benchmarks show that our algorithm achieves the best average and maximum cell movements and significantly fewer technology constraint violations, in a comparable runtime. The experimental results based on the modified 2015 ISPD Contest benchmarks also demonstrate the effectiveness of our algorithm in minimizing the average and maximum cell movements, compared with state-of-the-art mixed-cell-height legalizers.

Two Fast Complex-Valued Algorithms for Solving Complex Quadratic Programming Problems

Abstract: In this paper, we propose two fast complex-valued optimization algorithms for solving complex quadratic programming problems: 1) with linear equality constraints and 2) with both an $ {l_{1}}$ -norm constraint and linear equality constraints. By using Brandwood’s analytic theory, we prove the convergence of the two proposed algorithms under mild assumptions. The two proposed algorithms significantly generalize the existing complex-valued optimization algorithms for solving complex quadratic programming problems with an $ {l_{1}}$ -norm constraint only and unconstrained complex quadratic programming problems, respectively. Numerical simulations are presented to show that the two proposed algorithms have a faster speed than conventional real-valued optimization algorithms.

Solving Nonlinear Optimization Problems of Real Functions in Complex Variables by Complex-Valued Iterative Methods.

Abstract: Much research has been devoted to complex-variable optimization problems due to their engineering applications. However, the complex-valued optimization method for solving complex-variable optimization problems is still an active research area. This paper proposes two efficient complex-valued optimization methods for solving constrained nonlinear optimization problems of real functions in complex variables, respectively. One solves the complex-valued nonlinear programming problem with linear equality constraints. Another solves the complex-valued nonlinear programming problem with both linear equality constraints and an -norm constraint. Theoretically, we prove the global convergence of the proposed two complex-valued optimization algorithms under mild conditions. The proposed two algorithms can solve the complex-valued optimization problem completely in the complex domain and significantly extend existing complex-valued optimization algorithms. Numerical results further show that the proposed two algorithms have a faster speed than several conventional real-valued optimization algorithms.