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.

On the α-spectra of Uniform Hypergraphs and Its Associated Graphs

Abstract: For 0 ≤ α < 1 and a k-uniform hypergraph H, the tensor Aα(H) associated with H is defined as Aα(H) = αD(H) + (1 − α)A(H), where D(ℋ) and A(H) are the diagonal tensor of degrees and the adjacency tensor of H, respectively. The α-spectra of H is the set of all eigenvalues of Aα(H) and the α-spectral radius ρα(H) is the largest modulus of the elements in the spectrum of Aα(H). In this paper we define the line graph L(H) of a uniform hypergraph H and prove that $${\rho _\alpha}\left(H \right)\, \le {1 \over \kappa}{\rho _\alpha}\left({L\left(H \right)} \right) + 1 + \alpha \left({{\rm{\Delta}} - 1 - {{{\delta^*}} \over k}} \right)$$ , where Δ and δ* are the maximum degree of H and the minimum degree of L(H), respectively. We also generalize some results on α-spectra of Gk,s, which is obtained from G by blowing up each vertex into an s-set and each edge into a k-set where 1 ≤ s ≤ k/2.

Combining Clustered Adaptive Multistart and Discrete Dynamic Convexized Method for the Max-Cut Problem

Abstract: Given an undirected graph with edge weights, the max-cut problem is to find a partition of the vertices into two subsets, such that the sum of the weights of the edges crossing different subsets is maximized. Heuristics based on auxiliary function can obtain high-quality solutions of the max-cut problem, but suffer high solution cost when instances grow large. In this paper, we combine clustered adaptive multistart and discrete dynamic convexized method to obtain high-quality solutions in a reasonable time. Computational experiments on two sets of benchmark instances from the literature were performed. Numerical results and comparisons with some heuristics based on auxiliary function show that the proposed algorithm is much faster and can obtain better solutions. Comparisons with several state-of-the-science heuristics demonstrate that the proposed algorithm is competitive.

A network access control mechanism based on role and behavior

Abstract: Current Role-Based Access Control (RBAC) can't assign permissions dynamically and can't update access control policies automatically. In this paper we present a new network access control (NAC) mechanism based on role and behavior (RB-NAC) which enhances role-based access control by establishing clusters of behavior to limit permissions of user dynamically and incorporating an incremental-learning algorithm to update the policies without manual intervention. RB-NAC as an enhanced access control mechanism shows its efficient flexibility and scalability in access control.

Iteratively weighted thresholding homotopy method for the sparse solution of underdetermined linear equations

Abstract: Recently, iteratively reweighted methods have attracted much interest in compressed sensing, outperforming their unweighted counterparts in most cases. In these methods, decision variables and weights are optimized alternatingly, or decision variables are optimized under heuristically chosen weights. In this paper, we present a novel weighted $l_1$-norm minimization problem for the sparsest solution of underdetermined linear equations. We propose an iteratively weighted thresholding method for this problem, wherein decision variables and weights are optimized simultaneously. Furthermore, we prove that the iteration process will converge eventually. Using the homotopy technique, we enhance the performance of the iteratively weighted thresholding method. Finally, extensive computational experiments show that our method performs better in terms of both running time and recovery accuracy compared with some state-of-the-art methods.

An Effective Genetic Algorithm for VLSI Standard Cell Array Placement

Abstract: This paper presents a genetic algorithm for solving the problem of VLSI standard cell array placement with up to tens of thousands to millions of cells,and for obtaining high quality placement results in a reasonable running time.For producing high quality placement results,a new kind of crossover operator on nets and a new type of local search method for the 2-D placement problem are designed,and an innovative algorithm framework with three phases is proposed to coordinate the global search and the local search of this algorithm.For the purpose of enabling the algorithm to hundle large-scale problem,the ideas of crossover localization,and small size population are adopted to reduce time and space complexities of the genetic algorithm.Meanwhile,various strategies for maintaining population diversity are used to improve the evolution performance of a small size population.Experimental results on Peko suite3 and suite4benchmark circuits verify that the genetic algorithm with these strategies is efficient.