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.

Homotopy Methods Based on $l_{0}$ -Norm for Compressed Sensing

Abstract: This paper proposes two homotopy methods for solving the compressed sensing (CS) problem, which combine the homotopy technique with the iterative hard thresholding (IHT) method. The homotopy methods overcome the difficulty of the IHT method on the choice of the regularization parameter value, by tracing solutions of the regularized problem along a homotopy path. We prove that any accumulation point of the sequences generated by the proposed homotopy methods is a feasible solution of the problem. We also show an upper bound on the sparsity level for each solution of the proposed methods. Moreover, to improve the solution quality, we modify the two methods into the corresponding heuristic algorithms. Computational experiments demonstrate effectiveness of the two heuristic algorithms, in accurately and efficiently generating sparse solutions of the CS problem, whether the observation is noisy or not.

Simple algorithms for perfect phylogeny and triangulating colored graphs

Abstract: This paper presents an O((r–n/m)mrnm) algorithm for determining whether a set of n species has a perfect phylogeny, where m is the number of characters used to describe a species and r is the maximum number of states that a character can be in. The perfect phylogeny algorithm leads to an O((2e/k)ke2k) algorithm for triangulating a k-colored graph having e edges.

Analytic connectivity of k-uniform hypergraphs

Abstract: In this paper, we study the analytic connectivity of a k-uniform hypergraph H, denoted by . In addition to computing the analytic connectivity of a complete k-graph, we present several bounds on analytic connectivity that relate it with other graph invariants, such as degree, vertex connectivity, diameter and isoperimetric number.