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.

Asymmetric colouring of locally compact permutation groups

Abstract: Let $G \leq \mathrm{Sym} (X)$ for a countable set $X$. Call a colouring of $X$ asymmetric, if the identity is the only element of $G$ which preserves all colours. The motion (also called minimal degree) of $G$ is the minimal number of elements moved by an element $g \in G \setminus\{\mathrm{id}\}$. We show that every locally compact, closed permutation group with infinite motion admits an asymmetric $2$-colouring. This generalises a recent result by Babai and confirms a conjecture by Imrich, Smith, Tucker, and Watkins from 2015.

A note on classes of subgraphs of locally finite graphs

Abstract: We investigate the question how `small' a graph can be, if it contains all members of a given class of locally finite graphs as subgraphs or induced subgraphs. More precisely, we give necessary and sufficient conditions for the existence of a connected, locally finite graph $H$ containing all elements of a graph class $\mathcal G$. These conditions imply that such a graph $H$ exists for the class $\mathcal G_d$ consisting of all graphs with maximum degree $

Sparse Group Feature Selection by Weighted Thresholding Homotopy Method

Abstract: In this paper, we investigate the sparse group feature selection problem, in which covariates posses a grouping structure sparsity at the level of both features and groups simultaneously. We reformulate the feature sparsity constraint as an equivalent weighted $l_1$ -norm constraint in the sparse group optimization problem. To solve the reformulated problem, we first propose a weighted thresholding method based on a dynamic programming algorithm. Then we improve the method to a weighted thresholding homotopy algorithm using homotopy technique. We prove that the algorithm converges to an $L$ -stationary point of the original problem. Computational experiments on synthetic data show that the proposed algorithm is competitive with some state-of-the-art algorithms.

A memetic algorithm for the max-cut problem

Abstract: Given an undirected graph G = V, E with a set V of vertices, and a set E of edges with weights, the max-cut problem consists of partitioning all vertices into two independent sets such that the sum of the weights of the edges between different sets is maximised. The max-cut problem is an NP-hard problem. An efficient memetic algorithm is proposed in this paper for the problem. The proposed memetic algorithm uses a local search procedure and a new crossover operator based on the encoding characteristic of the max-cut problem to generate new offsprings. Then the algorithm uses a function, which takes into account both the solution quality and the diversity of population, to control the population updating. Experiments were performed on three sets of benchmark instances of size up to 10,000 vertices. Experiment results and comparisons demonstrate the effectiveness of the proposed algorithm in both solution quality and computational time.