ABSTRACT This article proposes an implicit enumeration approach to solve the maximum ratio ‐plex and the maximum ratio ‐defective clique problems. The approach is inspired by the classical Bron‐Kerbosch algorithm for enumerating all maximal cliques in a graph, which is extended to enumerating structures that are hereditary on induced subgraphs. Such structures include ‐plexes and ‐defective cliques, among many others. The performance of the proposed approach is compared with that of the methods based on mixed integer linear programming (MILP), binary search, and Newton's iteration through numerical experiments on randomly generated and real‐life network instances.

Cauchy Reed-Solomon (CRS) codes are a class of erasure-resilient codes which are widely applicable in modern data storage systems. Several existing works have considered making the coding process of the extended CRS codes more efficient. It has been found that this efficiency is highly dependent on the underlying Cauchy coding matrices, particularly, the density of the associated bitmatrices. In this work, we revisit the problem of optimizing the coding bitmatrices, and propose three approaches aiming to find the bitmatrices with the lowest density in this context, namely a mixed integer linear programming approach, a local optimal algorithm with heuristic perturbation, and a branch-and-bound algorithm. Experimental results show that the proposed approaches are able to find bitmatrices with significantly lower density than those found using existing techniques. Moreover, the local optimal algorithm with heuristic perturbation is surprisingly efficient in finding good solutions under constrained computation time.