Covering compact metric spaces greedily

A general greedy approach to construct coverings of compact metric spaces by metric balls is given and analyzed. The analysis is a continuous version of Chvatal's analysis of the greedy algorithm for the weighted set cover problem. The approach is demonstrated in an exemplary manner to construct efficient coverings of the n-dimensional sphere and n-dimensional Euclidean space to give short and transparent proofs of several best known bounds obtained from deterministic constructions in the literature on sphere coverings.Comment: (v2) 10 pages, minor revision, accepted in Acta Math. Hunga

A Codebook Generation Algorithm for Document Image Compression

Pattern-matching-based document-compression systems (e.g. for faxing) rely on finding a small set of patterns that can be used to represent all of the ink in the document. Finding an optimal set of patterns is NP-hard; previous compression schemes have resorted to heuristics. This paper describes an extension of the cross-entropy approach, used previously for measuring pattern similarity, to this problem. This approach reduces the problem to a k-medians problem, for which the paper gives a new algorithm with a provably good performance guarantee. In comparison to previous heuristics (First Fit, with and without generalized Lloyd's/k-means postprocessing steps), the new algorithm generates a better codebook, resulting in an overall improvement in compression performance of almost 17%

A heuristic algorithm for the multi-criteria set-covering problems

AbstractA simple greedy heuristic algorithm for the multi-criteria set-covering problem is presented. This result is a multi-criteria generalization of the results established previously by Chvatal

On combinatorial optimisation in analysis of protein-protein interaction and protein folding networks

Abstract: Protein-protein interaction networks and protein folding networks represent prominent research topics at the intersection of bioinformatics and network science. In this paper, we present a study of these networks from combinatorial optimisation point of view. Using a combination of classical heuristics and stochastic optimisation techniques, we were able to identify several interesting combinatorial properties of biological networks of the COSIN project. We obtained optimal or near-optimal solutions to maximum clique and chromatic number problems for these networks. We also explore patterns of both non-overlapping and overlapping cliques in these networks. Optimal or near-optimal solutions to partitioning of these networks into non-overlapping cliques and to maximum independent set problem were discovered. Maximal cliques are explored by enumerative techniques. Domination in these networks is briefly studied, too. Applications and extensions of our findings are discussed