A Note on: `Algorithms for Connected Set Cover Problem and Fault-Tolerant Connected Set Cover Problem'

A flaw in the greedy approximation algorithm proposed by Zhang et al. for minimum connected set cover problem is corrected, and a stronger result on the approximation ratio of the modified greedy algorithm is established. The results are now consistent with the existing results on connected dominating set problem which is a special case of the minimum connected set cover problem.Comment: 6 pages, 1 figure, submitted to Theoretical Computer Scienc

Scalar resonance at 750 GeV as composite of heavy vector-like fermions

We study a model of scalars which includes both the SM Higgs and a scalar singlet as composites of heavy vector-like fermions. The vector-like fermions are bounded by the super-strong four-fermion interactions. The scalar singlet decays to SM vector bosons through loop of heavy vector-like fermions. We show that the surprisingly large production cross section of di-photon events at 750 GeV resonance and the odd decay properties can all be explained. This model serves as a good model for both SM Higgs and a scalar resonance at 750 GeV.Comment: 12 pages, no figure, references updated, version for publicatio