Consider the problem of computing the minimum-weight multicast route in an optical network with both nonsplitting and splitting nodes. This problem can be reduced to the minimum Hamiltonian path problem when all nodes are nonsplitting, and the Steiner minimum tree problem when all nodes are splitting. Therefore, the problem is NP-hard. Previously, the best known polynomial-time approximation ha...

We consider the minimum vertex cover problem in hypergraphs in which every hyperedge has size k (also known as minimum hitting set problem, or minimum set cover with element frequency k). Simple algorithms exist that provide k-approximations, and this is believed to be the best possible approximation achievable in polynomial time. We show how to exploit density and regularity properties of the ...

We introduce an interpolation process based on some of the zeros of the mth generalized Freud polynomial. Convergence results and error estimates are given. In particular we show that, in some important function spaces, the interpolating polynomial behaves like the best approximation. Moreover the stability and the convergence of some quadrature rules are proved.