The VPN problems with concave costs

Only recently Goyal, Olver and Shepherd (Proc. STOC, 2008) proved that the symmetric Virtual Private Network Design (sVPN) problem has the tree routing property, namely, that there always exists an optimal solution to the problem whose support is a tree. Combining this with previous results by Fingerhut, Suri and Turner (J. Alg., 1997) and Gupta, Kleinberg, Kumar, Rastogi and Yener (Proc. STOC, 2001), sVPN can be solved in polynomial time. In this paper we investigate an APX-hard generalization of sVPN, where the contribution of each edge to the total cost is proportional to some non-negative, concave and non-decreasing function of the capacity reservation. We show that the tree routing property extends to the new problem, and give a constant-factor approximation algorithm for it. We also show that the undirected uncapacitated single-source minimum concave-cost flow problem has the tree routing property when the cost function has some property of symmetry

New experimental limits on the alpha decays of lead isotopes

For the first time a PbWO4 crystal was grown using ancient Roman lead and it was run as a cryogenic detector. Thanks to the simultaneous and independent read-out of heat and scintillation light, the detector was able to discriminate beta/gamma interactions with respect to alpha particles down to low energies. New more stringent limits on the alpha decays of the lead isotopes are presented. In particular a limit of T_{1/2} > 1.4*10^20 y at a 90% C.L. was evaluated for the alpha decay of 204Pb to 200Hg