In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present two facility location problems with stochastic demand and exponential servers, respectively inventory. We present a (1 + , 1)-reduction of the facility location problem with subadditive costs to a soft capacitated facility location problem, which i...

We determine the optimal income tax schedule when individuals have possibility of avoiding paying taxes. Considering a convex concealment cost function, we find that subset individuals, located in interior distribution, should be allowed to avoid taxes, provided marginal first euro is sufficiently small. This contrasts with results Grochulski who shows that, using subadditive all report their t...

In this note we prove an explicit formula for the lower semicontinuous envelope of some functionals defined on real polyhedral chains. More precisely, denoting by H : R → [0,∞) an even, subadditive, and lower semicontinuous function with H(0) = 0, and by ΦH the functional induced by H on polyhedral m-chains, namely

We survey a few concentration inequalities for submodular and fractionally subadditive functions of independent random variables, implied by the entropy method for self-bounding functions. The power of these concentration bounds is that they are dimension-free, in particular implying standard deviation O( √ E[f ]) rather than O( √ n) which can be obtained for any 1Lipschitz function of n variab...