We consider the problem of recovering an unknown $k$-factor, hidden in a weighted random graph. For $k=1$ this is planted matching problem, while $k=2$ case closely related to travelling salesman problem. The inference solved by exploiting information arising from use two different distributions for weights on edges inside and outside sub-graph. argue that, large size limit, phase transition ca...

In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center problem and the set cover problem, with uncertainty characterized by a probability distribution over set of points or elements to be covered. We consider these ...

This paper considers a generalization of the capacitated spanning tree, in which some of the nodes have capacity K, and the others have capacity k < K. We prove that the problem can be approximated within a constant factor, and present better approximations when k is 1 or 2.

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees that need to be constructed for different groups of users. In our model we allow a preprocessing phase, when some information of the input graph G = (V,E) is s...