Stochastic optimization has established itself as a major method to handle uncertainty in various optimization problems by modeling the uncertainty by a probability distribution over possible realizations.Traditionally,the main focus in stochastic optimization has been various stochastic mathematical programming(such as linear programming,convex programming).In recent years,there has been a surge of interest in stochastic combinatorial optimization problems from the theoretical computer science community.In this article,we survey some of the recent results on various stochastic versions of classical combinatorial optimization problems.Since most problems in this domain are NP-hard(or#P-hard,or even PSPACE-hard),we focus on the results which provide polynomial time approximation algorithms with provable approximation guarantees.Our discussions are centered around a few representative problems,such as stochastic knapsack,stochastic matching,multi-armed bandit etc.We use these examples to introduce several popular stochastic models,such as the fixed-set model,2-stage stochastic optimization model,stochastic adaptive probing model etc,as well as some useful techniques for designing approximation algorithms for stochastic combinatorial optimization problems,including the linear programming relaxation approach,boosted sampling,content resolution schemes,Poisson approximation etc.We also provide some open research questions along the way.Our purpose is to provide readers a quick glimpse to the models,problems,and techniques in this area,and hopefully inspire new contributions.
Schrodinger＇s thought experiment to prepare a cat in a superposition of both alive and dead states reveals profound consequences of quantum mechanics and has attracted enormous interests. Here we propose a straight- forward method to create quantum superposition states of a living microorganism by putting a small cryopreserved bacterium on top of an electromechanical oscillator. Our proposal is based on recent developments that the center- of-mass oscillation of a 15-pro-diameter aluminum mem- brane has been cooled to its quantum ground state （Teufel et al. in Nature 475：359, 2011）, and entangled with a microwave field （Palomaki et al. in Science 342：710, 2013）. A microorganism with a mass much smaller than the mass of the electromechanical membrane will not signifi- cantly affect the quality factor of the membrane and can be cooled to the quantum ground state together with themembrane. Quantum superposition and teleportation of its center-of-mass motion state can be realized with the help of superconducting microwave circuits. More importantly, the internal states of a microorganism, such as the electron spin of a glycine radical, can be entangled with its center-of- mass motion and teleported to a remote microorganism. Our proposal can be realized with state-of-the-art tech- nologies. The proposed setup is a quantum-limited mag- netic resonance force microscope. Since internal states of an organism contain information, our proposal also pro- vides a scheme for teleporting information or memories between two remote organisms.
