Optimization Problems and Algorithms from Computer Science

Combinatorial optimization The search for an optimal 18 configuration in terms of a cost function on a discrete 19 set of allowed configurations. 20 Ground state The configuration of a model for a physi21 cal system of many interacting degrees of freedom de22 scribed by a Hamiltonian or energy function that has 23 the lowest energy. Also dented as the global minimum 24 of the energy of the system. 25 Disordered system A physical system with frozen in or 26 quenched inhomogeneities, usually modeled by an en27 ergy function containing parameters that are random 28 numbers obeying in prescribed probability distribu29 tion. 30 Universal properties Properties that do not depend on 31 microscopic details of a physical system, like the criti32 cal exponents at a continuous phase transition or fractal 33 dimensions. 34 Network flows A function defined on the edges of a graph 35 that obeys mass balance constraints at each node. 36 A number of polynomial optimization problems rele37 vant for disordered systems can be formulated as net38 work flow models. 39