In this thesis, we study three problems related to various algorithmic and game-theoretic aspects of scheduling. First, we apply ideas from cooperative game theory to study situations in which a set of agents faces supermodular costs. These situations appear in a variety of scheduling contexts, as well as in some settings related to facility location and network design. Although cooperation is ...

Given a graph H = (V, F ) with edge weights {we : e ∈ F}, the weighted degree of a node v in H is ∑ {wvu : vu ∈ F}. We give bicriteria approximation algorithms for problems that seek to find a minimum cost directed graph that satisfies both intersecting supermodular connectivity requirements and weighted degree constraints. The input to such problems is a directed graph G = (V,E) with edge-cost...

The theories of supermodular optimization and games provide a framework for the analysis of systems marked by complementarity. We summarize the principal results of these theories and indicate their usefulness by applying them to study the shift to 'modern manufacturing'. We also use them to analyze the characteristic features of the Lincoln Electric Company's strategy and structure.

For the Erlang loss system with s servers and offered load a, we show that: (i) the load carried by the last server is strictly increasing in a; (ii) the carried load of the whole system is strictly supermodular on {(s, a)|s = 0, 1, . . . and a > 0}.

For a calculation of divergent fermion string amplitudes a regularization procedure invariant under the supermodular group is constructed. By this procedure superstring amplitudes of an arbitrary genus are calculated using both partition functions and superfield vacuum correlators computed early. A finiteness of superstring amplitudes and related topics are discussed. E-mail address: danilov@th...

We consider the scheduling problem of minimizing a weighted sum of completion times under release dates. We present a relaxation which is a supermodular polyhedron. We show that this relaxation is precisely the projection of a time-indexed relaxation introduced by Dyer and Wolsey.

We prove the convexity and compactness of the closure of the lower partition range of an Rn-valued, nonatomic, supermodular capacity, employing a useful relationship between convex games and their Choquet integrals. The main result is applied to fair division problems, and the existence of Pareto optimal α-fair partitions is demonstrated for the case of nonadditive measures.

We consider the problem of selecting labels in vertices of the graph in order to maximize sum of weights, assigned to pairs of labels ( (max,+) problem, MAP MRF, minimization of Gibbs energy). We construct upper bounds on the goal function as sum of two auxiliary superand submodular problems. The tightest possible bound of this type can be found by solving a special case of LP. It's solution al...