We present combinatorial interior point methods for the generalized minimum cost flow and the generalized circulation problems based on Wallacher and Zimmermann’s combinatorial interior point method for the minimum cost network flow problem. The algorithms have features of both a combinatorial algorithm and an interior point method. They work towards optimality by iteratively reducing the value...

Given a product design and a repair network for capital goods, a level of repair analysis determines for each component in the product (1) whether it should be discarded or repaired upon failure and (2) at which location in the repair network to do this. In this paper, we show how the problem can be modelled as a minimum cost flow problem with side constraints. Advantages are that (1) solving o...

We introduce a broad class of algorithms for finding a minimum cost flow in a capacitated network. The algorithms are of the primal-dual type. They maintain primat feasibility with respect to capacity constraints, while trying to satisfy the conservation of flow equation at each node by means of a wide variety of procedures based on flow augmentation, price adjustment, and ascent of a dual func...

We present a combinatorial method for the min-cost flow problem and prove that its expected running time is bounded by Õ(m3/2). This matches the best known bounds, which previously have only been achieved by numerical algorithms or for special cases. Our contribution contains three parts that might be interesting in their own right: (1) We provide a construction of an equivalent auxiliary netwo...

“The Price of Robustness” by Bertsimas and Sim [4] represented a breakthrough in the development of a tractable robust counterpart of Linear Programming Problems. However, the central modeling assumption that the deviation band of each uncertain parameter is single may be too limitative in practice: experience indeed suggests that the deviations distribute also internally to the single band, so...

The submodular flow problem is extended by considering a nonseparable cost function, which is assumed to enjoy a variant of the exchange property of the base polyhedron of a submodular system. Two optimality criteria are established, one in terms of potentials associated with vertices and the other in terms of negative cycles in an auxiliary graph. These are natural extensions of the well-known...

In this paper, we study inverse optimization problems defined as follows: Let S denote the set of feasible solutions of an optimization problem P, let c be a specified cost vector, and x0 be a given feasible solution. The solution x0 may or may not be an optimal solution of P with respect to the cost vector c. The inverse optimization problem is to perturb the cost vector c to d so that x0 is a...

We investigate the complexity and approximability of the budget-constrained minimum cost flow problem, which is an extension of the traditional minimum cost flow problem by a second kind of costs associated with each edge, whose total value in a feasible flow is constrained by a given budget B. This problem can, e.g., be seen as the application of the ε-constraint method to the bicriteria minim...

For a simple bipartite graph and an integer t ≥ 2, we consider the problem of finding a minimum-weight t-factor under the restriction that it contains no complete bipartite graph Kt,t as a subgraph. When t = 2, this problem amounts to the minimum-weight square-free 2-factor problem in a bipartite graph, which is NP-hard. We propose, however, a strongly polynomial algorithm for a certain case wh...

Comparing word contexts is a key component of many NLP tasks, but rarely is it used in conjunction with additional ontological knowledge. One problem is that the amount of overhead required can be high. In this paper, we provide a graphical method which easily combines an ontology with contextual information. We take advantage of the intrinsic graphical structure of an ontology for representing...