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...

Periodic global updates of dual variables have been shown to yield a substantial speed advantage in implementations of push-relabel algorithms for the maximum flow and minimum cost flow problems. In this paper, we show that in the context of the bipartite matching and assignment problems, global updates yield a theoretical improvement as well. For bipartite matching, a pushrelabel algorithm tha...

The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. Although some aspects generalize , surprising counterexamples are found. We speculate that the phenomena revealed may be of interest in both spin systems in condensed matter and in quantum gravity.

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...

Ravindra K. Ahuja and Dorit S. Hochbaum Abstract In this paper, we study capacitated dynamic lot sizing problems with or without backorders, under the assumption that production costs are linear, that is, there are no set up costs. These two dynamic lot sizing problems (with or without backorders) are minimum cost flow problems on an underlying network that possess a special structure. We show ...

We introduce the maximum integer skew-symmetric ow problem (MSFP) which generalizes both the maximum ow and maximum matching problems. We establish analogs of the classical ow decomposition, augmenting path, and max-ow min-cut theorems for skew-symmetric ows. These theoretical results are then used to develop an O(M(n; m) + nm) time algorithm for solving the MSFP, where M(n; m) is the time need...