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We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1 + by a piecewise-linear minimization problem over the same feasible set. Our main result is that when the feasible set is a polyhedron, the number of resulting pieces is polynomial in the input size of… (More)

- Thomas L. Magnantia, Dan Stratilab, Thomas L. Magnanti, Dan Stratila
- 2012

We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixed-charge counterpart of the problem. For many practical concave cost problems, the fixed-charge… (More)

In this paper we study the dynamic version of the nonlinear minimum-cost flow problem on networks. We consider the problem on dynamic networks with nonlinear cost functions on edges that depend on time and flow. Moreover, we assume that the demand function and capacities of edges also depend on time. To solve the problem we propose an algorithm, which is… (More)

We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1 + by a piecewise-linear minimization problem over the same feasible set. Our main result is that when the feasible set is a polyhedron, the number of resulting pieces is polynomial in the input size of… (More)

We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixed-charge counterpart of the problem. For many practical concave cost problems, the fixed-charge… (More)

- Dan Stratila, Colin de Verdière
- 2005

Loosely speaking, an embedding of a graph G in R r consists of an injective mapping ψ : V → R r , and a correspondence from each edge ij ∈ E to a simple curve in R r with endpoints ψ(i) and ψ(j). Here a curve can be taken to be the image of a continuous injective function φ : [0, 1] → R r. An embedding in S 2 is defined similarly. In a planar embedding… (More)

- Dan Stratila
- 2003

Based primarily on: Gil Kalai. A subexponential randomized simplex algorithm (extended abstract).

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