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- Thomas L. Magnanti, Dan Stratila
- IPCO
- 2004

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 + 2 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… (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 fixedcharge counterpart of the problem. For many practical concave cost problems, the fixed-charge counterpart… (More)

- Dmitrii Lozovanu, Dan Stratila
- Analysis and Optimization of Differential Systems
- 2002

In this paper we study the dynamic version of the nonlinear minimumcost 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)

Consider a separable concave minimization problem with nondecreasing costs over a general ground set X ⊆ R+. We show how to efficiently approximate this problem to a factor of 1+2 in optimal cost by a single piecewise linear minimization problem over X. The number of pieces is linear in 1/2 and polynomial in the logarithm of certain ground set parameters;… (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 + 2 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… (More)

- Michel X. Goemans, Dan Stratila, ‖f∆− f∆v
- 2006

This implies that f is an embedding into l2 with distortion O( √ log n). However, this does not work for weighted graphs, since diam(G) is no longer bounded by n. We next show how to proceed in the weighted case. Let each edge e have a weight w(e), and consider ∆ = 4, . . . , 2k. For each ∆, we introduce a graph G∆ obtained by contracting all edges with… (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 fixedcharge counterpart of the problem. For many practical concave cost problems, the fixed-charge counterpart… (More)

- Dan Stratila, Colin de Verdière
- 2005

Loosely speaking, an embedding of a graph G in Rr consists of an injective mapping ψ : V → Rr, and a correspondence from each edge ij ∈ E to a simple curve in Rr 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] → Rr. An embedding in S2 is defined similarly. In a planar embedding images of… (More)

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