Combinatorial optimization problems are abundant in the telecommunications industry. In this paper, we present four real-world telecommunications applications where combinatorial optimization plays a major role. The first problem concerns the optimal location of modem pools for an internet service provider. The second problem deals with the optimal routing of permanent virtual circuits for a fr...

Protein engineering by combinatorial site-directed mutagenesis evaluates a portion of the sequence space near a target protein, seeking variants with improved properties (e.g., stability, activity, immunogenicity). In order to improve the hit-rate of beneficial variants in such mutagenesis libraries, we develop methods to select optimal positions and corresponding sets of the mutations that wil...

Combinatorial method/high throughput strategies, which have long been used in the pharmaceutical industry, have recently been applied to hydrogel optimization for tissue engineering applications. Although many combinatorial methods have been developed, few are suitable for use in tissue engineering hydrogel optimization. Currently, only three approaches (design of experiment, arrays and continu...

In "classical" optimization, all data of a problem instance are considered given. The standard theory and the usual algorithmic techniques apply to such cases only. Online optimization is different. Many decisions have to be made before all data are available. In addition, decisions once made cannot be changed. How should one act "best" in such an environment? In this paper we survey online pro...

T his is a survey designed for mathematical programming people who do not know molecular biology and want to learn the kinds of combinatorial optimization problems that arise. After a brief introduction to the biology, we present optimization models pertaining to sequencing, evolutionary explanations, structure prediction, and recognition. Additional biology is given in the context of the probl...

We introduce the convex combinatorial optimization problem, a far-reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications.

In this paper we extend and unify the results of [20] and [19]. As a consequence, the results of [20] are generalized from the framework of ideal polyhedra in H to that of singular Euclidean structures on surfaces, possibly with an infinite number of singularities (by contrast, the results of [20] can be viewed as applying to the case of non-singular structures on the disk, with a finite number...

This paper reports about research projects of the University of Paderborn in the eld of distributed combinatorial optimization. We give an introduction into combinatorial optimization and a brief deenition of some important applications. As a rst exact solution method we describe branch & bound and present the results of our work on its distributed implementation. Results of our distributed imp...

Proof: ⇐: Fix a strongly-connected orientation D. For any non-empty U ⊂ V , we may choose u ∈ U and v ∈ V \ U . Since D is strongly connected, there is a directed u-v path and a directed v-u path. Thus |δ D(U)| ≥ 1 and |δ − D(U)| ≥ 1, implying |δG(U)| ≥ 2. ⇒: Since G is 2-edge-connected, it has an ear decomposition. We proceed by induction on the number of ears. If G is a cycle then we may orie...

Now we turn our attention to the proof of Theorem 1. Proof of Theorem 1. Let x be an extreme solution for the polytope (∗). Suppose that M has a loop e. Since rM ({e}) = 0, it follows that x(e) = 0 and we are done. Therefore we may assume that M does not have any loops and thus the polytope (∗) is full dimensional1. Now suppose that x(e) ∈ (0, 1) for all elements e ∈ S. Let n denote the number ...