Peter Recht

On maximal entries in the principal eigenvector of graphs

Abstract For an undirected, connected graph it is well known that an eigenvector belonging to the principal eigenvalue of G can be given such that all entries are positive. We ask whether this vector carries information on the structure of the graph and approach this question by investigating the values that can occur in its maximal entry.

On locally-Lipschitz quasi-differentiate functions in Banach-spaces

In this paper quasi-differentiable functions in the sense of V. F. Demyanov and A. N. Rubinov [1] are studied. For locally Lipschitz functions defined on finite dimensional Banach-spaces, a characterization of the quasi-differentiability is given, which is closely related to the Fe-differentiability.

Packing edge-disjoint cycles in graphs and the cyclomatic number

For a graph G let @m(G) denote the cyclomatic number and let @n(G) denote the maximum number of edge-disjoint cycles of G. We prove that for every k>=0 there is a finite set P(k) such that every 2-connected graph G for which @m(G)-@n(G)=k arises by applying a simple extension rule to a graph in P(k). Furthermore, we determine P(k) for k@?2 exactly.

Online Dial-A-Ride Problem with Time Windows: An Exact Algorithm Using Status Vectors

The Dial-A-Ride Problem (DARP) has often been used to organize transport of elderly and handicapped people, assuming that these people can book their transport in advance. But the DARP can also be used to organize usual passenger or goods transportation in real online scenarios with time window constraints. This paper presents an efficient exact algorithm with significantly reduced calculation times.

Identifying non-active restrictions in convex quadratic programming

Abstract. Convex quadratic programming (QP) is of reviving interest in the last few years, since in connection with interior point methods Sequential Quadratic Programming (SQP) has been assessed as a powerful algorithmic scheme for solving nonlinear constraint optimization problems.  In this paper we contribute to the investigation of detecting constraints that cannot be active at an optimal point of a QP-problem. It turns out that simple calculations performed at the beginning of (or even during) an optimization procedure allow early decisions on the deletion of such superfluous restrictions. For feasible point procedures or active set strategies such information are essential to shrink down the problem size and to speed up iterations. For practical applications the necessary computations only depend on data of the QP-problem. Comparing those quantities with (current) values of the objective function deliver conditions for the elimination of constraints.

Redundancies in Positive-Semidefinite Quadratic Programming

The question investigated is how to detect nonactive restrictions in positive-semidefinite quadratic programming. If the optimization problem satisfies some regularity conditions, we can use parametric optimization techniques for that analysis. It turns out that results obtained in Ref. 1, where only positive-definite matrices are considered, can be generalized to the semidefinite case. Simple calculations based exclusively on the problem data allow one to delete superfluous restrictions for this problem class during an optimization procedure.

Packing Euler graphs with traces

For a graph G = (V,E) and a vertex v ∈ V, let T(v) be a local trace at v, i.e. T(v) is an Eulerian subgraph of G such that every walkW(v), with start vertex v can be extended to an Eulerian tour in T(v). In general, local traces are not unique. We prove that if G is Eulerian every maximum edge-disjoint cycle packing Z* of G induces maximum local traces T(v) at v for every v ∈ V. In the opposite, if the total size

Unterstützung von verbundorientierten Sortimentsentscheidungen durch eine Sortimentserfolgsrechnung

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