In this paper we introduce the incremental assignment problem. In this problem, a new pair of vertices and their incident edges are added to a weighted bipartite graph whose maximum weighted matching is already known, and the maximum weighted matching of the extended graph is sought. We propose an O(|V |2) algorithm for the problem.

A variation of the channel assignment problem is naturally modeled by L(2, 1)-labelings of graphs. An L(2, 1)-labeling of a graph G is an assignment of labels from {0, 1, . . . , λ} to the vertices of G such that vertices at distance two get different labels and adjacent vertices get labels that are at least two apart and the λ-number λ(G) of G is the minimum value λ such that G admits an L(2, ...

There are n graduate students and n faculty members. Each student will be assigned a scholarship by the joint faculty. The socially optimal outcome is tbat the best studcnt should get the most prestigious scholarship, the second-best student should get the second most prcstigious scholarship, and so on. The socially optimal outcome is common knowledge among all faculty members. Each professor w...

The hypergraph assignment problem (HAP) is the generalization of assignments from directed graphs to directed hypergraphs. It serves, in particular, as a universal tool to model several train composition rules in vehicle rotation planning for long distance passenger railways. We prove that even for problems with a small hyperarc size and hypergraphs with a special partitioned structure the HAP ...

ii Ich versichere, dass ich diese Diplomarbeit selbständig verfasst und nur die angegebe-nen Quellen und Hilfsmittel verwendet habe.

There has been considerable recent interest in the dynamic vehicle routing problem, but the complexities of this problem class have generally restricted research to myopic models. In this paper, we address the simpler dynamic assignment problem, where a resource (container, vehicle or driver) can only serve one task at a time. We propose a very general class of dynamic assignment models, and pr...

This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems related to the QAP, e.g. the biquadra...

This paper proposed a state-of-the-art local search for solving Flexible Demand Assignment problem (FDA) which considers the balance between revenue and cost in demand assignment. Different than the published studies, our research splits the FDA problem into three core subproblems as operators for neighborhood construction. The three specified subproblems One Bin Repack, Two Bins Repack and Unp...

A branch and bound algorithm for finding the minimal cost symmetric assignment is discussed. The matching problem in graph theory and the Chinese postman puzzle are all special cases of the symmetric assignment problem, and hence this algorithm can be applied to solve them.

The Aircraft Assignment problem is the problem of assigning flights to aircraft in such a way that some operational constraints are satisfied, and possibly that some objective function is optimized. We propose an approach to aircraft assignment which captures all operational constraints, including minimum connection times, airport curfews, maintenance, and preassigned activities. It also allows...