Physical Sciences and Mathematics Commons^™

Design And Analysis Of Efficient Algorithms To Solve The Maximum Concurrent Flow Problem, Farhad Shahrokhi

Dissertations

The maximum concurrent flow (MCFP) is a generalized commodity flow problem, where every pair of entities can send and receive flow Ma85 , BM86 , MS86 . We develop efficient labeling algorithms to solve the MCFP. We explore the combinatorial structure of the MCFP and show that the problem of associating costs (distances) to the edges so as to maximize the minimum cost of routing the concurrent flow is the dual of the MCFP. This duality covers max-flow min-cut theorem as a special case. Applications in packet switched networks At81 and cluster analysis Ma86 are discussed.

Jacobi Moments In Applied Mathematics With Computer Applications, John A. Kapenga

Dissertations

This work provides solid asymptotic representations, sharp error bounds and stable recurrence methods (both three term and two dimensional) for the Jacobi moments. These moments are currently used in several areas of numerical analysis (numerical integration, integral equations and boundary value problems).

A powerful representation theorem, due to H. Gingold, which uses the Jacobi moments is extended and analyzed. Applications of this theorem to multi-turning point problems and several other areas are given.

For a number of important problems in mathematical physics it is not possible to prove that the currently employed methods of solution converge, or are valid in …

Generalized Connectivity In Graphs, Ortrud R. Oellermann

Dissertations

The connectivity of a graph G is the minimum number of vertices in G whose deletion produces a disconnected or trivial graph, while the edge-connectivity of G is the minimum number of edges having this property. In this dissertation several generalizations and variations of these two parameters are introduced and studied.

Chapter I is an overview to the history of connectivity and provides a background for the chapters that follow. In Chapter II major n-connected subgraphs are introduced. Through this concept, the connectivities (of subgraphs) that are most representative in a given graph are studied.

Chapter III is devoted to …