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An Incremental Algorithm for a Generalization of the ShortestPath Problem
, 1992
"... The grammar problem, a generalization of the singlesource shortestpath problem introduced by Knuth, is to compute the minimumcost derivation of a terminal string from each nonterminal of a given contextfree grammar, with the cost of a derivation being suitably defined. This problem also subsume ..."
Abstract

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The grammar problem, a generalization of the singlesource shortestpath problem introduced by Knuth, is to compute the minimumcost derivation of a terminal string from each nonterminal of a given contextfree grammar, with the cost of a derivation being suitably defined. This problem also subsumes the problem of finding optimal hyperpaths in directed hypergraphs (under varying optimization criteria) that has received attention recently. In this paper we present an incremental algorithm for a version of the grammar problem. As a special case of this algorithm we obtain an efficient incremental algorithm for the singlesource shortestpath problem with positive edge lengths. The aspect of our work that distinguishes it from other work on the dynamic shortestpath problem is its ability to handle "multiple heterogeneous modifications": between updates, the input graph is allowed to be restructured by an arbitrary mixture of edge insertions, edge deletions, and edgelength changes.
On the Computational Complexity of Dynamic Graph Problems
 THEORETICAL COMPUTER SCIENCE
, 1996
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Volume II Multicommodity Network Flow Optimization in Flexible Manufacturing Systems
, 1976
"... The problem of choosing an optimal mix of operating strategies in a flexible manufacturing system is solved by a network flow optimization approach. Mathematical methods which exploit the structure of the problem to generate manufacturing strategies are outlined. Numerical results show that the meth ..."
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The problem of choosing an optimal mix of operating strategies in a flexible manufacturing system is solved by a network flow optimization approach. Mathematical methods which exploit the structure of the problem to generate manufacturing strategies are outlined. Numerical results show that the method produces results which agree with intuition and simulation for two and fourworkstation systems.1ACKNOWLEDGMENTS Acknowledgements are due to several people who made this research possible. Thanks go to Professor Michael Athans for his comments, suggestions, and discussion. The contribution of the members of the Manufacturing Group at L.I.D.S., in particular John Ward for the CANQ results, G. SeccoSuardo and Konrad Hitz for discussion on the network of queues models and the scheduling problem, respectively, and Yehiam