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An Algorithmic Characterization of Antimatroids
In an article entitled "Optimal sequencing of a single machine subject to precedence constraints," E.L. Lawler presented a now classical minmax result for job scheduling. In essence, Lawler's proof demonstrated that the properties of partially ordered sets were sufficient to solve the posed scheduling problem. These properties are, in fact, common to a more general class of combinatorial structures known as antimatroids, which have recently received considerable attention in the literature. It is demonstrated that the properties of antimatroids are not only sufficient but necessary to solve the scheduling problem posed by Lawler, thus yielding an algorithmic characterization of antimatroids. Examples of problems solvable by the general result are provided....
A Combinatorial Abstraction of One Shortest Path Problem and Its Relationship to Greedoids
A natural generalization of the shortest path problem to arbitrary set systems is presented that captures a number of interesting problems, including the usual graph-theoretic shortest path problem and the problem of finding ...
The Lagrangian as a Primal Cutting Plane Method for Linear Integer Programming Problems
Lagrangian relaxation and more recently cutting plane techniques have both proven to be powerful methods in the solution of integer problems. This paper explores the relationship between these techniques by interpreting ...