James B. Orlin

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In this paper, we present a new strongly polynomial time algorithm for the minimum cost flow problem, based on a refinement of the Edmonds-Karp scaling technique. Our algorithm solves the uncapacitated minimum cost flow problem as a sequence of O(n log n) shortest path problems on networks with n nodes and m arcs and runs in O(n log n (m + n log n)) time.(More)
Many optimization problems of practical interest are computationally intractable. Therefore, a practical approach for solving such problems is to employ heuristic (approximation) algorithms that can find nearly optimal solutions within a reasonable amount of computation time. An improvement algorithm generally starts with a feasible solution and iteratively(More)
Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the <italic>radix heap</italic>, is proposed for use in this algorithm. On a network with <italic>n</italic> vertices, <italic>m</italic> edges, and nonnegative integer arc costs bounded by <italic>C</italic>, a one-level form of radix heap gives a(More)
We use Fibonacci heaps to improve a parametric shortest path algorithm of Karp and Orlin, and we combine our algorithm and the method of Schneider and Schneider’s minimum-balance algorithm to obtain a faster minimum-balance algorithm. For a graph with n vertices and m edges, our parametric shortest path algorithm and our minimum-balance algorithm both run(More)
The capacitated miinimum spanning tree (CMST) problem is to find a minimum cost spanning tree with an additional cardinality constraint on the sizes of the subtrees incident to a given root node. The CMST problem is an NP-complete problem, and existing exact algorithms can solve only small size problems. Currently, the best available heuristic procedures(More)
In this paper we suggest new scaling algorithms for the assignment and minimum mean cycle problems. Our assignment algorithm is based on applying scaling to a hybrid version of the recent auction algorithm of Bertsekas and the successive shortest path algorithm. The algorithm proceeds by relaxing the optimality conditions, and the amount of relaxation is(More)
The Quadratic Assignment Problem (QAP) is one of the classical combinatorial optimization problems and is known for its diverse applications. In this paper, we suggest a genetic algorithm for the QAP and report its computational behavior. The genetic algorithm incorporates many greedy principles in its design and, hence, we refer to it as a greedy genetic(More)