Improved Primal Simplex Algorithms for Shortest Path, Assignment and Minimum Cost Flow Problems : November, 1988 (Classic Reprint)

A practical look at faster network optimization methods for flow and path problems.

This work presents a new primal scaling pivot rule for the network simplex algorithm and shows how it improves worst‑case performance for the minimum cost flow problem, with specialized results for the assignment and shortest path problems. It blends theory with concrete bounds and practical implementation ideas.

The approach centers on scaling the pivot rule to maintain strong feasibility and to reduce the number of pivots. By embedding scaling into Dantzig’s rule, the method achieves competitive running times and clearer performance guarantees across key combinatorial problems. The discussion covers data structures, complexity, and how the technique translates to specific problem settings.

• Introduction of a scaling network simplex pivot rule for flow problems
• Specialized results for the assignment and shortest path problems
• Analyses of pivot counts and running times with practical implementation notes
• Discussion of data structures and feasibility concepts to support efficient pivots

Ideal for readers seeking a solid, implementable approach to network optimization and its common applications.