Some Recent Advances in Network Flows

Ravindra K. Ahuja, Thomas L. Magnanti, James B. Orlin
1991 SIAM Review  
The literature on network flow problems is extensive, and over the past 40 years researchers have made continuous improvements to algorithms for solving several classes of problems. However, the surge of acti ty concerning the algorithmic aspects of network flow problems over the past few years has been particularly striking. Several tecnniques nave oven to De very successIul in permitting researchers to make these recent contributions: (i) scaling of the problem data; (ii) improved analysis of
more » ... algorithms, especially amortized worstcase performance and the use of potential functions; and (iii) enhanced data structures. This survey illustrates some of these techniques and their usefulness in developing faster network flow algorithms. The discussion focuses on the design of faster algorithms from the worst-case perspective, and is limited to the following fundamental problems: the shortest path problem, the maximum flow problem, and the minimum cost flow problem. Several representative algorithms from each problem class are considered, including the radix heap algorithm for the shortest path problem, preflow push algorithms for the maximum flow problem, and the pseudoflow push algorithms for the minimum cost flow problem. Key words. network flows, network algorithms, network optimization, shortest path problem, maximum flow problem, minimum-cost flow problem AMS(MOS) subject classifications. 90B I0, 90C35, 9002 *
doi:10.1137/1033048 fatcat:cmjqcdhw6rhtti4slnnzwb4lyy