Efficient implementations of minimum-cost flow algorithms

TL;DR

This paper introduces efficient implementations of minimum-cost flow algorithms, incorporating practical heuristics and a novel application of Goldberg's partial augment-relabel method, with performance comparisons showing superior efficiency over existing solvers.

Contribution

The paper presents new, highly optimized implementations of minimum-cost flow algorithms, including a novel use of Goldberg's partial augment-relabel method within the cost-scaling algorithm.

Findings

Cost-scaling and network simplex implementations outperform LEDA and MCF.

Cost-scaling implementation is competitive with CS2.

RelaxIV is slower overall but effective on specific instances.

Abstract

This paper presents efficient implementations of several algorithms for solving the minimum-cost network flow problem. Various practical heuristics and other important implementation aspects are also discussed. A novel result of this work is the application of Goldberg's recent partial augment-relabel method in the cost-scaling algorithm. The presented implementations are available as part of the LEMON open source C++ optimization library (\url{http://lemon.cs.elte.hu/}). The performance of these codes is compared to well-known and efficient minimum-cost flow solvers, namely CS2, RelaxIV, MCF, and the corresponding method of the LEDA library. According to thorough experimental analysis, the presented cost-scaling and network simplex implementations turned out to be more efficient than LEDA and MCF. Furthermore, the cost-scaling implementation is competitive with CS2. The RelaxIV algorithm is often much slower than the other codes, although it is quite efficient on particular problem instances.