Flow Is Best, Fast and Scalable: The Incremental Parametric Cut for Maximum Density and Other Ratio Subgraph Problems

Dorit Hochbaum

2024

Abstract

The maximum density subgraph, or densest subgraph, problem has numerous applications in analyzing graph and community structures in social networks, DNA networks and financial networks. The densest subgraph problem has been the subject of study since the early 80s and polynomial time flow-based algorithms are known, yet research in the last couple of decades has been focused on developing heuristic methods for solving the problem claiming that flow computations are computationally prohibitive. We introduce here a new polynomial time algorithm, the incremental parametric cut algorithm (IPC) that solves the maximum density subgraph problem and many other max or min ratio problems in the complexity of a single minimum-cut. A characterization of all these efficiently solvable ratio problems is given here as problems with monotone integer programming formulations. IPC is much more efficient than the parametric cut algorithm since instead of generating all breakpoints it explores only a tiny fraction of those breakpoints. Compared to the heuristic methods, IPC not only guarantees optimality, but also runs orders of magnitude faster than the heuristic methods, as shown in an accompanying experimental study.

Paper Citation

in Harvard Style

Hochbaum D. (2024). Flow Is Best, Fast and Scalable: The Incremental Parametric Cut for Maximum Density and Other Ratio Subgraph Problems. In Proceedings of the 16th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1: KDIR; ISBN 978-989-758-716-0, SciTePress, pages 275-282. DOI: 10.5220/0012917300003838

in Bibtex Style

@conference{kdir24,
author={Dorit Hochbaum},
title={Flow Is Best, Fast and Scalable: The Incremental Parametric Cut for Maximum Density and Other Ratio Subgraph Problems},
booktitle={Proceedings of the 16th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1: KDIR},
year={2024},
pages={275-282},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012917300003838},
isbn={978-989-758-716-0},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1: KDIR
TI - Flow Is Best, Fast and Scalable: The Incremental Parametric Cut for Maximum Density and Other Ratio Subgraph Problems
SN - 978-989-758-716-0
AU - Hochbaum D.
PY - 2024
SP - 275
EP - 282
DO - 10.5220/0012917300003838
PB - SciTePress