KIT | KIT-Bibliothek | Impressum | Datenschutz

Efficiently computing maximum flows in scale-free networks

Bläsius, Thomas ORCID iD icon; Friedrich, Tobias; Weyand, Christopher


We study the maximum-flow/minimum-cut problem on scale-free networks, i.e., graphs whose degree distribution follows a power-law. We propose a simple algorithm that capitalizes on the fact that often only a small fraction of such a network is relevant for the flow. At its core, our algorithm augments Dinitz’s algorithm with a balanced bidirectional search. Our experiments on a scale-free random network model indicate sublinear run time. On scale-free real-world networks, we outperform the commonly used highest-label Push-Relabel implementation by up to two orders of magnitude. Compared to Dinitz’s original algorithm, our modifications reduce the search space, e.g., by a factor of 275 on an autonomous systems graph.
Beyond these good run times, our algorithm has an additional advantage compared to Push-Relabel. The latter computes a preflow, which makes the extraction of a minimum cut potentially more difficult. This is relevant, for example, for the computation of Gomory-Hu trees. On a social network with 70000 nodes, our algorithm computes the Gomory-Hu tree in 3 seconds compared to 12 minutes when using Push-Relabel.

Zugehörige Institution(en) am KIT Institut für Theoretische Informatik (ITI)
Publikationstyp Forschungsbericht/Preprint
Publikationsdatum 21.09.2020
Sprache Englisch
Identifikator KITopen-ID: 1000138421
Nachgewiesen in arXiv
Relationen in KITopen
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page