Bläsius, Thomas; Friedrich, Tobias; Weyand, Christopher Efficiently Computing Maximum Flows in Scale-Free NetworksEuropean Symposium on Algorithms (ESA) 2021: 21:1–21:14
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.
Bläsius, Thomas; Fischbeck, Philipp; Gottesbüren, Lars; Hamann, Michael; Heuer, Tobias; Spinner, Jonas; Weyand, Christopher; Wilhelm, Marcus PACE Solver Description: The KaPoCE Exact Cluster Editing AlgorithmInternational Symposium on Parameterized and Exact Computation (IPEC) 2021: 27:1–27:3
The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the exact cluster editing algorithm of the KaPoCE framework (contains also a heuristic solver), submitted to the exact track of the 2021 PACE challenge.
Bläsius, Thomas; Fischbeck, Philipp; Gottesbüren, Lars; Hamann, Michael; Heuer, Tobias; Spinner, Jonas; Weyand, Christopher; Wilhelm, Marcus PACE Solver Description: KaPoCE: A Heuristic Cluster Editing AlgorithmInternational Symposium on Parameterized and Exact Computation (IPEC) 2021: 31:1–31:4
The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the heuristic cluster editing algorithm of the Karlsruhe and Potsdam Cluster Editing (KaPoCE) framework, submitted to the heuristic track of the 2021 PACE challenge.