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Efficient Algorithms for Pseudoarboricity Computation in Large Static and Dynamic Graphs

Published: 30 August 2024 Publication History

Abstract

The arboricity a(G) of a graph G is defined as the minimum number of edge-disjoint forests that the edge set of G can be partitioned into. It is a fundamental metric and has been widely used in many graph analysis applications. However, computing a(G) is typically a challenging task. To address this, an easier-to-compute alternative called pseudoarboricity was proposed. Pseudoarboricity has been shown to be closely connected to many important measures in graphs, including the arboricity and the densest subgraph density ρ(G). Computing the exact pseudoarboricity can be achieved by employing a parametric max-flow algorithm, but it becomes computationally expensive for large graphs. Existing 2-approximation algorithms, while more efficient, often lack satisfactory approximation accuracy. To overcome these limitations, we propose two new approximation algorithms with theoretical guarantees to approximate the pseudoarboricity. We show that our approximation algorithms can significantly reduce the number of times the max-flow algorithm is invoked, greatly improving its efficiency for exact pseudoarboricity computation. In addition, we also study the pseudoarboricity maintenance problem in dynamic graphs. We propose two novel and efficient algorithms for maintaining the pseudoarboricity when the graph is updated by edge insertions or deletions. Furthermore, we develop two incremental pseudoarboricity maintenance algorithms specifically designed for insertion-only scenarios. We conduct extensive experiments on 195 real-world graphs, and the results demonstrate the high efficiency and scalability of the proposed algorithms in computing pseudoarboricity for both static and dynamic graphs.

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          cover image Proceedings of the VLDB Endowment
          Proceedings of the VLDB Endowment  Volume 17, Issue 11
          July 2024
          1039 pages
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          Published: 30 August 2024
          Published in PVLDB Volume 17, Issue 11

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