Efficient Algorithms for Maximal k-Biplex Enumeration

TL;DR

This paper introduces iTraversal, an efficient algorithm for enumerating all maximal k-biplexes in bipartite graphs, significantly improving speed and scalability over previous methods by employing a reverse search framework with optimized techniques.

Contribution

The paper develops iTraversal, a novel algorithm that achieves polynomial delay and high efficiency for maximal k-biplex enumeration, overcoming limitations of existing approaches.

Findings

iTraversal is up to 10,000 times faster than previous algorithms.

The algorithm handles graphs with over one billion edges effectively.

It guarantees polynomial delay in enumeration.

Abstract

Mining maximal subgraphs with cohesive structures from a bipartite graph has been widely studied. One important cohesive structure on bipartite graphs is k-biplex, where each vertex on one side disconnects at most k vertices on the other side. In this paper, we study the maximal k-biplex enumeration problem which enumerates all maximal k-biplexes. Existing methods suffer from efficiency and/or scalability issues and have the time of waiting for the next output exponential w.r.t. the size of the input bipartite graph (i.e., an exponential delay). In this paper, we adopt a reverse search framework called bTraversal, which corresponds to a depth-first search (DFS) procedure on an implicit solution graph on top of all maximal k-biplexes. We then develop a series of techniques for improving and implementing this framework including (1) carefully selecting an initial solution to start DFS, (2) pruning the vast majority of links from the solution graph of bTraversal, and (3) implementing abstract procedures of the framework. The resulting algorithm is called iTraversal, which has its underlying solution graph significantly sparser than (around 0.1% of) that of bTraversal. Besides, iTraversal provides a guarantee of polynomial delay. Our experimental results on real and synthetic graphs, where the largest one contains more than one billion edges, show that our algorithm is up to four orders of magnitude faster than existing algorithms.