Many real-world networks can be modeled as graphs, where identifying dense subgraphs is a fundamental task in graph mining. In this paper, we extend the densest subgraph problem, by seeking multiple disjoint dense subgraphs rather than a single solution. More formally, given a graph and an input parameter k, our goal is to find k disjoint subgraphs maximizing the minimum induced density of the k subgraphs. We prove that this problem is NP-hard even for k=2 . To tackle this, we present an exact algorithm based on mixed integer programming and propose 3 quadratic-time heuristics using dynamic programming. To ensure scalability for large-scale datasets, we introduce linear-time variants of these heuristics by limiting the sizes of the subgraphs. Our extensive experimental study compares these approaches against two baseline greedy heuristics. The results demonstrate that our algorithms accurately recover ground truth in synthetic datasets and produce good solutions in real-world datasets when compared to the baselines.
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