Efficient Exact Minimum k-Core Search in Real-World Graphs

The k-core, which refers to the induced subgraph with a minimum degree of at least k, is widely used in cohesive subgraph discovery and has various applications. However, the k-core in real-world graphs tends to be extremely large, which hinders its effectiveness in practical applications. This challenge has motivated researchers to explore a variant of the k-core problem known as the minimum k-core search problem. This problem has been proven to be NP-Hard, and most of the existing studies naturally either deal with approximate solutions or suffer from inefficiency in practice. In this paper, we focus on designing efficient exact algorithms for the minimum k-core search problem. In particular, we develop an iterative-based framework that decomposes an instance of the minimum k-core search problem into a list of problem instances on another well-structured graph pattern. Based on this framework, we propose an iterative-based branch-and-bound algorithm, namely IBB, with additional pruning and reduction techniques. We show that, with a n-vertex graph, IBB runs in cⁿn^O(1) time for some c < 2, achieving better theoretical performance than the trivial bound of 2ⁿn^O(1). Finally, our experiments on real-world graphs demonstrate that IBB is up to three orders of magnitude faster than the state-of-the-art algorithms on real-world datasets.