Density Guarantee on Finding Multiple Subgraphs and Subtensors

Dense subregion (subgraph & subtensor) detection is a well-studied area, with wide range of applications, and numerous efficient approaches algorithms have been proposed. Approximation are commonly used for detecting dense subregions due to the complexity exact methods. Existing generally subtensor subgraph detection, can perform well in many applications. However, most existing works utilize state-or-the-art greedy 2-approximation algorithm capably provide solutions loose theoretical density guarantee. The main drawback these that they estimate only one subtensor, or subgraph, at time, low guarantee on its density. While some methods can, other hand, multiple subtensors, give respect input tensor first estimated subsensor only. We address drawbacks by providing both practical solution estimating subtensors data giving higher lower bound In particular, we prove lower-bound subtensors. also propose novel approach show there greater than state-of-the-art algorithms. evaluate our extensive experiments several real-world datasets, which demonstrates efficiency feasibility.