Finding Subgraphs with Maximum Total Density and Limited

Finding Subgraphs with Maximum Total Density and Limited Overlap Ding Wentao

Definitions •

Greedy-based Approximation • NAIVE

Finding Densest Subgraph • A lower bound:

Finding Densest Subgraph •

Greedy-Based Approximation •

Finding Minimal Densest Subgraph •

Finding Minimal Densest Subgraph

Finding Minimal Densest Subgraph •

Finding Minimal Densest Subgraphs

Experiments • Environment • on a Linux server with Intel Xeon E 7 -4870 at 2. 40 GHz, while limiting the total amount of main memory available to 64 GB. Solve linear programs with the Gurobi Optimizer version 5. 6. 3. All algorithms are implemented in Java.

Experiments • Results of group 1

Experiments • Results of group 1

Experiments • Results of group 2

Reference • Charikar M. Greedy approximation algorithms for finding dense components in a graph[M]//Approximation Algorithms for Combinatorial Optimization. Springer Berlin Heidelberg, 2000: 84 -95. • Balalau O D, Bonchi F, Chan T H, et al. Finding subgraphs with maximum total density and limited overlap[C]//Proceedings of the Eighth ACM International Conference on Web Search and Data Mining. ACM, 2015: 379 -388.

Thanks for listening • Q&A