Matroid

Operating system

Algorithm

Combinatorics

Discrete mathematics

Mathematical optimization

Graph

Mathematical analysis

Rounding

Approximation algorithm

Mathematics

Partition problem

Computer science

Partition (number theory)

Disjoint sets

Graph partition

Greedy algorithm

Discretization

Theoretical computer science

IEEE Transactions on Network Science and Engineering

Community partition is of great importance in social networks because of the rapid increasing network scale, data and applications. We consider the community partition problem under LT model in social networks, which is a combinatorial optimization problem that divides the social network to disjoint $m$ communities. Our goal is to maximize the sum of influence propagation through maximizing it within each community. As the influence propagation function of community partition problem is supermodular under LT model, we use the method of Lov{$\acute{a}$}sz Extension to relax the target influence function and transfer our goal to maximize the relaxed function over a matroid polytope. Next, we propose a continuous greedy algorithm using the properties of the relaxed function to solve our problem, which needs to be discretized in concrete implementation. Then, random rounding technique is used to convert the fractional solution to integer solution. We present a theoretical analysis with $1-1/e$ approximation ratio for the proposed algorithms. Extensive experiments are conducted to evaluate the performance of the proposed continuous greedy algorithms on real-world online social networks datasets and the results demonstrate that continuous community partition method can improve influence spread and accuracy of the community partition effectively.

Continuous Influence-Based Community Partition for Social Networks