# Combinatorial Dual Bounds on the Least Cost Influence Problem

André Vignatti,
Renato S. de Melo,
Flávio K. Miyazawa,
Matheus J. Ota

November, 2023

### Abstract

The Least Cost Influence Problem is a combinatorial optimization problem that appears in the context of social networks. The objective is to give incentives to individuals of a network, such that some information spreads to a desired fraction of the network at minimum cost. We introduce a problem-dependent algorithm in a branch-and-bound scheme to compute a dual bound for this problem. The idea is to exploit the connectivity properties of sub-graphs of the input graph associated with each node of the branch-and-bound tree and use it to increase each sub-problem’s lower bound. Our algorithm works well and finds a lower bound tighter than the LP-relaxation in linear time in the size of the graph. Computational experiments with synthetic graphs and real-world social networks show improvements in using our proposed bounds. The improvements are gains in running time or gap reduction for exact solutions to the problem.

Publication

In *Pesquisa Operacional 2023, Volume 43*