Page 15 - 第四届运筹青年论坛会议手册-0615

青年报告 | 第四届中国运筹青年论坛 13

Some New Results on Influence Maximization

in Social Networks

刘彬 中国海洋大学

The influence maximization problem, which asks for a small node set of maximum influence,

is a key algorithmic problem in social influence analysis, and has been extensively studied over the

past decade. It has wide applications to viral marketing, outbreak detection, rumor monitoring, etc.

Meanwhile, there are several related problems, such as the profit maximization problem, rumor

blocking problem, etc. In most of the known results, the submodularity of the influence function

under different propagating models plays a vital role for designing efficient and theoretical bounded

solutions. In this talk, I will show some new results obtained by our group.

Recent Progress on Spherical Designs and its Applications

周洋 山东师范大学

A spherical -design is a set of points on the unit sphere that are nodes of a quadrature rule with

positive equal weights that is exact for all spherical polynomials of degree ≤ . The existence of

spherical -designs with a constant number of points is only proved for some well-setting cases.

Moreover, how to choose a set of points from the set of interval enclosures to obtain a spherical -

2
design with ( + 1) points is not given. In this report we utilize a new concept named spherical -

design (0 ≤ ϵ ≤ 1) to study the perturbation property of spherical $t$-designs. We show that any
point set chosen from a small enough neighborhood of a spherical $t$-design is a spherical -

design. The approximation quality of this kind of perturbation when applied to numerical integration

and polynomial approximation on the sphere is also studied.