Lecture 2-1

Submodular Maximization

Weili Wu Ding-Zhu DuUniversity of Texas at Dallas

Outline• Kate Middleton effect• Max Submodular Function

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The trend effect that Kate, Duchess of Cambridge has on others, from cosmetic surgery for brides, to sales of coral-colored jeans.”

“Kate Middleton effect

Kate Middleton effect

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According to Newsweek, "The Kate Effect may be worth £1 billion to the UK fashion industry."

Tony DiMasso, L. K. Bennett’s US president, stated in 2012, "...when she does wear something, it always seems to go on a waiting list."

Hike in Sales of Special Products

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• Influential persons often have many friends.

• Kate is one of the persons that have many friends in this social network.

For more Kates, it’s not as easy as you might think!

How to Find Kate?

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•Given a digraph and k>0,

•Find k seeds (Kates) to maximize the number of influenced persons (in one step).

Domination Maximization

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Outline• Kate Middleton effect• Submodular Maximization

8

Max Coverage

Given a collection C of subsets of a set E, find a subcollection C’ of C, with |C’|<k, to maximize the number of elements covered by C’ .

Influence Maximization is a special case of Max Coverage.

Max Coverage

Given a collection C of subsets of a set E, find a subcollection C’ of C, with |C’|<k, to maximize the number of elements covered by C’ .

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Section 2.1-2.2

17

Independent System

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