We consider the problem of \ffinding a set of k vertices of maximal total influence in a given undirected network, under the independent cascade (IC) model of influence spread. It is known that influence is submodular in the IC model, and hence a greedy algorithm achieves a (1 –\u00a01\/e) approximation to this problem; moreover, it is known to be NP-hard to achieve a better approximation factor in directed networks. We show that for undirected networks, this approximation barrier can be overcome: the greedy algorithm obtains an (1 –\u00a01\/e + c) approximation to the set of optimal influence, for some constant c > 0. Our proof proceeds via probabilistic analysis of bond percolation in arbitrary \ffinite networks. We also show that the influence maximization problems remains APX-hard in undirected networks.<\/p>\n","protected":false},"excerpt":{"rendered":"
We consider the problem of \ffinding a set of k vertices of maximal total influence in a given undirected network, under the independent cascade (IC) model of influence spread. It is known that influence is submodular in the IC model, and hence a greedy algorithm achieves a (1 –\u00a01\/e) approximation to this problem; moreover, it […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13561,13546],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-319631","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-research-area-computational-sciences-mathematics","msr-locale-en_us"],"msr_publishername":"","msr_edition":"Symposium on Discrete 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