scalable influence maximization for prevalent viral marketing in...

Scalable Influence Maximization for Prevalent Viral Marketing in Large-

Scale Social Network

Wei Chen*, Chi Wang$, and Yajun Wang**Microsoft Research Asia, $UIUC

Problem Definition-I

• Influence maximization, defined by Kempe, Kleinberg, and Tardos (2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models.

• Proven to be NP-hard

Problem Definition-II

• Given– Graph G(v,e)– Threshold k– Information Cascade model

• Find– k nodes in G (v, e) such that under the IC model,

the expected number of nodes activated by the k seeds is the largest.

Algorithms

• Classic: Independent IC model and greedy algorithm

• Proposed: MIA model and greedy algorithm• Proposed: MIA model and more efficient

greedy algorithm• Proposed: Prefix excluding MIA model and

greedy algorithm (PMIA)

Independent IC model and Greedy algorithm

• Independent cascade (IC) model– Each edge (u; v) in the graph is associated with a

propagation probability pp(u; v)– pp(u, v) = p(v is activated by u at step t+1| u is

activated at step t)

Independent IC model and Greedy algorithm

• The algorithm iteratively selects new seed u that maximizes the incremental change of f into the seed set S until k seeds are selected.

Proposed: MIA model and greedy algorithm

Proposed: MIA model and greedy algorithm

Proposed: MIA model and greedy algorithm

• Let the activation probability of any node u in MIIA(v; \theta), denoted as ap(u; S; MIIA(v; \theta)), be the probability that u is activated when the seed set is S and influence is propagated in MIIA(v; \theta).

Proposed: MIA model and greedy algorithm

Proposed: MIA model and more efficient greedy algorithm

• A batch update scheme– Take advantage of influence linearity to add

multiple nodes to set S in each iteration

Proposed: Prefix excluding MIA model and greedy algorithm (PMIA)

Proposed: Prefix excluding MIA model and greedy algorithm (PMIA)

General summary

• First compute maximum influence paths (MIP) between every pair of nodes in the network via a Dijkstrashortest-path algorithm, and ignore MIPs with probability smaller than an influence threshold \theta, effectively restricting influence to a local region.

• Then union the MIPs starting or ending at each node into the tree structures, which represent the local influence regions of each node.

• Only consider influence propagated through these local tree, and we refer to this model as the maximum influence arborescence (MIA) model

Experiments

Evaluation

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Evaluation

Evaluation

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Contribution

• Heuristic-based– The heuristic is the main contribution– Construct local tree structure for calculating

influence spread• Scalable to millions of nodes and edges• Much faster than existing greedy algorithms• A simple tunable parameter for users to

control the balance between the running time and the influence spread of the algorithm