On time versus size for monotone dynamic monopolies in regular topologies

Flocchini, Paola; Královič, Rastislav; Růžička, Peter; Roncato, Alessandro; Santoro, Nicola

doi:10.1016/s1570-8667(03)00022-4

Cited by 68 publications

(58 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This type of influence propagation process can be captured by applying the strict majority rule. Moreover, as an illustrative example of the linear threshold model [26], the strict majority propagation model is suitable for modeling transient faults in fault tolerant systems [17,31,18], and also used in verifying convergence of consensus problems on social networks [29]. Here we study the non-progressive influence models under the strict majority rule.…”

Section: Introductionmentioning

confidence: 99%

“…Tight or nearly tight bounds on the P P T S(G) are known for special types of graphs such as torus, hypercube, butterfly and chordal rings [16,17,27,31,32]. The best bounds for progressive strict majority model in general graphs are due to Chang and Lyuu.…”

Section: Introductionmentioning

confidence: 99%

“…The problem of maximizing social influence for specific family of graphs has been studied under the name of dynamic monopolies in the combinatorics literature [16,17,27,31,32,8,1,7]. All these results are for the progressive model.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On non-progressive spread of influence through social networks

Fazli

Ghodsi

Habibi

et al. 2014

Theoretical Computer Science

View full text Add to dashboard Cite

Abstract. The spread of influence in social networks is studied in two main categories: the progressive model and the non-progressive model (see e.g. the seminal work of Kempe, Kleinberg, and Tardos in KDD 2003). While the progressive models are suitable for modeling the spread of influence in monopolistic settings, non-progressive are more appropriate for modeling non-monopolistic settings, e.g., modeling diffusion of two competing technologies over a social network. Despite the extensive work on the progressive model, non-progressive models have not been studied well. In this paper, we study the spread of influence in the nonprogressive model under the strict majority threshold: given a graph G with a set of initially infected nodes, each node gets infected at time τ iff a majority of its neighbors are infected at time τ − 1. Our goal in the MinPTS problem is to find a minimum-cardinality initial set of infected nodes that would eventually converge to a steady state where all nodes of G are infected. We prove that while the MinPTS is NP-hard for a restricted family of graphs, it admits an improved constant-factor approximation algorithm for power-law graphs. We do so by proving lower and upper bounds in terms of the minimum and maximum degree of nodes in the graph. The upper bound is achieved in turn by applying a natural greedy algorithm. Our experimental evaluation of the greedy algorithm also shows its superior performance compared to other algorithms for a set of realworld graphs as well as the random power-law graphs. Finally, we study the convergence properties of these algorithms and show that the nonprogressive model converges in at most O(|E(G)|) steps.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On non-progressive spread of influence through social networks

Fazli

Ghodsi

Habibi

et al. 2014

Theoretical Computer Science

View full text Add to dashboard Cite

show abstract

“…Strictly related is also the area of dynamic monopolies (see [29,40], for instance). In terms of our second formulation of the TWC-TSS problem, the classical Target Set Selection problem can be viewed as an extreme case in which it is assumed that people have unbounded memory.…”

Section: The Model the Context And The Resultsmentioning

confidence: 99%

Influence Diffusion in Social Networks under Time Window Constraints

Gargano

Hell

Peters

et al. 2013

Structural Information and Communication Complexity

View full text Add to dashboard Cite

We study a combinatorial model of the spread of influence in networks that generalizes existing schemata recently proposed in the literature. In our model, agents change behaviors/opinions on the basis of information collected from their neighbors in a time interval of bounded size whereas agents are assumed to have unbounded memory in previously studied scenarios. In our mathematical framework, one is given a network G = (V, E), an integer value t(v) for each node v ∈ V , and a time window size λ. The goal is to determine a small set of nodes (target set) that influences the whole graph. The spread of influence proceeds in rounds as follows: initially all nodes in the target set are influenced; subsequently, in each round, any uninfluenced node v becomes influenced if the number of its neighbors that have been influenced in the previous λ rounds is greater than or equal to t(v). We prove that the problem of finding a minimum cardinality target set that influences the whole network G is hard to approximate within a polylogarithmic factor. On the positive side, we design exact polynomial time algorithms for paths, rings, trees, and complete graphs.

show abstract

“…is the set of positive integers. Consider the following cascading process [32][33][34]53,74]. A set S of vertices, called the seeds, are active initially.…”

Section: Introductionmentioning

confidence: 99%

Triggering cascades on undirected connected graphs

Chang

2011

Information Processing Letters

View full text Add to dashboard Cite

On time versus size for monotone dynamic monopolies in regular topologies

Cited by 68 publications

References 2 publications

On non-progressive spread of influence through social networks

On non-progressive spread of influence through social networks

Influence Diffusion in Social Networks under Time Window Constraints

Triggering cascades on undirected connected graphs

Contact Info

Product

Resources

About