Dynamic monopolies in tori

Flocchini, Paola; Lodi, Elena; Luccio, Fabrizio; Pagli, Linda; Santoro, Nicola

doi:10.1016/s0166-218x(03)00261-0

Cited by 65 publications

(81 citation statements)

References 13 publications

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“…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%

On non-progressive spread of influence through social networks

Fazli

Ghodsi

Habibi

et al. 2014

Theoretical Computer Science

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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.

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Section: Introductionmentioning

confidence: 99%

On non-progressive spread of influence through social networks

Fazli

Ghodsi

Habibi

et al. 2014

Theoretical Computer Science

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“…For other different types of alliances, the reader is referred to [5,10,19] for (strong) defensive alliances, [6,17,18] for (strong) offensive alliances, and [2] for powerful alliances. A generalized version of global defensive alliance problem called defensive (offensive) r-alliance problem was introduced in [7] in which every vertex v in an offensive set S is asked to have |N S [v]|/2 + r − 1 closed neighbors in S. Besides, defensive alliances have related concept in the context of coalition, monopolies, and distributed computing [9,14,15]. A relatively new concept of alliances (defensive or offensive) in network graphs has recently attracted a great deal of attention due to some interesting applications in web communities [8,12] and fault-tolerant computing [15,20,21].…”

Section: Graph Classes A(g)â(g)mentioning

confidence: 99%

Global defensive alliances in star graphs

Hsu

Wang

2009

Discrete Applied Mathematics

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a b s t r a c tA defensive alliance in a graph G = (V , E) is a set of vertices S ⊆ V satisfying the condition that, for each v ∈ S, at least one half of its closed neighbors are in S. A defensive alliance S is called a critical defensive alliance if any vertex is removed from S, then the resulting vertex set is not a defensive alliance any more. An alliance S is called global if every vertex in V (G)\S is adjacent to at least one member of the alliance S. In this paper, we shall propose a way for finding a critical global defensive alliance of star graphs. After counting the number of vertices in the critical global defensive alliance, we can derive an upper bound to the size of the minimum global defensive alliances in star graphs.

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“…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%

“…With various threshold functions φ(·), the above cascading process models the propagation of faults in majority-based fault-tolerant systems [32][33][34]53], socio-economic contagion [40,74], cascading failures in infrastructure and organizational networks [74], spread of epidemics [29] and E-mail address: clchang@saturn.yzu.edu.tw. 1 complex propagation [20].…”

Section: Introductionmentioning

confidence: 99%

“…Other popular motivations for studying min-seed(G, φ) include graph-theoretical interests and determining the minimum number of individuals that can spread a disease or an opinion throughout a network. Bounds on min-seed(G, φ) are derived when G is a complete tree, ring, butterfly, wrapped butterfly, cube-connected cycle, shuffle-exchange graph, DeBruijn graph, hypercube [33,53], toroidal mesh [29,34,49,51,67], torus cordalis, torus serpentinus [29,34,51], chordal ring [32], multidimensional cube [12], Cartesian product of graphs, tensor product of graphs [2], complete multipartite graph [2,29], regular graph [29], Erdős-Rényi random graph [22,24,26], undirected connected graph [25] or directed graph with positive indegrees [1,22,25] (similar yet less complete lists appear in [22,23,25]). …”

Section: Introductionmentioning

confidence: 99%

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