Spreading messages

Chang, Ching-Lueh; Lyuu, Yuh‐Dauh

doi:10.1016/j.tcs.2009.03.032

Cited by 25 publications

(26 citation statements)

References 14 publications

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“…Chang and Lyuu [Chang and Lyuu, 2008] study the spreading of messages in undirected graphs under the assumption that each vertex is convinced of a message when more than half of its neighboring vertices are convinced. In their setting, a message initially convinces a set of vertices called the seeds.…”

Section: Introductionmentioning

confidence: 99%

“…Chang and Lyuu [Chang and Lyuu, 2008] show that min-seed(n, p) = Ω (min {n, 1/p}) holds with high probability over G(n, p), n ∈ N, p ∈ (0, 1].…”

Section: Introductionmentioning

confidence: 99%

“…Prior to our paper, Watts [Watts, 2002], Gleeson and Cahalane [Gleeson and Cahalane, 2007] and Chang and Lyuu [Chang and Lyuu, 2008] also consider the more general case where each vertex v is assigned a threshold α(v) and is convinced of the message when at least α(v) of v's neighbors are convinced. However, unlike the work of Chang and Lyuu [Chang and Lyuu, 2008] and the current paper, Watts [Watts, 2002] and Gleeson and Cahalane [Gleeson and Cahalane, 2007] do not prove (lower or upper) bounds on the minimum number of vertices needed to convince all or a large fraction of vertices in a graph.…”

Section: Introductionmentioning

confidence: 99%

“…

AbstractChang and Lyuu [Chang and Lyuu, 2008] study the spreading of a message in an Erdős-Rényi random graph G(n, p) starting from a set of vertices that are convinced of the message initially. In their strictmajority scenario, whenever more than half of the neighbors of a vertex v are convinced of a message, v itself also becomes convinced.

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confidence: 99%

“…The spreading proceeds asynchronously until no more vertices can be convinced. Following Chang and Lyuu [Chang and Lyuu, 2008], we derive lower bounds on the minimum number min-seed(n, p) of vertices that need to be convinced initially so that all vertices will be convinced at the end. Our main results are that min-seed(n, p) = Ω min n, p 2 n 2 and min-seed(n, p) = Ω n 2/3 hold with high probability.…”

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Spreading of Messages in Random Graphs

Chang

Lyuu

2010

Theory Comput Syst

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Chang and Lyuu [Chang and Lyuu, 2008] study the spreading of a message in an Erdős-Rényi random graph G(n, p) starting from a set of vertices that are convinced of the message initially. In their strictmajority scenario, whenever more than half of the neighbors of a vertex v are convinced of a message, v itself also becomes convinced. The spreading proceeds asynchronously until no more vertices can be convinced. Following Chang and Lyuu [Chang and Lyuu, 2008], we derive lower bounds on the minimum number min-seed(n, p) of vertices that need to be convinced initially so that all vertices will be convinced at the end. Our main results are that min-seed(n, p) = Ω min n, p 2 n 2 and min-seed(n, p) = Ω n 2/3 hold with high probability. We also consider the case of random seeds. For any sufficiently large constant d > 0 and any s ≤ n/(d ln n), we show that if one picks the set of seeds uniformly at random from the family of all s-sized sets, then with high probability, not all vertices will be convinced at the end.

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Section: Introductionmentioning

confidence: 99%

“…Chang and Lyuu [Chang and Lyuu, 2008] show that min-seed(n, p) = Ω (min {n, 1/p}) holds with high probability over G(n, p), n ∈ N, p ∈ (0, 1].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…

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confidence: 99%

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Spreading of Messages in Random Graphs

Chang

Lyuu

2010

Theory Comput Syst

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Parameterized Inapproximability of Target Set Selection and Generalizations

Bazgan

Chopin

Nichterlein

et al. 2014

Language, Life, Limits

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International audienceIn this paper, we consider the Target Set Selection problem: given a graph and a threshold value thr(v) for any vertex v of the graph, find a minimum size vertex-subset to "activate" s.t. all the vertices of the graph are activated at the end of the propagation process. A vertex v is activated during the propagation process if at least thr(v) of its neighbors are activated. This problem models several practical issues like faults in distributed networks or word-to-mouth recommendations in social networks. We show that for any functions f and ρ this problem cannot be approximated within a factor of ρ(k) in f(k)⋅nO(1) time, unless FPT = W[P], even for restricted thresholds (namely constant and majority thresholds). We also study the cardinality constraint maximization and minimization versions of the problem for which we prove similar hardness results

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