Variants of Spreading Messages

Reddy, T. Varahala; Krishna, D. Sai; Rangan, C. Pandu

doi:10.1007/978-3-642-11440-3_22

“…Clearly, for each clique C X of G X there is a cluster C in G[V \ X] such that C X ⊆ C. Let S X ⊆ V be an optimal solution for G X . Note that S X can be computed in linear time [22,26]. By construction of G X it is clear that |S X | is a lower bound for the size of any target set for G. Furthermore, S X ∪X is a target set for G. Hence, if k < |S X | we can immediately answer no and if k ≥ |S X | + |X| = |S X | + we can answer yes.…”

Section: See Proof 4 (Appendix)mentioning

confidence: 99%

“…4 Recently, further parameterized complexity studies for the structural graph parameters "diameter", "cluster editing number", "vertex cover number", and "feedback edge set number" have been undertaken [22]. Moreover, polynomial-time algorithms for TSS restricted to special graph classes including chordal graphs and block-cactus graphs have been developed [4,6,26].…”

Section: Introductionmentioning

confidence: 99%

Constant Thresholds Can Make Target Set Selection Tractable

Chopin¹,

Nichterlein

²

,

Niedermeier

³

et al. 2013

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Abstract. Target Set Selection, which is a prominent NP-hard problem occurring in social network analysis and distributed computing, is notoriously hard both in terms of achieving useful approximation as well as fixed-parameter algorithms. The task is to select a minimum number of vertices into a "target set" such that all other vertices will become active in course of a dynamic process (which may go through several activation rounds). A vertex, which is equipped with a threshold value t, becomes active once at least t of its neighbors are active; initially, only the target set vertices are active. We contribute further insights into islands of tractability for Target Set Selection by spotting new parameterizations characterizing some sparse graphs as well as some "cliquish" graphs and developing corresponding fixed-parameter tractability and (parameterized) hardness results. In particular, we demonstrate that upper-bounding the thresholds by a constant may significantly alleviate the search for efficiently solvable, but still meaningful special cases of Target Set Selection.

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“…When λ is large enough, for instance equal to the number n of nodes, our Time Window Constrained Target Set Selection problem is equivalent to the classical Target Set Selection problem studied in [1,6,7,11,14,17,18,19,20,21,23,41,46], among the others. Strictly related is also the area of dynamic monopolies (see [29,40], for instance).…”

Section: The Model the Context And The Resultsmentioning

confidence: 99%

Influence Diffusion in Social Networks under Time Window Constraints

Gargano

¹

,

Hell

²

,

Peters

³

et al. 2013

Structural Information and Communication Complexity

8

0

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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.

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“…X can be computed in linear time [22,26]. By construction of G X it is clear that |S X | is a lower bound for the size of any target set for G. Furthermore, S X ∪X is a target set for G. Hence, if k < |S X | we can immediately answer no and if k ≥ |S X | + |X| = |S X | + we can answer yes.…”

Section: See Proof 3 (Appendix)mentioning

confidence: 99%

“…We contribute to this line of research by starting from the following: While TSS is linear-time solvable both on trees [5] and on cliques [22,26], it turns hard if the treewidth is unbounded [2] (more specifically, it is W[1]-hard with respect to the parameter treewidth of the graph) and it is NP-hard on graphs with diameter two [22] (cliques are exactly the diameter-one graphs). In this work, we focus on parameterizations measuring the distance from being a tree or forest and parameterizations measuring the distance from being a clique or cluster graph.…”

Section: Introductionmentioning

confidence: 99%

Constant Thresholds Can Make Target Set Selection Tractable

Chopin

¹

,

Nichterlein²,

Niedermeier³

et al. 2012

Lecture Notes in Computer Science

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Abstract. Target Set Selection, which is a prominent NP-hard problem occurring in social network analysis and distributed computing, is notoriously hard both in terms of achieving useful approximation as well as fixed-parameter algorithms. The task is to select a minimum number of vertices into a "target set" such that all other vertices will become active in course of a dynamic process (which may go through several activation rounds). A vertex, which is equipped with a threshold value t, becomes active once at least t of its neighbors are active; initially, only the target set vertices are active. We contribute further insights into islands of tractability for Target Set Selection by spotting new parameterizations characterizing some sparse graphs as well as some "cliquish" graphs and developing corresponding fixed-parameter tractability and (parameterized) hardness results. In particular, we demonstrate that upper-bounding the thresholds by a constant may significantly alleviate the search for efficiently solvable, but still meaningful special cases of Target Set Selection.

show abstract

Variants of Spreading Messages

Cited by 19 publications

References 7 publications

Constant Thresholds Can Make Target Set Selection Tractable

Constant Thresholds Can Make Target Set Selection Tractable

Influence Diffusion in Social Networks under Time Window Constraints

Constant Thresholds Can Make Target Set Selection Tractable

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