Irreversible conversion of graphs

Centeno, Carmen C.; Dourado, Mitre C.; Penso, Lúcia Draque; Rautenbach, Dieter; Szwarcfiter, Jayme Luiz

doi:10.1016/j.tcs.2011.03.029

Cited by 115 publications

(62 citation statements)

References 26 publications

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“…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%

“…For instance, Dreyer and Roberts [10] showed NP-hardness for TSS when all vertices have a threshold of t, t ≥ 3. Centeno et al [4] and Chiang et al [6] exploited threshold values being upper-bounded by two to develop polynomial-time algorithms for TSS on chordal graphs. Most interesting in our context, however, is the result of Ben-Zwi et al [2] On the one hand, we generalize from trees, thus in a way following previous work [2,22] and consider further parameters measuring tree-likeness or sparseness, and, on the other hand we spot several parameters measuring distance to "cliquish" graphs.…”

Section: Introductionmentioning

confidence: 99%

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Constant Thresholds Can Make Target Set Selection Tractable

Chopin¹,

Nichterlein

Niedermeier

et al. 2013

Theory Comput Syst

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Constant Thresholds Can Make Target Set Selection Tractable

Chopin¹,

Nichterlein

Niedermeier

et al. 2013

Theory Comput Syst

View full text Add to dashboard Cite

show abstract

“…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

Hell

Peters

et al. 2013

Structural Information and Communication Complexity

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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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“…The P 3 convexity was first considered for directed graphs [21,25]. For undirected graphs, the P 3 convexity was studied in [5,8,9].…”

Section: The Carathéodory Number Cth(g) Is the Smallest Integer C Sucmentioning

confidence: 99%

Inapproximability Results for Graph Convexity Parameters

Coelho

Dourado

Sampaio

2014

Approximation and Online Algorithms

Self Cite

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Abstract. In this paper, we prove several inapproximability results on the P3-convexity and the geodetic convexity on graphs. We prove that determining the P3-hull number and the geodetic hull number are APXhard problems. We prove that the Carathéodory number, the Radon number and the convexity number of both convexities are O(n 1−ε )-inapproximable in polynomial time for every ε > 0, unless P=NP. We also prove that the interval numbers of both convexities are W [2]-hard and O(log n)-inapproximable in polynomial time, unless P=NP. Moreover, these results hold for bipartite graphs in the P3-convexity.

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Irreversible conversion of graphs

Cited by 115 publications

References 26 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

Inapproximability Results for Graph Convexity Parameters

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