The complexity of finding harmless individuals in social networks

Bazgan, Cristina; Chopin, Morgan

doi:10.1016/j.disopt.2014.09.004

Cited by 6 publications

(23 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A somewhat dual problem to TARGET SET SELECTION is HARMLESS SET, where given the same input, the question is to find a set of at least b vertices in which each vertex has less than f (v) neighbors [3].…”

Section: Related Workmentioning

confidence: 99%

“…An AND gadget is removed if both of its inputs are removed. However, note that the variable gadget for x [1] is not completely removed after v (3,4) is removed from the graph. In particular, the vertex v (1,4) has still degree m(b + 1) > 3 (where m is the maximum fan-out of all variables) after all vertices are removed since the AND gadgets it connects to are not removed.…”

Section: Counterexamplesmentioning

confidence: 99%

“…In particular, the vertex v (1,4) has still degree m(b + 1) > 3 (where m is the maximum fan-out of all variables) after all vertices are removed since the AND gadgets it connects to are not removed. It follows that the graph is not 2-degenerate after removing v (3,4) and hence the reduction is not correct.…”

Section: Counterexamplesmentioning

confidence: 99%

“…number of variables set to true). It is easy to check that x [1] = x [2] = false, x [3] = true is the only satisfying assignment that has at most one variable set to true. The AND gates in the red area have two outgoing connections each, hence the corresponding AND gadgets have fan-out gadgets attached to them…”

Section: Counterexamplesmentioning

confidence: 99%

“…Note that r-DEGENERATE VERTEX DELETION is known to be NP-hard for all r ≥ 0. 3 Hence, we also know that COLLAPSED k-CORE is NP-hard for k ≤ 2 and all x ≥ 0. However, the parameterized complexity with respect to b is open in this case.…”

Section: Corollary 1 Collapsed K-core Is Np-hard and W[p]mentioning

confidence: 99%

See 4 more Smart Citations

A Parameterized Complexity View on Collapsing k-Cores

2021

View full text Add to dashboard Cite

We study the -hard graph problem Collapsed k-Core where, given an undirected graph G and integers b, x, and k, we are asked to remove b vertices such that the k-core of remaining graph, that is, the (uniquely determined) largest induced subgraph with minimum degree k, has size at most x. Collapsed k-Core was introduced by Zhang et al. (2017) and it is motivated by the study of engagement behavior of users in a social network and measuring the resilience of a network against user drop outs. Collapsed k-Core is a generalization of r-Degenerate Vertex Deletion (which is known to be -hard for all r ≥ 0) where, given an undirected graph G and integers b and r, we are asked to remove b vertices such that the remaining graph is r-degenerate, that is, every its subgraph has minimum degree at most r. We investigate the parameterized complexity of Collapsed k-Core with respect to the parameters b, x, and k, and several structural parameters of the input graph. We reveal a dichotomy in the computational complexity of Collapsed k-Core for k ≤ 2 and k ≥ 3. For the latter case it is known that for all x ≥ 0 Collapsed k-Core is -hard when parameterized by b. For k ≤ 2 we show that Collapsed k-Core is -hard when parameterized by b and in when parameterized by (b + x). Furthermore, we outline that Collapsed k-Core is in when parameterized by the treewidth of the input graph and presumably does not admit a polynomial kernel when parameterized by the vertex cover number of the input graph.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Counterexamplesmentioning

confidence: 99%

Section: Counterexamplesmentioning

confidence: 99%

Section: Counterexamplesmentioning

confidence: 99%

Section: Corollary 1 Collapsed K-core Is Np-hard and W[p]mentioning

confidence: 99%

See 3 more Smart Citations

A Parameterized Complexity View on Collapsing k-Cores

2021

View full text Add to dashboard Cite

show abstract

On the Harmless Set Problem Parameterized by Treewidth

Gaikwad

Maity

2022

WALCOM: Algorithms and Computation

View full text Add to dashboard Cite

Harmless Sets in Sparse Classes

Drange

Muzi

Reidl

2022

Lecture Notes in Computer Science

View full text Add to dashboard Cite

In the classic Target Set Selection problem, we are asked to minimise the number of nodes to activate so that, after the application of a certain propagation process, all nodes of the graph are active. Bazgan and Chopin [Discrete Optimization, 14:170-182, 2014] introduced the opposite problem, named Harmless Set, in which they ask to maximise the number of nodes to activate such that not a single additional node is activated.In this paper we investigate how sparsity impacts the tractability of Harmless Set. Specifically, we answer two open questions posed by the aforementioned authors, namely a) whether the problem is FPT on planar graphs and b) whether it is FPT parametrised by treewidth. The first question can be answered in the positive using existing meta-theorems on sparse classes, and we further show that Harmless Set not only admits a polynomial kernel, but that it can be solved in subexponential time. We then answer the second question in the negative by showing that the problem is W[1]-hard when parametrised by a parameter that upper bounds treewidth.

show abstract

The complexity of finding harmless individuals in social networks

Cited by 6 publications

References 26 publications

A Parameterized Complexity View on Collapsing k-Cores

A Parameterized Complexity View on Collapsing k-Cores

On the Harmless Set Problem Parameterized by Treewidth

Harmless Sets in Sparse Classes

Contact Info

Product

Resources

About