Size bounds for dynamic monopolies
Discrete Applied Mathematics
Fault-local distributed mending
Journal of Algorithms
An improved testing scheme for catastrophic fault patterns
Information Processing Letters
Mining the network value of customers
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Distributed probabilistic polling and applications to proportionate agreement
Information and Computation
Optimal irreversible dynamos in chordal rings
Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
Dynamic monopolies of constant size
Journal of Combinatorial Theory Series B
Local majorities, coalitions and monopolies in graphs: a review
Theoretical Computer Science
On Majority Voting Games in Trees
SOFSEM '01 Proceedings of the 28th Conference on Current Trends in Theory and Practice of Informatics Piestany: Theory and Practice of Informatics
The power of small coalitions in graphs
Discrete Applied Mathematics
Maximizing the spread of influence through a social network
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
On time versus size for monotone dynamic monopolies in regular topologies
Journal of Discrete Algorithms
Listen to Your Neighbors: How (Not) to Reach a Consensus
SIAM Journal on Discrete Mathematics
Information Processing Letters
Discrete Applied Mathematics
Random Structures & Algorithms
The south zone: distributed algorithms for alliances
SSS'11 Proceedings of the 13th international conference on Stabilization, safety, and security of distributed systems
On the radon number for p3 convexity
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Characterization and recognition of Radon-independent sets in split graphs
Information Processing Letters
Reversible iterative graph processes
Theoretical Computer Science
Bounding the sizes of dynamic monopolies and convergent sets for threshold-based cascades
Theoretical Computer Science
Immediate versus eventual conversion: comparing geodetic and hull numbers in P3-convexity
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Constant thresholds can make target set selection tractable
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
On the Carathéodory number of interval and graph convexities
Theoretical Computer Science
| Hi-index | 5.23 |
Given a graph G, a function f:V(G)-Z, and an initial 0/1-vertex-labelling c"1:V(G)-{0,1}, we study an iterative 0/1-vertex-labelling process on G where in each round every vertex v never changes its label from 1 to 0, and changes its label from 0 to 1 if at least f(v) neighbours have label 1. Such processes model opinion/disease spreading or fault propagation and have been studied under names such as irreversible threshold/majority processes in a large variety of contexts. Our contributions concern computational aspects related to the minimum cardinality irr"f(G) of sets of vertices with initial label 1 such that during the process on G all vertices eventually change their label to 1. Such sets are known as irreversible conversion sets, dynamic irreversible monopolies, or catastrophic fault patterns. Answering a question posed by Dreyer and Roberts [P.A. Dreyer Jr., F.S. Roberts, Irreversible k-threshold processes: graph-theoretical threshold models of the spread of disease and of opinion, Discrete Appl. Math. 157 (2009) 1615-1627], we prove a hardness result for irr"f(G) where f(v)=2 for every v@?V(G). Furthermore, we describe a general reduction principle for irr"f(G), which leads to efficient algorithms for graphs with simply structured blocks such as trees and chordal graphs.