On an application of convexity to discrete systems
Discrete Applied Mathematics
The Computer Journal
The number of fixed points of the majority rule
Discrete Mathematics
A note on the efficiency of an interval routing algorithm
The Computer Journal - Special issue on data structures
The r-majority vote action on 0-1 sequences
Discrete Mathematics
Fault-local distributed mending (extended abstract)
Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing
Local majorities, coalitions and monopolies in graphs: a review
Theoretical Computer Science
Informative Labeling Schemes for Graphs
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Euro-Par '98 Proceedings of the 4th International Euro-Par Conference on Parallel Processing
Optimal Irreversible Dynamos in Chordal Rings
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Local Majority Voting, Small Coalitions and Controlling Monopolies in Graphs: A Review
Local Majority Voting, Small Coalitions and Controlling Monopolies in Graphs: A Review
Graph Immunity Against Local Influence
Graph Immunity Against Local Influence
Irreversible conversion of graphs
Theoretical Computer Science
Triggering cascades on undirected connected graphs
Information Processing Letters
Reversible iterative graph processes
Theoretical Computer Science
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We consider the following synchronous colouringg ame played on a simple connected graph with vertices coloured black or white. During one step of the game, each vertex is recoloured according to the majority of its neighbours. The variants of the model differ by the choice of a particular tie-breaking rule and possible rule for enforcing monotonicity. Two tie-breaking rules we consider are simple majority and strong majority, the first in case of a tie recolours the vertex black and the latter does not change the colour. The monotonicity-enforcing rule allows the votingonly in white vertices, thus leaving all black vertices intact. This model is called irreversible.These synchronous dynamic systems have been extensively studied and have many applications in molecular biology, distributed systems modelling, etc.In this paper we give two results describing the behaviour of these systems on trees. First we count the number of fixpoints of strongma jority rule on complete binary trees to be asymptotically 4N 驴 (2驴)N where N is the number of vertices and 0.7685 驴 a 驴 0.7686.The second result is an algorithm for testing whether a given configuration on an arbitrary tree evolves into an all-black state under irreversible simple majority rule. The algorithm works in time O(t log t) where t is the number of black vertices and uses labels of length O(logN).