eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-08-13
710
725
10.4230/LIPIcs.APPROX-RANDOM.2015.710
article
The Minimum Bisection in the Planted Bisection Model
Coja-Oghlan, Amin
Cooley, Oliver
Kang, Mihyun
Skubch, Kathrin
In the planted bisection model a random graph G(n,p_+,p_-) with n vertices is created by partitioning the vertices randomly into two classes of equal size (up to plus or minus 1). Any two vertices that belong to the same class are linked by an edge with probability p_+ and any two that belong to different classes with probability (p_-) <(p_+) independently. The planted bisection model has been used extensively to benchmark graph partitioning algorithms. If (p_+)=2(d_+)/n and (p_-)=2(d_-)/n for numbers 0 <= (d_-) <(d_+) that remain fixed as n tends to infinity, then with high probability the "planted" bisection (the one used to construct the graph) will not be a minimum bisection. In this paper we derive an asymptotic formula for the minimum bisection width under the assumption that (d_+)-(d_-) > c * sqrt((d_+)ln(d_+)) for a certain constant c>0.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol040-approx-random2015/LIPIcs.APPROX-RANDOM.2015.710/LIPIcs.APPROX-RANDOM.2015.710.pdf
Random graphs
minimum bisection
planted bisection
belief propagation.