TITLE:
Improved Approximation of Layout Problems on Random Graphs
AUTHORS:
Kevin K. H. Cheung, Patrick Girardet
KEYWORDS:
Graph Arrangements, Random Graphs, Approximation Algorithms, Undirected Graphs, Directed Acyclic Graphs
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.10 No.1,
January
10,
2020
ABSTRACT: Inspired by previous work of Diaz, Petit, Serna, and Trevisan (Approximating layout problems on random graphs, Discrete Mathematics, 235, 2001, 245-253), we show that several well-known graph layout problems are approximable to within a factor arbitrarily close to 1 of the optimal with high probability for random graphs drawn from an Erdös-Renyi distribution with appropriate sparsity conditions using only elementary probabilistic analysis. Moreover, we show that the same results hold for the analogous problems on directed acyclic graphs.