Implementing Huge Sparse Random Graphs

Consider a scenario where one desires to simulate the execution of some graph algorithm on random input graphs of huge, perhaps even exponential size. Sampling and storing these huge random graphs is clearly infeasible, but can they be emulated by ‘random looking’ graphs that are efficiently computable? Recently, Goldreich et al. [8], and Naor et al. [13] presented efficient implementations of the canonical (dense) random graphs G(N, p) where N = 2n labeled vertices are fixed and each edge independently appears with probability p = pn. We continue this line of research by emulating sparse G(N, p) graphs. The reasonable model for accessing the latter is by efficiently evaluating the entire (small) neighborhood Γ(v) in response to a query-vertex v. We cover a wide range of densities including random graphs’ famous threshold density for containing a giant component (p ∼ 1/N), and for achieving connectivity (p ∼ ln N/N). Our graphs faithfully emulate random graphs in the sense...

• Type: Conference
• Year: 2007
• Where: APPROX
• Authors: Moni Naor, Asaf Nussboim
• Keywords: Algorithms, APPROX 2007, Huge Random Graphs, Random Graphs, Random Input Graphs