The Power of D-hops in Matching Power-Law Graphs

This paper studies seeded graph matching for power-law graphs. Assume that two edge-correlated graphs are independently edge-sampled from a common parent with degree distribution. A set of correctly matched vertex-pairs is chosen at random and revealed as initial seeds. Our goal to use the seeds recover remaining latent vertex correspondence between Departing existing approaches focus on high-degree in $1$-hop neighborhoods, we develop an efficient algorithm exploits low-degree suitably-defined D-hop neighborhoods. Specifically, first match appropriate degrees (which refer slice) based number their approach significantly reduces needed trigger cascading process rest Under Chung-Lu model n vertices, max Θ(√n), exponent 2<β<3, show soon D> 4-β/3-β, by optimally choosing slice, high probability our can constant fraction true pairs without any error, provided only Ω((log n)4-β) result achieves exponential reduction seed size requirement, best previously known requires n1/2+ε (for small ε>0). Performance evaluation synthetic real data further corroborates improved performance algorithm.