On finding common neighborhoods in massive graphs

Adam L. Buchsbaum, Raffaele Giancarlo, Jeffery R. Westbrook
2003 Theoretical Computer Science  
We consider the problem of ÿnding pairs of vertices that share large common neighborhoods in massive graphs. We prove lower bounds on the resources needed to solve this problem on resource-bounded models of computation. In streaming models, in which algorithms can access the input only a constant number of times and only sequentially, we show that, even with randomization, any algorithm that determines if there exists any pair of vertices with a large common neighborhood must essentially store
more » ... nd process the input graph o line. In sampling models, in which algorithms can only query an oracle for the common neighborhoods of speciÿed vertex pairs, we show that any algorithm must sample almost every pair of vertices for their respective common neighborhoods.
doi:10.1016/s0304-3975(02)00569-8 fatcat:7kngisrfqjdkdajs4ogtizpkla