Spanders: distributed spanning expanders

We consider self-stabilizing and self-organizing distributed construction of a spanner that forms an expander. The following results are presented. • A randomized technique to reduce the number of edges of an arbitrary expander graph, while preserving expansion properties and incurring an additive stretch factor of O(log n). • Given the randomized nature of our algorithms, a monitoring technique is presented for ensuring the desired results. The monitoring is based on the fact that expanders have a rapid mixing time and the possibility of examining the rapid mixing time by O(n) short (O(log n) length) random walks even for non regular expanders. • We then employ our results to construct a hierarchical sequence of spanders, each of them an expander spanning the previous graph. Such a sequence of spanders may be used to achieve different quality of service assurances in different applications. • A snap-stabilizing reset algorithm for message passing systems is presented and ut...

• Type: Conference
• Year: 2010
• Where: SAC
• Authors: Shlomi Dolev, Nir Tzachar
• Keywords: Applied Computing, Arbitrary Expander Graph, Message Passing Systems, Rapid Mixing Time, SAC 2010