Compact Routing in Power-Law Graphs

Abstract. We adapt the compact routing scheme by Thorup and Zwick to optimize it for power-law graphs. We analyze our adapted routing scheme based on the theory of unweighted random power-law graphs with fixed expected degree sequence by Aiello, Chung, and Lu. Our result is the first theoretical bound coupled to the parameter of the power-law graph model for a compact routing scheme. In particular, we prove that, for stretch 3, instead of routing tables with ˜O(n1/2 ) bits as in the general scheme by Thorup and Zwick, expected sizes of O(nγ log n) bits are sufficient, and that all the routing tables can be constructed at once in expected time O(n1+γ log n), with γ = τ−2 2τ−3 + ε, where τ ∈ (2, 3) is the power-law exponent and ε > 0. Both bounds also hold with probability at least 1−1/n (independent of ε). The routing scheme is a labeled scheme, requiring a stretch-5 handshaking step and using addresses and message headers with O(log n log log n) bits, with proba...

• Type: Conference
• Year: 2009
• Where: WDAG
• Authors: Wei Chen, Christian Sommer 0002, Shang-Hua Teng, Yajun Wang
• Keywords: Algorithms, Compact Routing Scheme, Power-law Graphs, Routing Scheme, WDAG 2009