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Issue No. 02 - February (2009 vol. 20)
ISSN: 1045-9219
pp: 171-179
Jie Gao , Stony Brook University, Stony Brook
Li Zhang , Microsoft Research Silicon Valley, Mountain View
An unweighted graph has density \rho and growth rate k if the number of nodes in every ball with radius r is bounded by \rho r^{k}. The communication graphs of wireless networks and peer-to-peer networks often have constant bounded density and small growth rate. In this paper, we study the trade-off between two quality measures for routing in growth-restricted graphs. The two measures we consider are the stretch factor, which measures the lengths of the routing paths, and the load-balancing ratio, which measures the evenness of the traffic distribution. We show that if the routing algorithm is required to use paths with stretch factor c, then its load-balancing ratio is bounded by O(\rho^{1/k}(n/c)^{1 - 1/k}), and the bound is tight in the worst case. We show the application and extension of the trade-off to the wireless network routing and VLSI layout design. We also present a load-balanced routing algorithm with the stretch factor constraint in an online setting, in which the routing requests come one by one.
Routing, load balancing, wireless networks, growth-restricted graphs.

J. Gao and L. Zhang, "Trade-Offs between Stretch Factor and Load-Balancing Ratio in Routing on Growth-Restricted Graphs," in IEEE Transactions on Parallel & Distributed Systems, vol. 20, no. , pp. 171-179, 2008.
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