| Summary: | Minimizing the size of routing tables and reducing the lookup latency have established the ground rules for several structured peer-to-peer lookup algorithms. The motivation behind this is that updating large routing tables require significant maintenance traffic that will eventually compete with regular traffic for bandwidth. Moreover, reducing the lookup latency is specifically pertinent to decreasing the number of hops the lookup needs to traverse. On the other hand, scalability becomes an additional constraint for several lookup mechanisms: increasing the number of nodes in the overlay is usually associated with an increase in the number of hops the lookup takes. In this direction, constant degree overlays mount as a practical solution to large networks with minimized lookup latency and limited routing tables. In this paper, we present degree-scalable, homogenous, addressing mechanism (d-SHAM), a simple, scalable, and robust constant degree algorithm that can adapt to frequent changes in the status of the overlay. It is applicable to large networks and reflects high load balancing capabilities. In d-SHAM, lookups are bounded within O(d) and each node holds entries for d.N<sup>1/d</sup> other nodes, where N is the number of nodes in the overlay and d is the number of its dimensions.
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