Title:
On the Fundamental Tradeoffs between Routing Table Size and Network Diameter in Peer-to-Peer Networks
On the Fundamental Tradeoffs between Routing Table Size and Network Diameter in Peer-to-Peer Networks
Author(s)
Xu, Jun
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Abstract
In this work, we study a fundamental tradeoff issue in designing dynamic
hash table (DHT) in peer-to-peer networks: the size of the routing table
v.s. the network diameter. It was observed in Ratnasamy et al. that
existing DHT schemes either (a) have a routing table of size of O(log₂n)
and network diameter of O(log₂n), or (b) have a routing table of size d
and network diameter of O(n [superscript 1/d]). They asked whether this represents
the best asymptotic "state-efficiency" tradeoffs. Our first major result
is to show that there are routing algorithms which achieve better asymptotic
tradeoffs. However, such algorithms all cause severe congestion on certain
network nodes, which is undesirable in a P2P network. We then define the
notion of "congestion-free" and conjecture that the above tradeoffs are
asymptotically optimal for a congestion-free network. Though we are not
able to prove (or disprove) this conjecture in full generality, our rigorous
formulation of the problem and techniques introduced in proving slightly
weaker results serve as the basis for further exploration of this problem.
Our second major result is to prove that, if the routing algorithms are symmetric, the aforementioned tradeoffs
are asymptotically optimal. Furthermore, for symmetric algorithms, we find
that O(log₂n) is a magic threshold point for routing table size as
follows. The "congestion" factor dominates the "reachability" factor in
determining the minimum network diameter when the routing table size is
asymptotically smaller than or equal to O(log₂ n), and it is the other way around when the routing table
size is asymptotically larger than O(log₂n). Our third and final major
result is to study the exact (instead of asymptotic) optimal tradeoffs. We
propose a new routing algorithm that reduces the routing table size and the
network diameter of Chord both by 21.4% without introducing any other
overhead, based on a novel number-theoretical technique.
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Date Issued
2002
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268457 bytes
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Text
Resource Subtype
Technical Report