Space-efficient schemes for message routing in distributed networks

Ravi Janardan, Purdue University

Abstract

A primary function in a distributed network is to route messages between pairs of nodes. Often, a cost is associated with each edge, making it desirable to route along shortest paths. Although this can be accomplished easily by storing a complete routing table at each node, this approach is expensive, using $\Theta$($n\sp2$) items of routing information for an n-node network. The focus of this research is to identify classes of networks for which considerably less routing information can be maintained, given the freedom to name nodes suitably. Node naming and message routing schemes are given for a number of network classes, including outerplanar networks, c-decomposable networks, for c a constant, and planar networks. These schemes use considerably less space than complete routing tables, keep node names to O(log n) bits, and still route along either shortest or near-shortest paths. The scheme for outerplanar networks uses $\Theta$(n) items and routes along shortest paths. The key idea here is a naming of the nodes with integers between 1 and n in a way that allows shortest paths information at every node to be encoded succinctly as a subinterval of (1,n) labeling each incident edge. Outerplanar networks are shown to be precisely the networks possessing this interval property. For c-decomposable networks, O(cn log n) items are stored, and, in worst case, any routing is at most 2/$\alpha$ + 1 times longer than a shortest routing, where $\alpha$ $>$ 1 is a certain function of c. A novel approach is used where information about relative magnitudes of distances is compactly encoded within the node names. The scheme for planar networks uses O(n$\sp{1+\epsilon}$) items and O((1/$\epsilon$) log n)-bit names, for any constant $\epsilon$, 0 $<$ $\epsilon$ $<$ 1/3. A worst-case bound of 7 on the routings is achieved. To obtain this result, the network is decomposed using structured cycle-separators and a powerful multi-interval graph labeling technique is applied to succinctly encode routing information. The issue of fault-tolerance is also addressed. For outerplanar networks, a scheme is given which, in the presence of t node and edge faults, uses O(t$\alpha$n) items to route with a worst case bound of (($\alpha$ + 1)/($\alpha$-1))$\sp{\rm t}$, where $\alpha$ $>$ 1 is an odd-valued integer parameter.

Degree

Ph.D.

Advisors

Frederickson, Purdue University.

Subject Area

Computer science

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