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Multiconstrained QoS Routing: A Norm Approach
June 2007 (vol. 56 no. 6)
pp. 859-863
A fundamental problem in quality-of-service (QoS) routing is the multiconstrained path (MCP) problem, where one seeks a source-destination path satisfying K \ge 2 additive QoS constraints in a network with K additive QoS parameters. The MCP problem is known to be NP-complete. One popular approach is to use the shortest path with respect to a single edge weighting function as an approximate solution to MCP. In a pioneering work, Jaffe showed that the shortest path with respect to a scaled 1-norm of the K edge weights is a 2--approximation to MCP in the sense that the sum of the larger of the path weight and its corresponding constraint is within a factor of 2 from minimum. In a recent paper, Xue et al. showed that the shortest path with respect to a scaled \infty-norm of the K edge weights is a K-approximation to MCP, in the sense that the largest ratio of the path weight over its corresponding constraint is within a factor of K from minimum. In this paper, we study the relationship between these two optimization criteria and present a class of provably good approximation algorithms to MCP. We first prove that a good approximation according to the second optimization criterion is also a good approximation according to the first optimization criterion, but not vice versa. We then present a class of very simple K-approximation algorithms according to the second optimization criterion, based on the computation of a shortest path with respect to a single edge weighting function.
Index Terms:
QoS routing, multiple additive QoS parameters, approximation algorithms, scaled p{\hbox{-}}\rm norm.
Citation:
Guoliang Xue, S. Kami Makki, "Multiconstrained QoS Routing: A Norm Approach," IEEE Transactions on Computers, vol. 56, no. 6, pp. 859-863, June 2007, doi:10.1109/TC.2007.1016
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