Issue No. 06 - June (2007 vol. 56)

ISSN: 0018-9340

pp: 859-863

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2007.1016

S. Kami Makki , IEEE

Guoliang Xue , IEEE

ABSTRACT

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

S. Kami Makki, Guoliang Xue, "Multiconstrained QoS Routing: A Norm Approach",

*IEEE Transactions on Computers*, vol. 56, no. , pp. 859-863, June 2007, doi:10.1109/TC.2007.1016