Multiconstrained QoS Routing: A Norm Approach

• Published in: IEEE transactions on computers Vol. 56; no. 6; pp. 859 - 863
• Main Authors: Xue, G., Makki, S.K.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-06-2007; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Approximation; approximation algorithms; Criteria; Mathematical analysis; multiple additive QoS parameters; Optimization; QoS routing; Routing (telecommunications); scaled p{\hbox{-}}\rm norm; Shortest-path problems; Studies; Weighting functions
• ISSN: 0018-9340; 1557-9956
• DOI: 10.1109/TC.2007.1016

A fundamental problem in quality-of-service (QoS) routing is the multiconstrained path (MCP) problem, where one seeks a source-destination path satisfying K > 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 oc-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