Finding a Path Subject to Many Additive QoS Constraints

A fundamental problem in quality-of-service (QoS) routing is to find a path between a source-destination node pair that satisfies two or more end-to-end QoS constraints. We model this problem using a graph with n vertices and m edges with K additive QoS parameters associated with each edge, for any constant Kges2. This problem is known to be NP-hard. Fully polynomial time approximation schemes (FPTAS) for the case of K=2 have been reported in the literature. We concentrate on the general case and make the following contributions. 1) We present a very simple (Km+nlogn) time K-approximation algorithm that can be used in hop-by-hop routing protocols. 2) We present an FPTAS for one optimization version of the QoS routing problem with a time complexity of O(m(n/epsi)^K-1). 3) We present an FPTAS for another optimization version of the QoS routing problem with a time complexity of O(nlogn+m(H/epsi)^K-1) when there exists an H-hop path satisfying all QoS constraints. When K is reduced to 2, our results compare favorably with existing algorithms. The results of this paper hold for both directed and undirected graphs. For ease of presentation, undirected graph is used