Approximation of Pareto optima in multiple-objective, shortest-path problems
Operations Research
Approximation schemes for the restricted shortest path problem
Mathematics of Operations Research
IEEE/ACM Transactions on Networking (TON)
A randomized algorithm for finding a path subject to multiple QoS requirements
Computer Networks: The International Journal of Computer and Telecommunications Networking
Heuristic algorithms for multiconstrained quality-of-service routing
IEEE/ACM Transactions on Networking (TON)
Hop-by-hop quality of service routing
Computer Networks: The International Journal of Computer and Telecommunications Networking
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An improved FPTAS for restricted shortest path
Information Processing Letters
Computer Networks: The International Journal of Computer and Telecommunications Networking
Concepts of exact QoS routing algorithms
IEEE/ACM Transactions on Networking (TON)
An efficient quality of service routing algorithm for delay-sensitive applications
Computer Networks: The International Journal of Computer and Telecommunications Networking
Approximation Algorithms for Multiconstrained Quality-of-Service Routing
IEEE Transactions on Computers
IEEE Transactions on Computers
Finding a path subject to many additive QoS constraints
IEEE/ACM Transactions on Networking (TON)
A simple efficient approximation scheme for the restricted shortest path problem
Operations Research Letters
Quality-of-service routing for supporting multimedia applications
IEEE Journal on Selected Areas in Communications
Near linear time (1 + ε)-approximation for restricted shortest paths in undirected graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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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.