Approximation of Pareto optima in multiple-objective, shortest-path problems
Operations Research
Approximation schemes for the restricted shortest path problem
Mathematics of Operations Research
QoS routing in networks with uncertain parameters
IEEE/ACM Transactions on Networking (TON)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Journal of the ACM (JACM)
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Multiconstrained QoS Routing: A Norm Approach
IEEE Transactions on Computers
Polynomial time approximation algorithms for multi-constrained QoS routing
IEEE/ACM Transactions on Networking (TON)
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
A survey on multi-constrained optimal path computation: Exact and approximate algorithms
Computer Networks: The International Journal of Computer and Telecommunications Networking
Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems
SIAM Journal on Computing
A simple efficient approximation scheme for the restricted shortest path problem
Operations Research Letters
Maintaining shortest paths under deletions in weighted directed graphs: [extended abstract]
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We present a significantly faster algorithm for the restricted shortest path problem, in which we are given two vertices s, t, and the goal is to find the shortest path that is subject to a side constraint. More formally, rather than just having a single weight, each edge has two weights: a cost-weight, and a delay-weight. We are given a threshold T which corresponds to the maximum delay we can afford, and the goal is to find the s -- t path that minimizes total cost while still having delay-length at most T. There are many applications for this problem, as it can model situations where we need a path that has to achieve some balanced trade off between two different parameters. The exact version of the problem is known to be NP-hard [3], but there has been a series of results on (1 + ε) approximations, which culminated in a Õ(mn) algorithm for general graphs in 1999 [4, 8]. We present the first result to break though this barrier, achieving a close to linear running time -- technically it is [EQUATION]. It does have several draw-backs, however. It is randomized (Las Vegas), it only works for undirected graphs, and it approximates both parameters (previous algorithms found a (1 + ε) shortest path with delay exactly T or less, or a shortest path with delay at most (1 + ε)T, whereas our algorithm incurs a (1 + ε) approximation on both counts.) Our result presents an entirely new approach to the problem, which could potentially be generalized to work for directed graphs and to approximate only one of the parameters.