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Constraint-based path selection is an invaluable part of a full-fledged quality of service (QoS) architecture. Internet service providers want to be able to select paths for QoS flows that optimize network utilization and satisfy user requirements and as such increase revenues. Unfortunately, finding a path subject to multiple constraints is known to be an NP-complete problem. Hence, accurate constraint-based path selection algorithms with a fast running time are scarce. Numerous heuristics and a few exact algorithms have been proposed. In this article we compare most of these algorithms. We focus on the restricted shortest path algorithms and multi-constrained path algorithms. The performance evaluation of these two classes of algorithms is presented based on complexity analysis and simulation results and may shed some light on the difficult task of selecting the proper algorithm for a QoS-capable network.