Finding a path in a network based on multiple constraints (the MCP problem) is often referred to as QoS routing. QoS routing with constraints on multiple additive metrics has been proven to be NP-complete. This proof has dramatically influenced the research community, resulting into the common belief that exact QoS routing is intractable in practice. Hence, many heuristics for this problem were proposed, while hardly any exact algorithms. However, to our best knowledge, no one has ever examined which "worst-cases" cause NP-complete behavior. In fact, the MCP problem is not strong NP-complete, suggesting that in practice an exact QoS algorithm may work in polynomial time, making guaranteed QoS routing possible. The goal of this paper is to provide some properties and simulation results that indicate that NP-complete behavior hinges on a specific correlation structure between the link weights, which will be hardly ever encountered in practice.
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