Is dynamic dedicated path protection tractable?
Ireneusz Szcześniak, Ireneusz Olszewski, Bożena Woźna-Szcześniak
TL;DR
The paper proves that dynamic dedicated path protection in optical networks is tractable when route costs are unbounded, by employing a generic Dijkstra algorithm on a polynomially-bounded search space through a polynomial-bounded label ordering, $ preceq'$. It introduces a refined framework for label efficiency with three comparisons, and shows that previous exponential behavior arising from spectrum-contiguity constraints can be mitigated by $ preceq'$, while the original $ preceq$ may still be used for the limited-cost variant at exponential cost. The work reconciles tractability with realistic spectrum constraints, and generalizes the exact solution approach to all two link-disjoint routes (start/end at the same or different nodes) under the stated assumptions. Overall, it clarifies when dynamic DDPP can be solved exactly in optical networks and highlights the critical role of the contiguity constraint in bounding the search space.
Abstract
Intractable is the problem of finding two link-disjoint paths of minimal cost if the path cost is limited since it can be a special case of the partition problem. In optical networks, this limit can be introduced by the signal modulation reach. Even without this limit, the existing literature suggested the problem intractable because of the spectrum continuity and contiguity constraints, but we show that the problem can be solved exactly with the recently-proposed generic Dijkstra algorithm over a polynomially-bounded search space, thus proving the problem tractable.