Formal complexity and optimality-gap analysis of the heuristic

Establish a formal analysis of the computational complexity and optimality gap of the greedy wavelength-borrowing and two-hop water-filling heuristic for joint wavelength assignment and traffic detouring in the proposed optical spine-leaf architecture.

Background

The paper formulates joint wavelength borrowing and two-hop traffic detouring as a mixed-integer optimization problem and then uses a heuristic that decomposes the problem into water-filling, greedy borrowing, and self-wavelength refinement phases. Because the optimization is combinatorial and continuous, the authors state that exact methods become computationally intractable for practical network sizes.

The heuristic is evaluated empirically, including a runtime observation for a 64-leaf network with borrowing degree B=16. However, the paper does not provide a formal complexity bound or a formal characterization of how far the heuristic can deviate from the optimum. These analyses are explicitly left unresolved.

References

As this paper aims to provide initial results on the complexity-reconfigurability tradeoff enabled by the borrowing architecture, we leave a formal analysis of the heuristic's computational complexity and optimality gap to future work.

— A Wavelength Borrowing Architecture for Optical Data Center Networks - Extended Version  (2609.04874 - Detti et al., 4 Sep 2026) in Section 4, subsection “Heuristic Resource Allocation”

The resource allocation problem for TDMA-based solutions, as well as the architectural extensions in Appendix I in , are left for future work.

— A Wavelength Borrowing Architecture for Optical Data Center Networks - Extended Version  (2609.04874 - Detti et al., 4 Sep 2026) in Section 3, Section 2 discussion of the base architecture and Appendix I