I. Introduction
Optical networks that utilize wavelength division multiplexing (WDM) technology often waste spectral resources due to their coarse-grained channel provision capabilities [1]. Elastic optical networks (EONs) [2] that use advanced m-ary quadrature amplitude modulations (M-QAM) and bandwidth variable transponders (BVT) technologies have been introduced to provide finer network connections. Additionally, space division multiplexing (SDM) [3], [4], [5] technology based on multi-core fibers (MCFs) [6], [7] has been developed to further enhance the transmission capacity of EONs from the space dimension. With the rapid advancement of cloud computing technology [8], [9], computing resources in data centers are now highly virtualized. This has led to the emergence of SDM elastic optical data center networks (SDM-EODCNs), which accelerate the integration of computing and optical networks [10], [11]. This integration provides a solid foundation for the digital transformation of various aspects of life.