## 1 Introduction  
Elastic optical path networks represent a promising communication infrastructure that can accommodate the rapidly increasing traffic in a future networked society [1, 2]. In elastic optical path networks, frequency-spectrum resources are divided into small segments (typically 12.5 GHz) called frequency slots (FSs). Therefore, they can be allocated to communication channels more flexibly than conventional wavelength-division-multiplexing-based optical path networks. Furthermore, with the application of multilevel modulation, such as Quadrature Amplitude Modulation (QAM), elastic optical path networks enable us to enhance the utilization of frequency-spectrum resources [3, 4]. Multi-core fibers, which are expected to be used as network links in future optical networks [5, 6], consist of multiple cores, where optical signals with the same FSs usingdifferent cores can be simultaneously transmitted, considerably enhancing the transmission capacity of optical fibers. However, the use of multi-core fibers induces inter-core crosstalk [7; 8] among the optical signals that pass through adjacent cores, which degrades the quality of the optical signals. In order to ensure high communication quality, the optical signal-to-noise ratio (OSNR) should exceed a certain threshold at the receiver nodes [9]. Because the accumulation of the inter-core crosstalk leads to the violation of this criterion, it is essential to maintain inter-core crosstalk at a low level. In this paper, we propose a dynamic routing, core, and spectrum allocation (RCSA) method to address this problem. RCSA is one of the most important technical issues in elastic optical networks, where data are transmitted via routes assigned FSs named lightpaths [10; 11]. RCSA methods determine routes, cores in multi-core fibers, and FSs to establish lightpaths, assuming static or dynamic scenarios [12; 13]. In the static scenario, the traffic matrix, i.e., the traffic demand of all senders and receivers in an elastic optical path network, is provided in advance. We can determine routes, cores, and FSs for lightpaths to be established by adopting optimization methods such as meta-heuristic algorithms and mathematical programming. On the other hand, in the dynamic scenario, the traffic matrix is not provided. Instead, we dynamically establish lightpaths in response to lightpath-setup requests generated stochastically over time while satisfying two constraints: spectrum continuity and spectrum contiguity. The spectrum continuity constraint establishes that common FSs in all links along the route must be used for the establishment of each lightpath. The spectrum contiguity constraint establishes that each lightpath must use successive FSs. Lightpath establishment is blocked in the case where there are no candidates satisfying these constraints. Therefore, when designing elastic optical path networks in the dynamic scenario, we should consider the blocking of lightpath establishment in addition to the impact of inter-core crosstalk. One simple strategy to mitigate the impact of inter-core crosstalk is to avoid the use of the same FSs in adjacent cores. However, this strategy wastes frequency-spectrum resources. As a result, it increases the blocking probability of lightpath establishment, which is an important performance metric of optical networks assuming dynamic RCSA. Furthermore, for the efficient use of frequency-spectrum resources, we should consider situations where the number of available cores is limited compared with the number of FSs required by newly established lightpaths. In such situations, it becomes challenging to simultaneously prevent the blocking of lightpath establishment and suppress inter-core crosstalk. The proposed method allows one to overcome this difficulty by grouping lightpath-setup requests according to their required number of FSs. By assigning lightpath-setup requests belonging to the same group to cores according to their priority, the proposed method aims to suppress inter-core crosstalk.