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In this paper, a diverse range of routing algorithms is classified into a new family of routings called zone-ordered label-based routing algorithms. The proposed classification is based on three common steps (factors) for generating such routings, namely, graph labeling, deadlock-free zones, and zone ordering. The main goal of this classification is to define several new routing concepts and streamline the knowledge on routing algorithms. Following the classification, a novel methodology is proposed to generate routing algorithms for irregular networks. The methodology uses the three mentioned steps to generate deadlock-free routings. Consequently, the methodology-based routings fall into the category of zone-ordered label-based routings. However, the graph labeling method (first step) used in the methodology is based on multiple spanning tree construction on the network. The simulation results show that constructing further spanning trees may result in routing algorithm with better performance.