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Two efficient time slot assignment algorithms, called the two-phase algorithm for the nonhierarchical and the three-phase algorithm for the hierarchical time-division multiplex (TDM) switching systems, are proposed. The simple idea behind these two algorithms is to schedule the traffic on the critical lines/trunks of a traffic matrix first. The time complexities of these two algorithms are found to be O(LN 2 ) and O(LM 2 ), where L is the frame length, N is the switch size, and M is the numberdoi:10.1109/26.905898 fatcat:sahdmay4pbe3fojp7lqrmmhf3a