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Light trail is a unidirectional optical bus between the source and the destination node of a WDM network. In this paper, a novel algorithm is proposed for dynamic light trail assignment, which competently works for unicast dynamic connection requests. The routing is based on Hoffman k-shortest path algorithm. The proposed algorithm is solvable in polynomial time complexity and generates better results when compared with other existing algorithms. The existing algorithms are either dependent on the complex auxiliary graph, or they have a huge run time complexity. This motivated us to lay down our research work, which is free from the complex auxiliary graph and works in lesser time complexity. The aim of the paper is to satisfy the dynamic connection requests by assigning minimum number of dynamic light trails with the objective of minimizing the blocking probability, while maximizing the capacity utilization of each dynamic light trail assigned.