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We present a novel approach in describing and detecting the composite video events based on scenarios, which constrain the configurations of target events by temporal-logical structures of primitive events. We propose a new scenario description method to represent composite events more fluently and efficiently, and discuss an on-line event detection algorithm based on a combinatorial optimization. For this purpose, constraint flow-a dynamic configuration of scenario constraints-is first generated automatically by our scenario parsing algorithm. Then, composite event detection is formulated by a constrained discrete optimization problem, whose objective is to find the best video interpretation with respect to the constraint flow. Although the search space for the optimization problem is prohibitively large, our on-line event detection algorithm based on constraint flow using dynamic programming reduces the search space dramatically, handles preprocessing errors effectively, and guarantees a globally optimal solution. Experimental results on natural videos demonstrate the effectiveness of our algorithm.