This paper investigates improvements of an online handwriting stroke-order analysis algorithm -- cube search, based on cube graph stroke-order generation model and dynamic programming (DP). By dividing character into radicals, the model is decomposed into intra-radical graphs and an inter-radical graph. This decomposition considerably reduces the time complexity of stroke-order search DP. Experimental results showed an significant improvements in operational speed. Additionally, recognition accuracy was also improved by prohibiting unnatural stroke-order.