For the parsimony this paper presents model a polynomial time greedy algorithm and a compound algorithm that combines the greedy policy with the branch-and-bound strategy in a uniform framework.

Also developed for the PRA tree is an enhanced predictive range aggregate (EPRA) query algorithm which USES a more precise branch and bound searching strategy, reducing the disk I?

Concerning path search in the motion graph, this paper used the area between two curves as the target function and improved the strategy of incremental search and the strategy of branch and bound.