New algorithms for the LCA problem and the binary tree reconstruction problem

In parallel algorithm design, a fundamental problem called the all nearest smaller value problem has recently been introduced. This problem is addressed by an analysis that defines a structure called the R-forest. The analysis examines its relation with other data structures, then uses these relations to develop new algorithms for the lowest common ancestor (LCA) problem and the binary tree reconstruction problem. The approach to solving the LCA problem is simpler than the existing ones, while maintaining complexity optimality. The analysis shows that if the preorder and postorder traversals of the tree are available, then the LCA problem can be solved in O(log*n) time using an optimal number of processors on the concurrent read concurrent write parallel random access machine. This result, along with the result on the binary tree reconstruction problem, adds to an extremely short list of problems known to be solvable faster than O(log log n) parallel time.