Binary trees are essential structures in Computer Science. The leaf (leaves) of a binary tree is one of the most significant aspects of it. In this study, we prove that the order of a leaf (leaves) of a binary tree is the same in the main tree traversals; preorder, inorder, and postorder. Then, we prove that given the preorder and postorder traversals of a binary tree, the leaf (leaves) of a bi...

There are three classical algorithms to visit all the nodes of a binary tree – preorder, inorder and postorder traversal. From this one gets a natural labelling of the n internal nodes of a binary tree by the numbers 1; 2; : : : ; n, indicating the sequence in which the nodes are visited. For given n (size of the tree) and j (a number between 1 and n), we consider the statistics number of ascen...

one of the debates concerning concepts of “medial motion” and “traversal motion” is the question of which of these two concepts of motion corresponds to motion in the corporeal world. in the present article we intend to employ the language of mathematics to present a model for each of these two concepts to study the above mentioned problem. as a result, medial motion represents a covering funct...

We study the complexity of traversing tree-shaped workflows whose tasks require large I/O files. We target a heterogeneous architecture with two resource types, each with a different memory, such as a multicore node equipped with a dedicated accelerator (FPGA or GPU). The tasks in the workflow are colored according to their type and can be processed if all there input and output files can be st...

This paper presents a unified approach to parsing, in which top-down, bot tomup and left-corner parsers m:e related to preorder, postorder and inorder tree traversals. It is shown that the simplest bo t tom-up and left-corner parsers are left recursive and must be converted using an extended Greibach normal form. With further partial execution, the bo t tom-up and left-corner parsers collapse t...

We consider the Top-k Approximate Subtree Matching (TASM) problem: finding the k best matches of a small query tree, e.g., a DBLP article with 15 nodes, in a large document tree, e.g., DBLP with 26M nodes, using the canonical tree edit distance as a similarity measure between subtrees. Evaluating the tree edit distance for large XML trees is difficult: the best known algorithms have cubic runti...

We consider the NP{complete problem of generating evaluations for expression DAGs with a minimalnumber of registers. We restrict our attention to contiguous evaluations, because for nearly all of the DAGs derived from real application programs there exists a contiguous evaluation that is optimal w.r. to the register need. We present an algorithm that generates an optimal contiguous evaluation f...