Given a binary tree T with n vertices, we want to embed T onto a given set A of n points on the line so as to minimize the total embedded edge length. Polynomial time algorithms for the two following special cases of this problem can be found in literature: (1) When T is arbitrary but A = f1 : : : ng; (2) When T is a complete binary tree and A is arbitrary. To the best of our knowledge, the com...

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...

1 Binary Search Tree 1.1 Operations We want to design a data structure, an ordered set S that supports the following operations: 1. Search(k, S) 2. Insert(k, S) 3. Delete(k, S) 4. Range(k, k ′ , S) ≡ |{k ∈ S|k ≤ k ≤ k}| If only (1), (2), (3) are required, we could use a hash table. However, if we also need (4), then we will need a BST. Definition 1.1. T is a BST for keys S if: 1. T is an ordere...

In this paper we are concerned with the analysis of special recursive algorithms for traversing the nodes of a planted plane tree (ordered tree ; planar tree) . Some by now classical results in this area are due to KNUTH [7], DE BRUIJN, KNUTH and RICE [1], FLAJOLET [2], FLAJOLET and ODLYZKO [3], FLAJOLET, RAOULT and VUILLEMIN [4], KEMP [6] and others and are summarized in the next few lines : T...

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...

Since the marginal cost of operating powerful monolithic single core systems has become prohibitive, horizontal scaling has become the de-facto method for expanding computational power and maintaining acceptable levels of energy efficiency. While horizontal scaling is now the accepted means, there is still a debate as to whether this should be done with ”big” or ”little” architectures. While th...

In this note we streamline an earlier algorithm for constructing a binary tree from its inorder and preorder traversals. The new algorithm is conceptually simpler than the earlier algorithms and its time complexity has a smaller constant factor.