In pursuit of the dynamic optimality conjecture

In 1985, Sleator and Tarjan introduced the splay tree, a self-adjusting binary search tree algorithm. Splay trees were conjectured to perform within a constant factor as any offline rotation-based search tree algorithm on every sufficiently long sequence---any binary search tree algorithm that has this property is said to be dynamically optimal. However, currently neither splay trees nor any other tree algorithm is known to be dynamically optimal. Here we survey the progress that has been made in the almost thirty years since the conjecture was first formulated, and present a binary search tree algorithm that is dynamically optimal if any binary search tree algorithm is dynamically optimal.Comment: Preliminary version of paper to appear in the Conference on Space Efficient Data Structures, Streams and Algorithms to be held in August 2013 in honor of Ian Munro's 66th birthda

Verified Analysis of Functional Data Structures

In recent work the author has analyzed a number of classical functional search tree and priority queue implementations with the help of the theorem prover Isabelle/HOL. The functional correctness proofs of AVL trees, red-black trees, 2-3 trees, 2-3-4 trees, 1-2 brother trees, AA trees and splay trees could be automated. The amortized logarithmic complexity of skew heaps, splay trees, splay heaps and pairing heaps had to be proved manually

Enhanced User-driven Ranking System with Splay Tree

E-learning is one of the information and communication technology products used for teaching and learning process [35]. An efficient and effective way to construct trust relationship among peer users in e-learning environment is ranking. User-driven ranking systems are based only on the feedback or rating provided by the users. In [46-48] the authors provide a variety of trust and reputation methods. Certified Belief in Strength (CBS) [45] is a novel trust measurement method based on reputation and strength. In [38] author presents a recommendation system based on the relevant feedback review to predict the user's interests, that are ranked based on the recommendations history they provide previously. Users with higher rating obtain high reputation compared to less scored users. In question answering websites like StackOverflow, new or low scored users are ignored by the community. This discourage them and their involvement with the community reduces further down, as power law states, alleged low users are pushed to the bottom of the ranking list. Avoid this condition by encouraging less reputed users and prevent them from moving further down in ranking level. Thus, low reputed users are provided with few more chances to participate actively in the e-learning environments. A splay tree is a Binary Search Tree with self-balancing skill. The splay tree brings the recently accessed item to the top of the tree, thus active users are always on the top of the tree. A splay tree is used to represent user's ranks, and to semi-splay low ranked users again in the tree thus preventing them from further drowning in the ranking list. The focus of this research work is to find and enhance low reputed users in reputation system by providing few more chances to take part actively in the e-learning environment using the splay tree. Normalized discounted cumulative gain (NDCG) acts as a decision part for identifying drowning users

The Fresh-Finger Property

The unified property roughly states that searching for an element is fast when the current access is close to a recent access. Here, "close" refers to rank distance measured among all elements stored by the dictionary. We show that distance need not be measured this way: in fact, it is only necessary to consider a small working-set of elements to measure this rank distance. This results in a data structure with access time that is an improvement upon those offered by the unified property for many query sequences