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

Work based projects in the humanities : autonomous learners and satisfied students?

This paper will present the successes, challenges and key lessons learnt from the year-long Work Based Project modules (WBP) in the Humanities. the findings are based on a research project which was funded in the academic year 20109-10 by the Centre for Excellence in Teaching and Learning at Sheffield Hallam University. This project studied and evaluated second and final year undergraduate Humanities students' learning experience on WBP. The research focused specifically on the students' perceptions of how the WBP experience impacted on their development as autonomous learners, their awareness of skills and attributes in relation to employability, as well as the effect of reflective learning diaries and logs on their personal development processes

Online Dynamic Programming Speedups ⋆

Abstract. Consider the Dynamic Program h(n) = min1≤j≤n a(n, j) for n =1, 2,...,N. For arbitrary values of a(n, j), calculating all the h(n) requires Θ(N 2) time. It is well known that, if the a(n, j) satisfy the Monge property, then there are techniques to reduce the time down to O(N). This speedup is inherently static, i.e., it requires N to be known in advance. In this paper we show that if the a(n, j) satisfy a stronger condition, then it is possible, without knowing N in advance, to compute the values of h(n) in the order of n = 1, 2,...,N, in O(1) amortized time per h(n). This maintains the DP speedup online, in the sense that the time to compute all h(n) isO(N). A slight modification of our algorithm restricts the worst case time to be O(log N) perh(n), while maintaining the amortized time bound. For a(n, j) that satisfy our stronger condition, our algorithm is also simpler to implement than the standard Monge speedup. We illustrate the use of our algorithm on two examples from the literature. The first shows how to make the speedup of the D-medianona line problem in an online settings. The second shows how to improve the running time for a DP used to reduce the amount of bandwidth needed when paging mobile wireless users.