. We consider the problem of building a static (i.e. no updates are performed) skip list of n elements, given these n elements and the corresponding access probabilities or weights. We develop a dynamic programming algorithm that builds an optimal skip list in the sense that the average access cost is minimized. We also consider nearly optimal skip lists, whose average access cost is not optimal but good enough, and can be built more efficiently than optimal skip lists. Several related issues are also discussed, for instance, other approaches to the construction of nearly optimal skip lists or the construction of optimal skip lists that minimize different kinds of search costs. 1. Introduction There are many instances where we have to deal with a static data set, i.e. no insertions, deletions or modifications are needed, and therefore it is convenient to organize the information to make the accesses to that information as efficient as possible. Just to mention a few such instances, co...

Although skip lists were introduced as an alternative to balanced binary search trees (BSTs), we show that the skip list can be interpreted as a type of randomly-balanced BST whose simplicity and elegance is arguably on par with that of today’s most popular BST balancing mechanisms. In this paper, we provide a clear, concise description and analysis of the “BST ” interpretation of the skip list, and compare it to similar randomized BST balancing mechanisms. In addition, we show that any rotation-based BST balancing mechanism can be implemented in a simple fashion using a skip list.

We show that multi-splay trees have most of the properties that splay trees have. Specifically, we show that multi-splay trees have the following properties: the access lemma, static optimality, the static finger property, the working set property, and key-independent optimality. Moreover, we prove that multi-splay trees have the deque property, which was conjectured by Tarjan in 1985 for splay trees, but remains unproven despite a significant amount of research toward proving it. Efficiently maintaining and manipulating sets of elements from a totally ordered universe is a fundamental problem in computer science. Specifically, many algorithms need a data structure that can efficiently support at least the following operations: insert, delete, predecessor, and successor, as well as membership testing. A standard data structure that maintains a totally ordered set and

This thesis introduces the concept of a heterogeneous decomposition of a balanced search tree and apply it to the following problems: • How can finger search be implemented without changing the representation of a Red-Black Tree, such as introducing extra storage to the nodes? (Answer: Any degree-balanced search tree can support finger search without modification in its representation by maintaining an auxiliary data structure of logarithmic size and suitably modifying the search algorithm to make use of this auxiliary data structure.) • Do Multi-Splay Trees, which is known to be O(log log n)-competitive to the optimal binary search trees, have the Dynamic Finger property? (Answer: This is work in progress. We believe the answer is yes.)

Abstract. A range of attacks on network components, such as algorithmic denial-of-service attacks and cryptanalysis via timing attacks, are enabled by data structures for which an adversary can predict the durations of operations that he will induce on the data structure. In this paper we introduce the problem of designing data structures that confound an adversary attempting to predict the timing of future operations he induces, even if he has adaptive and exclusive access to the data structure and the timings of past operations. We also design a data structure for implementing a set (supporting membership query, insertion, and deletion) that exhibits timing unpredictability and that retains its efficiency despite adversarial attacks. To demonstrate these advantages, we develop a framework by which an adversary tracks a probability distribution on the data structure’s state based on the timings it emitted, and infers invocations to meet his attack goals. 1

Set intersection is a fundamental operation in information retrieval and database systems. This paper introduces linear space data structures to represent sets such that their intersection can be computed in a worst-case efficient way. In general, given k (preprocessed) sets, with totally n elements, we will show how to compute their intersection in expected time O(n / √ w + kr), where r is the intersection size and w is the number of bits in a machine-word. In addition,we introduce a very simple version of this algorithm that has weaker asymptotic guarantees but performs even better in practice; both algorithms outperform the state of the art techniques for both synthetic and real data sets and workloads. 1.