Learning-Augmented Skip Lists

We study the integration of machine learning advice into the design of skip lists to improve upon traditional data structure design. Given access to a possibly erroneous oracle that outputs estimated fractional frequencies for search queries on a set of items, we construct a skip list that provably provides the optimal expected search time, within nearly a factor of two. In fact, our learning-augmented skip list is still optimal up to a constant factor, even if the oracle is only accurate within a constant factor. We show that if the search queries follow the ubiquitous Zipfian distribution, then the expected search time for an item by our skip list is only a constant, independent of the total number $n$ of items, i.e., $\mathcal{O}(1)$, whereas a traditional skip list will have an expected search time of $\mathcal{O}(\log n)$. We also demonstrate robustness by showing that our data structure achieves an expected search time that is within a constant factor of an oblivious skip list construction even when the predictions are arbitrarily incorrect. Finally, we empirically show that our learning-augmented skip list outperforms traditional skip lists on both synthetic and real-world datasets

A Skip List Cookbook

Skip lists are a probabilistic list-based data structure that are a simple and efficient substitute for balanced trees. Skip list algorithms have the same asymptotic expected time bounds as balanced trees and are simpler, faster and use less space. The original paper on skip lists only presented algorithms for search, insertion and deletion. In this paper, we show that skip lists are as versatile as balanced trees. We describe and analyze algorithms to use search fingers, merge, split and concatenate skip lists, and implement linear list operations using skip lists. The skip list algorithms for these actions are simpler than their balanced tree cousins and at least as fast. The merge algorithm for skip lists we describe has better asymptotic time complexity than any previously described merge algorithm for balanced trees. (Also cross-referenced as UMIACS-TR-89-72.1

Concurrent Maintenance of Skip Lists

This papers describes a new approach to providing efficient concurrent access to a dynamic search structure. Previous approaches have attempted to solve this problem using search trees (either balanced or unbalanced). We describe methods for performing concurrent access and updates using skip lists. Skip lists are a probabilistic alternative to balanced trees that provide much of the simplicity of unbalanced trees, together with good worst-case expected performance. In this paper, we briefly review skip lists, describe simple methods for concurrent maintenance of sorted linked lists, formally prove the correctness of these methods, and show how they can be extended to provide simple and efficient algorithms for concurrent maintenance of skip lists. (Also cross-referenced as UMIACS-TR-90-80

On the search path length of random binary skip graphs

International audienceIn this paper we consider the skip graph data structure, a load balancing alternative to skip lists, designed to perform better in a distributed environment. We extend previous results of Devroye on skip lists, and prove that the maximum length of a search path in a random binary skip graph of size n is of order log n with high probability.Dans ce travail, nous nous intéressons aux "skip graphs", une alternative aux "skip lists" permettant un meilleur équlibrage de charges et conçue pour être plus efficace dans un environnement distribué. Nous étendons des résultats de Devroye sur les skip lists, et prouvons que la longueur maximale d'un chemin de recherche dans un skip graph binaire aléatoire de taille n, est d'ordre log(n) avec forte probabilité

Brief Announcement: On Self-Adjusting Skip List Networks

This paper explores the design of dynamic network topologies which adjust to the workload they serve, in an online manner. Such self-adjusting networks (SANs) are enabled by emerging optical technologies, and can be found, e.g., in datacenters. SANs can be used to reduce routing costs by moving frequently communicating nodes topologically closer. This paper presents SANs which provide, for the first time, provable working set guarantees: the routing cost between node pairs is proportional to how recently these nodes communicated last time. Our SANs rely on skip lists (which serve as the topology) and provide additional interesting properties such as local routing