Smooth heaps and a dual view of self-adjusting data structures

We present a new connection between self-adjusting binary search trees (BSTs) and heaps, two fundamental, extensively studied, and practically relevant families of data structures. Roughly speaking, we map an arbitrary heap algorithm within a natural model, to a corresponding BST algorithm with the same cost on a dual sequence of operations (i.e. the same sequence with the roles of time and key-space switched). This is the first general transformation between the two families of data structures. There is a rich theory of dynamic optimality for BSTs (i.e. the theory of competitiveness between BST algorithms). The lack of an analogous theory for heaps has been noted in the literature. Through our connection, we transfer all instance-specific lower bounds known for BSTs to a general model of heaps, initiating a theory of dynamic optimality for heaps. On the algorithmic side, we obtain a new, simple and efficient heap algorithm, which we call the smooth heap. We show the smooth heap to be the heap-counterpart of Greedy, the BST algorithm with the strongest proven and conjectured properties from the literature, widely believed to be instance-optimal. Assuming the optimality of Greedy, the smooth heap is also optimal within our model of heap algorithms. As corollaries of results known for Greedy, we obtain instance-specific upper bounds for the smooth heap, with applications in adaptive sorting. Intriguingly, the smooth heap, although derived from a non-practical BST algorithm, is simple and easy to implement (e.g. it stores no auxiliary data besides the keys and tree pointers). It can be seen as a variation on the popular pairing heap data structure, extending it with a "power-of-two-choices" type of heuristic.Comment: Presented at STOC 2018, light revision, additional figure

A Hardware Algorithm for Self-Balancing Binary Search Trees

Binary search trees are binary trees with an ordering mechanism that makes the time to search for any given item within the tree is greatly reduced compared to an unordered array of numbers. More specifically, a balanced binary search tree is faster at finding a specific item in the tree than an unbalanced tree. There are several algorithms that can automatically balance a binary search tree. Most of them do this through rotations directly in their respective insert functions. These algorithms are mostly implemented in software. This paper will present a hardware-based algorithm to balance binary search trees. This algorithm manipulates the ordering of a string representing a binary tree through swapping its elements in certain ways. It can then be used in software and hardware applications where sorting is used, such as in transducers, and priority queues are needed, such as in bandwidth management on transmission lines

Improved Bounds for Multipass Pairing Heaps and Path-Balanced Binary Search Trees

We revisit multipass pairing heaps and path-balanced binary search trees (BSTs), two classical algorithms for data structure maintenance. The pairing heap is a simple and efficient "self-adjusting" heap, introduced in 1986 by Fredman, Sedgewick, Sleator, and Tarjan. In the multipass variant (one of the original pairing heap variants described by Fredman et al.) the minimum item is extracted via repeated pairing rounds in which neighboring siblings are linked. Path-balanced BSTs, proposed by Sleator (cf. Subramanian, 1996), are a natural alternative to Splay trees (Sleator and Tarjan, 1983). In a path-balanced BST, whenever an item is accessed, the search path leading to that item is re-arranged into a balanced tree. Despite their simplicity, both algorithms turned out to be difficult to analyse. Fredman et al. showed that operations in multipass pairing heaps take amortized O(log n * log log n / log log log n) time. For searching in path-balanced BSTs, Balasubramanian and Raman showed in 1995 the same amortized time bound of O(log n * log log n / log log log n), using a different argument. In this paper we show an explicit connection between the two algorithms and improve both bounds to O(log n * 2^{log^* n} * log^* n), respectively O(log n * 2^{log^* n} * (log^* n)^2), where log^* denotes the slowly growing iterated logarithm function. These are the first improvements in more than three, resp. two decades, approaching the information-theoretic lower bound of Omega(log n)

Online machine learning approach to multicore data structures

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 175-180).As multicores become prevalent, the complexity of programming is skyrocketing. One major difficulty is eciently orchestrating collaboration among threads through shared data structures. Unfortunately, choosing and hand-tuning data structure algorithms to get good performance across a variety of machines and inputs is a herculean task to add to the fundamental difficulty of getting a parallel program correct. To help mitigate these complexities, this work develops a new class of parallel data structures called Smart Data Structures that leverage online machine learning to adapt themselves automatically. We prototype and evaluate an open source library of Smart Data Structures for common parallel programming needs and demonstrate signicant improvements over the best existing algorithms under a variety of conditions. Our results indicate that learning is a promising technique for balancing and adapting to complex, time-varying tradeoffs and achieving the best performance available.by Jonathan M. Eastep.Ph.D

09491 Abstracts Collection -- Graph Search Engineering

From the 29th November to the 4th December 2009, the Dagstuhl Seminar 09491 ``Graph Search Engineering \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Data structures

We discuss data structures and their methods of analysis. In particular, we treat the unweighted and weighted dictionary problem, self-organizing data structures, persistent data structures, the union-find-split problem, priority queues, the nearest common ancestor problem, the selection and merging problem, and dynamization techniques. The methods of analysis are worst, average and amortized case

Process Cooperativity as a Feedback Metric in Concurrent Message-Passing Languages

Runtime systems for concurrent languages have begun to utilize feedback mechanisms to influence their scheduling behavior as the application proceeds. These feedback mechanisms rely on metrics by which to grade any alterations made to the schedule of the multi-threaded application. As the application\u27s phase shifts, the feedback mechanism is tasked with modifying the scheduler to reduce its overhead and increase the application\u27s efficiency. Cooperativity is a novel possible metric by which to grade a system. In biochemistry the term cooperativity is defined as the increase or decrease in the rate of interaction between a reactant and a protein as the reactant concentration increases. This definition translates well as an information theoretic definition as: the increase or decrease in the rate of interaction between a process and a communication method as the number of processes increase. This work proposes several feedback mechanisms and scheduling algorithms which take advantage of cooperative behavior. It further compares these algorithms to other common mechanisms via a custom extensible runtime system developed to support swappable scheduling mechanisms. A minimalistic language with interesting characteristics, which lend themselves to easier statistical metric accumulation and simulated application implementation, is also introduced