Dynamic Ordered Sets with Exponential Search Trees

We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fully-dynamic linear space data structures. This leads to an optimal bound of O(sqrt(log n/loglog n)) for searching and updating a dynamic set of n integer keys in linear space. Here searching an integer y means finding the maximum key in the set which is smaller than or equal to y. This problem is equivalent to the standard text book problem of maintaining an ordered set (see, e.g., Cormen, Leiserson, Rivest, and Stein: Introduction to Algorithms, 2nd ed., MIT Press, 2001). The best previous deterministic linear space bound was O(log n/loglog n) due Fredman and Willard from STOC 1990. No better deterministic search bound was known using polynomial space. We also get the following worst-case linear space trade-offs between the number n, the word length w, and the maximal key U < 2^w: O(min{loglog n+log n/log w, (loglog n)(loglog U)/(logloglog U)}). These trade-offs are, however, not likely to be optimal. Our results are generalized to finger searching and string searching, providing optimal results for both in terms of n.Comment: Revision corrects some typoes and state things better for applications in subsequent paper

BATON: A Balanced Tree Structure for Peer-to-Peer Networks

We propose a balanced tree structure overlay on a peer-to-peer network capable of supporting both exact queries and range queries efficiently. In spite of the tree structure causing distinctions to be made between nodes at different levels in the tree, we show that the load at each node is approximately equal. In spite of the tree structure providing precisely one path between any pair of nodes, we show that sideways routing tables maintained at each node provide sufficient fault tolerance to permit efficient repair. Specifically, in a network with N nodes, we guarantee that both exact queries and range queries can be answered in O(logN) steps and also that update operations (to both data and network) have an amortized cost of O(logN). An experimental assessment validates the practicality of our proposal.Singapore-MIT Alliance (SMA

An Efficient Multiway Mergesort for GPU Architectures

Sorting is a primitive operation that is a building block for countless algorithms. As such, it is important to design sorting algorithms that approach peak performance on a range of hardware architectures. Graphics Processing Units (GPUs) are particularly attractive architectures as they provides massive parallelism and computing power. However, the intricacies of their compute and memory hierarchies make designing GPU-efficient algorithms challenging. In this work we present GPU Multiway Mergesort (MMS), a new GPU-efficient multiway mergesort algorithm. MMS employs a new partitioning technique that exposes the parallelism needed by modern GPU architectures. To the best of our knowledge, MMS is the first sorting algorithm for the GPU that is asymptotically optimal in terms of global memory accesses and that is completely free of shared memory bank conflicts. We realize an initial implementation of MMS, evaluate its performance on three modern GPU architectures, and compare it to competitive implementations available in state-of-the-art GPU libraries. Despite these implementations being highly optimized, MMS compares favorably, achieving performance improvements for most random inputs. Furthermore, unlike MMS, state-of-the-art algorithms are susceptible to bank conflicts. We find that for certain inputs that cause these algorithms to incur large numbers of bank conflicts, MMS can achieve up to a 37.6% speedup over its fastest competitor. Overall, even though its current implementation is not fully optimized, due to its efficient use of the memory hierarchy, MMS outperforms the fastest comparison-based sorting implementations available to date

Online Data Structures in External Memory

The original publication is available at www.springerlink.comThe data sets for many of today's computer applications are too large to t within the computer's internal memory and must instead be stored on external storage devices such as disks. A major performance bottleneck can be the input/output communication (or I/O) between the external and internal memories. In this paper we discuss a variety of online data structures for external memory, some very old and some very new, such as hashing (for dictionaries), B-trees (for dictionaries and 1-D range search), bu er trees (for batched dynamic problems), interval trees with weight-balanced B-trees (for stabbing queries), priority search trees (for 3-sided 2-D range search), and R-trees and other spatial structures. We also discuss several open problems along the way

Bulk Insertions into xBR+ -trees

Bulk insertion refers to the process of updating an existing index by inserting a large batch of new data, treating the items of this batch as a whole and not by inserting these items one-by-one. Bulk insertion is related to bulk loading, which refers to the process of creating a non-existing index from scratch, when the dataset to be indexed is available beforehand. The xBR + -tree is a balanced, disk-resident, Quadtree-based index for point data, which is very efficient for processing spatial queries. In this paper, we present the first algorithm for bulk insertion into xBR+ -trees. This algorithm incorporates extensions of techniques that we have recently developed for bulk loading xBR+ -trees. Moreover, using real and artificial datasets of various cardinalities, we present an experimental comparison of this algorithm vs. inserting items one-by-one for updating xBR+ -trees, regarding performance (I/O and execution time) and the characteristics of the resulting trees. We also present experimental results regarding the query-processing efficiency of xBR+ -trees built by bulk insertions vs. xBR+ -trees built by inserting items one-by-one