Very large database systems require distributed storage, which means that they need distributed search structures for fast and efficient access to the data. In this paper, we present an approach to maintaining distributed data structures that uses lazy updates, which take advantage of the semantics of the search structure operations to allow for scalable and low-overhead replication. Lazy updates can be used to design distributed search structures that support very high levels of concurrency. The alternatives to lazy update algorithms (vigorous updates) use synchronization to ensure consistency. Hence, lazy update algorithms are a distributed analogue of shared-memory lock-free search structure algorithms. Since lazy updates avoid the use of synchronization, they are much easier to implement than vigorous update algorithms. We demonstrate the application of lazy updates to the dB-tree, which is a distributed B + tree that replicates its interior nodes for highly parallel access. We d...

B-trees with relaxed balance have been defined to facilitate fast updating on shared-memory asynchronous parallel architectures. To obtain this, rebalancing has been uncoupled from the updating such that extensive locking can be avoided in connection with updates. We analyze B-trees with relaxed balance, and prove that each update gives rise to at most blog a (N=2)c + 1 rebalancing operations, where a is the degree of the Btree, and N is the bound on its maximal size since it was last in balance. Assuming that the size of nodes are at least twice the degree, we prove that rebalancing can be performed in amortized constant time. So, in the long run, rebalancing is constant time on average, even if any particular update could give rise to logarithmic time rebalancing. We also prove that the amount of rebalancing done at any particular level decreases exponentially going from the leaves towards the root. This is important since the higher up in the tree a lock due to a rebalancing operat...

This thesis develops a validated model of concurrent data structure algorithm performance, concentrating on concurrent B-trees. The thesis first develops two analytical tools, which are explained in the next two paragraphs, for the analysis. Yao showed that the space utilization of a B-tree built from random inserts is 69%. Assuming that nodes merge only when empty, we show that the utilization is 39% when the number of insert and delete operations is the same. However, if there are just 5% more inserts than deletes, then the utilization is at least 62%. In addition to the utilization, we calculate the probabilities of splitting and merging, important parameters for calculating concurrent B-tree algorithm performance. We compare merge-at-empty B-trees with merge-at-half B-trees. We conclude that merge-at-empty Btrees have a slightly lower space utilization but a much lower restructuring rate than merge-at-half B-trees, making merge-at-empty B-trees preferable for concurrent B-tree algo...

Providing high concurrency in B + -trees has been studied extensively. But few efforts have been documented for combining concurrency methods with a recovery scheme that preserves well-formed trees across system crashes. We describe an approach for this that works for a class of index trees that is a generalization of the B link -tree. A major feature of our method is that it works with a range of different recovery methods. It achieves this by decomposing structure changes in an index tree into a sequence of atomic actions, each one leaving the tree well-formed and each working on a separate level of the tree. All atomic actions on levels of the tree above the leaf level are independent of database transactions, and so are of short duration. Keywords: concurrency, recovery, indexing, access methods, B-trees c flDigital Equipment Corporation and Betty Salzberg 1991. All rights reserved. 1 College of Computer Science, Northeastern University, Boston, MA. This work was partially s...

We study the problem of storing an ordered set on an asynchronous shared memory parallel computer. We examine the case where we want to efficiently perform successor (least upper bound) queries on the set members that are stored. We also examine the case where processors insert and delete members of the set. Due to asynchrony, we require processors to perform queries and to maintain the structure independently. Although several such structures have been proposed, the analysis of these structures has been very limited. We here use the recently proposed QRQW PRAM model to provide upper and lower bounds on the performance of such data structures. In the asynchronous QRQW PRAM, the problem of processors concurrently and independently searching a shared data structure is very similar to the problem of routing packets through a network. Using this as a guide, we introduce the Search-Butterfly, a search structure that combines the efficient packet routing properties of the butterfly graph wit...

this paper, we prove that only an amortized constant amount of rebalancing is necessary after an update in a chromatic search tree. We also prove that the amount of rebalancing done at any particular level decreases exponentially, going from the leaves toward the root. These results imply that, in principle, a linear number of processes can access the tree simultaneously. We have included one interesting application of chromatic trees. Based on these trees, a priority queue with possibilities for a greater degree of parallelism than previous proposals can be implemented. ] 1997 Academic Press 1.

We investigate the problem of implementing a priority queue to be used in a parallel environment, where asynchronous processes have access to a shared memory. Chromatic trees are a generalization of red-black trees appropriate for applications in such an environment, and it turns out that an appropriate priority queue can be obtained via minor modifications of chromatic trees. As opposed to earlier proposals, our deletemin operation is worst-case constant time, and insert is carried out as a fast search and constant time update, followed by an amortized constant number of rebalancing operations, which can be performed later by other processes, one at a time. If a general delete is desired, it can be implemented as a fast search and constant time update, followed by an amortized constant number of rebalancing operations, which again can be performed later by other processes, one at time. The amortization results here extend the results previously obtained for chromatic search trees. Sin...

We present a highly concurrent priority queue algorithm based on the B-link tree, which is a B + -tree in which every node has a pointer to its right sibling. The algorithm is built on the concurrent B-link tree algorithms proposed by Lehman and Yao [15] and Sagiv [19]. Since the priority queue is based on highly concurrent search structure algorithms, a large number of insert operations can execute concurrently with little or no interference. We present two algorithms for executing the deletemin operation. The first algorithm executes deletemin operations serially, but we show that it can support a higher throughput that previous shared memory concurrent priority queue algorithms because most deletemin operations execute very quickly. The second deletemin algorithm uses the fetch-and-add operation to allow several deletemin operations to execute concurrently, and can support a much higher throughput. 1 Introduction A priority queue handles two operations: insert and deletemin. The ...

Rollback databases are multiversion databases that use transaction time to identify the versions of the data. Such databases support queries that request information "as-of" some specific past time. This report describes most of the technical aspects of supporting rollback databases. It shows how to to do the timestamping itself, including how to cope with distributed systems. Using the TSB-tree, we show how multi-version data can be efficiently indexed, efficient both in space and in query time. How one provides high concurrency while updating a TSB-tree is described next. Finally, we show how one can use a rollback database as a backup source to provide media failure recovery. Keywords: rollback databases, multiversions, timestamping, concurrency, media recovery c flDigital Equipment Corporation and Betty Salzberg 1992. All rights reserved. 1 College of Computer Science, Northeastern University, Boston, MA. This work was partially supported by NSF grant IRI-88-15707 and IRI-91-028...

Concurrent access to shared data objects must be regulated by a concurrency control protocol to ensure correctness. Many concurrency control protocols require that a process set a lock on the data it accesses. Recently, there has been considerable interest in lock-free concurrency control algorithms. Lock-free algorithms offer the potential for better system performance because slow or failed processes do not block fast processes. Process "slowdowns" can occur due to cache line faults, memory and bus contention, page faults, context switching, NUMA architectures, heterogeneous architectures, or differences in operation execution time. Much work has been done to characterize the performance of locking algorithms, but little has been done to characterize the performance of lock-free algorithms. In this paper, we present a performance model for analyzing lock-free algorithms that studies the effects of slowdowns on performance. We find that lock-free algorithms are better than locking alg...