AVL Trees With Relaxed Balance

AVL trees with relaxed balance were introduced with the aim of improving runtime per formance by allowing a greater degree of concurrency. This is obtained by uncoupling updating from rebalancing. An additional benefit is that rebalancing can be controlled separately. In particular, it can be postponed completely or partially until after peak working hours.We define a new collection of rebalancing operations which allows for a significantly greater degree of concurrency than the original proposal. Additionally, in contrast to the original proposal, we prove the complexity of our algorithm.If N is the maximum size of the tree, we prove that each insertion gives rise to at most I_ log_Phi(N + 3/2) + log_Phi(squareroot{5}) - 3 _I rebalancing operations and that each deletion gives rise to at most I_ log_Phi(N + 3/2) + log_Phi(squareroot{5}) - 4 _I rebalancing operations, where Phi is the golden ratio

DeltaTree: A Practical Locality-aware Concurrent Search Tree

As other fundamental programming abstractions in energy-e cient computing, search trees are expected to support both high parallelism and data locality. However, existing highly-concurrent search trees such as red-black trees and AVL trees do not consider data locality while existing locality-aware search trees such as those based on the van Emde Boas layout (vEB-based trees), poorly support concurrent (update) operations. This paper presents DeltaTree, a practical locality-aware concurrent search tree that combines both locality-optimisation techniques from vEB-based trees and concurrency-optimisation techniques from non-blocking highly-concurrent search trees. DeltaTree is a k-ary leaf-oriented tree of DeltaNodes in which each DeltaNode is a size- xed tree-container with the van Emde Boas layout. The expected memory transfer costs of DeltaTree's Search, Insert and Delete operations are O(logBN), where N;B are the tree size and the unknown memory block size in the ideal cache model, respectively. DeltaTree's Search operation is wait-free, providing prioritised lanes for Search operations, the dominant operation in search trees. Its Insert and Delete operations are non-blocking to other Search, Insert and Delete operations, but they may be occasionally blocked by maintenance operations that are sometimes triggered to keep DeltaTree in good shape. Our experimental evaluation using the latest implementation of AVL, red-black, and speculation friendly trees from the Synchrobench benchmark has shown that DeltaTree is up to 5 times faster than all of the three concurrent search trees for searching operations and up to 1.6 times faster for update operations when the update contention is not too high

O2-tree: a shared memory resident index in multicore architectures

Shared memory multicore computer architectures are now commonplace in computing. These can be found in modern desktops and workstation computers and also in High Performance Computing (HPC) systems. Recent advances in memory architecture and in 64-bit addressing, allow such systems to have memory sizes of the order of hundreds of gigabytes and beyond. This now allows for realistic development of main memory resident database systems. This still requires the use of a memory resident index such as T-Tree, and the B+-Tree for fast access to the data items. This thesis proposes a new indexing structure, called the O2-Tree, which is essentially an augmented Red-Black Tree in which the leaf nodes are index data blocks that store multiple pairs of key and value referred to as \key-value" pairs. The value is either the entire record associated with the key or a pointer to the location of the record. The internal nodes contain copies of the keys that split blocks of the leaf nodes in a manner similar to the B+-Tree. O2-Tree structure has the advantage that: it can be easily reconstructed by reading only the lowest value of the key of each leaf node page. The size is su ciently small and thus can be dumped and restored much faster. Analysis and comparative experimental study show that the performance of the O2-Tree is superior to other tree-based index structures with respect to various query operations for large datasets. We also present results which indicate that the O2-Tree outperforms popular key-value stores such as BerkelyDB and TreeDB of Kyoto Cabinet for various workloads. The thesis addresses various concurrent access techniques for the O2-Tree for shared memory multicore architecture and gives analysis of the O2-Tree with respect to query operations, storage utilization, failover and recovery