Efficient Rebalancing of Chromatic Search Trees

In PODS'91, Nurmi and Soisalon-Soininen presented a new type of binary search tree for databases, which they call a chromatic tree. The aim is to improve runtime performance by allowing a greater degree of concurrency, which, in turn, is obtained by uncoupling updating from rebalancing. This also allows rebalancing to be postponed completely or partially until after peak working hours.The advantages of the proposal of Nurmi and Soisalon-Soininen are quite significant, but there are definite problems with it. First, they give no explicit upper bound on the complexity of their algorithm. Second, some of their rebalancing operations can be applied many more times than necessary. Third, some of their operations, when removing one problem, create another.We define a new set of rebalancing operations which we prove give rise to at most I_ log_2(N+1) _I - 1 $ rebalancing operations per insertion and at most I_ log_2 (N+1)_I - 2 rebalancing operations per deletion, where N is the maximum'size the tree could ever have, given its initial size and the number of insertions performed. Most of these rebalancing operations, in fact, do no restructuring; they simply move weights around. The number of operations which actually change the structure of the tree is at most one per update

Efficient Rebalancing of Chromatic Search Trees

In PODS'91, Nurmi and Soisalon-Soininen presented a new type of binary search tree for databases, which they call a chromatic tree. The aim is to improve runtime performance by allowing a greater degree of concurrency, which, in turn, is obtained by uncoupling updating from rebalancing. This also allows rebalancing to be postponed completely or partially until after peak working hours.The advantages of the proposal of Nurmi and Soisalon-Soininen are quite significant, but there are definite problems with it. First, they give no explicit upper bound on the complexity of their algorithm. Second, some of their rebalancing operations can be applied many more times than necessary. Third, some of their operations, when removing one problem, create another.We define a new set of rebalancing operations which we prove give rise to at most I_ log_2(N+1) _I - 1 $ rebalancing operations per insertion and at most I_ log_2 (N+1)_I - 2 rebalancing operations per deletion, where N is the maximum'size the tree could ever have, given its initial size and the number of insertions performed. Most of these rebalancing operations, in fact, do no restructuring; they simply move weights around. The number of operations which actually change the structure of the tree is at most one per update

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

High Level Efficiency in Database Languages

The subject of this Ph.D. thesis is the design and implementation of database languages. The thesis consists of five articles:  [1] Joan F. Boyar and Kim S. Larsen. Efficient Rebalancing of Chromatic Search Trees. In O. Nurmi and E. Ukkonen, eds., LNCS 621: Algorithm Theory -- SWAT'92 , pp. 151-164. Springer-Verlag, 1992. [2] Kim S. Larsen. On Aggregation and Computation on Domain Values. PB-414, Computer Science Department, Aarhus University, 1992. [3] Kim S. Larsen. Strategies for Expression Evaluation Using Sort-Merge Algorithms. PB-415, Computer Science Department, Aarhus University, 1992. [4] Kim S. Larsen and Michael I. Schwartzbach. Injectivity of Unary Queries With Computation on Domain Values. Computer Science Department, Aarhus University, 1992. Revised version of PB-311. [5] Kim S. Larsen, Michael I. Schwartzbach and Erik M. Schmidt. A New Formalism for Relational Algebra. IPL , 41(3):163-168, 1992. and this survey paper. In [5], a new query language design is proposed. The expressive power of the language is determined in [2] and all reasonable extensions are considered. In [3, 4], we focus on the optimization issue of avoiding unnecessary sorting of relations. The results in these papers are directly applicable to any algebra-based query language. In addition to the query language part, a database system also has to offer update facilities. The theory of standard tuple based updates is quite well developed in the sequential case. In [1], we discuss a new concurrent implementation of balanced search trees for that purpose.This survey paper describes the results of the papers which form the thesis, and relates these results to each other and to the area in a broader sense than is customary in the introductions of individual papers. The paper is intended to be read in combination with the papers on which it is based

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

A Speculation-Friendly Binary Search Tree

We introduce the first binary search tree algorithm designed for speculative executions. Prior to this work, tree structures were mainly designed for their pessimistic (non-speculative) accesses to have a bounded complexity. Researchers tried to evaluate transactional memory using such tree structures whose prominent example is the red-black tree library developed by Oracle Labs that is part of multiple benchmark distributions. Although well-engineered, such structures remain badly suited for speculative accesses, whose step complexity might raise dramatically with contention. We show that our speculation-friendly tree outperforms the existing transaction-based version of the AVL and the red-black trees. Its key novelty stems from the decoupling of update operations: they are split into one transaction that modifies the abstraction state and multiple ones that restructure its tree implementation in the background. In particular, the speculation-friendly tree is shown correct, reusable and it speeds up a transaction-based travel reservation application by up to 3:5

Pattern Discovery from Biosequences

In this thesis we have developed novel methods for analyzing biological data, the primary sequences of the DNA and proteins, the microarray based gene expression data, and other functional genomics data. The main contribution is the development of the pattern discovery algorithm SPEXS, accompanied by several practical applications for analyzing real biological problems. For performing these biological studies that integrate different types of biological data we have developed a comprehensive web-based biological data analysis environment Expression Profiler (http://ep.ebi.ac.uk/)

Object-oriented engineering of visual languages

Visual languages are notations that employ graphics (icons, diagrams) to present information in a two or more dimensional space. This work focuses on diagrammatic visual languages, as found in software engineering, and their computer implementations. Implementation means the development of processors to automatically analyze diagrams and the development of graphical editors for constructing the diagrams. We propose a rigorous implementation technique that uses a formal grammar to specify the syntax of a visual language and that uses parsing to automatically analyze the visual sentences generated by the grammar. The theoretical contributions of our work are an original treatment of error handling (error detection, reporting, and recovery) in off-line visual language parsing, and the source-to-source translation of visual languages. We have also substantially extended an existing grammatical model for multidimensional languages, called atomic relational grammars. We have added support for meta-language expressions that denote optional and repetitive right-hand-side elements. We hav