B+-tree Index Optimization by Exploiting Internal Parallelism of Flash-based Solid State Drives

Previous research addressed the potential problems of the hard-disk oriented design of DBMSs of flashSSDs. In this paper, we focus on exploiting potential benefits of flashSSDs. First, we examine the internal parallelism issues of flashSSDs by conducting benchmarks to various flashSSDs. Then, we suggest algorithm-design principles in order to best benefit from the internal parallelism. We present a new I/O request concept, called psync I/O that can exploit the internal parallelism of flashSSDs in a single process. Based on these ideas, we introduce B+-tree optimization methods in order to utilize internal parallelism. By integrating the results of these methods, we present a B+-tree variant, PIO B-tree. We confirmed that each optimization method substantially enhances the index performance. Consequently, PIO B-tree enhanced B+-tree's insert performance by a factor of up to 16.3, while improving point-search performance by a factor of 1.2. The range search of PIO B-tree was up to 5 times faster than that of the B+-tree. Moreover, PIO B-tree outperformed other flash-aware indexes in various synthetic workloads. We also confirmed that PIO B-tree outperforms B+-tree in index traces collected inside the Postgresql DBMS with TPC-C benchmark.Comment: VLDB201

Suffix Tree of Alignment: An Efficient Index for Similar Data

We consider an index data structure for similar strings. The generalized suffix tree can be a solution for this. The generalized suffix tree of two strings $A$ and $B$ is a compacted trie representing all suffixes in $A$ and $B$. It has $|A|+|B|$ leaves and can be constructed in $O(|A|+|B|)$ time. However, if the two strings are similar, the generalized suffix tree is not efficient because it does not exploit the similarity which is usually represented as an alignment of $A$ and $B$. In this paper we propose a space/time-efficient suffix tree of alignment which wisely exploits the similarity in an alignment. Our suffix tree for an alignment of $A$ and $B$ has $|A| + l_d + l_1$ leaves where $l_d$ is the sum of the lengths of all parts of $B$ different from $A$ and $l_1$ is the sum of the lengths of some common parts of $A$ and $B$. We did not compromise the pattern search to reduce the space. Our suffix tree can be searched for a pattern $P$ in $O(|P|+occ)$ time where $occ$ is the number of occurrences of $P$ in $A$ and $B$. We also present an efficient algorithm to construct the suffix tree of alignment. When the suffix tree is constructed from scratch, the algorithm requires $O(|A| + l_d + l_1 + l_2)$ time where $l_2$ is the sum of the lengths of other common substrings of $A$ and $B$. When the suffix tree of $A$ is already given, it requires $O(l_d + l_1 + l_2)$ time.Comment: 12 page

The Russian Mission: Seventh-Day Adventism, Bolshevism, and the Imminent Apocalypse, 1881 - 1946

The first Adventist missionaries made their way into Russia in the late 1880’s, where they experienced imprisonment, exile, and sometimes both. The scope of my thesis concerns the Seventh-Day Adventist Church and how Adventist missionaries and leaders endeavored on the Russian Mission. Using the writings, letters, and correspondence of these missionaries, as well as the myriad Adventist periodicals, I explain and analyze the evolution of the Mission from its inception to the end of the Second World War. In what ways did Adventist missionaries or Adventist media outlets abroad understand, explain, or justify the Russian Mission and its hardships? What characterized the Russian Mission through this transitional period? How can we understand the Russian Mission, through the Seventh-Day Adventist Church’s own writings and words, during the imperial period, the revolutionary period, and the early Soviet period? Why, in 1928, did Adventist periodicals stop calling for more evangelical missions and start heralding the second advent of Christ? What is the cause and significance of apocalyptic rhetoric? The missionaries, proselytizing in Russia during the imperial era, only ever discussed the prophetic potential of the Russian Mission; Adventist periodicals mirrored these sentiments, despite circulating stories of persecution at the hands of the Russian Orthodox Church and the autocracy. Russia’s entrance into the Great War, the consequent Russian Revolutions and Civil War, and the subsequent Volga Famine created an era of uncertainty for the Russian Mission, lasting well into the 1920’s; again, Adventists in Russia and abroad heralded the Mission as an apostolic success. Beginning in 1924, these feelings of hope began to fade, as missionary groups on the ground lost contact and communication with domestic Adventist centers. Instead of the hope-filled calls to Russia, however, outlets of the Adventist media began developing an understanding of the coming apocalypse. By 1928, the activities and goals of the Russian Mission had disappeared, and Adventists came to see Russia as the staging ground for an imminent and personal second advent of Christ

Tree-chromatic number is not equal to path-chromatic number

For a graph $G$ and a tree-decomposition $(T, \mathcal{B})$ of $G$, the chromatic number of $(T, \mathcal{B})$ is the maximum of $\chi(G[B])$, taken over all bags $B \in \mathcal{B}$. The tree-chromatic number of $G$ is the minimum chromatic number of all tree-decompositions $(T, \mathcal{B})$ of $G$. The path-chromatic number of $G$ is defined analogously. In this paper, we introduce an operation that always increases the path-chromatic number of a graph. As an easy corollary of our construction, we obtain an infinite family of graphs whose path-chromatic number and tree-chromatic number are different. This settles a question of Seymour. Our results also imply that the path-chromatic numbers of the Mycielski graphs are unbounded.Comment: 11 pages, 0 figure

The factorizable amplitude in B0→π+π−B^0 \to \pi^+ \pi^-

Using the measured spectrum shape for $B \to \pi \ell \nu$, the rate for $B^+ \to \pi^+ \pi^0$, information on the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{ub}|$, and theoretical inputs from factorization and lattice gauge theory, we obtain an improved estimate of the ``tree'' contribution to $B^0 \to \pi^+ \pi^-$. We find the branching ratio \b(B^0 \to \pi^+ \pi^-)|_{\rm tree} = (5.25^{+1.67}_{-0.50}) \times 10^{-6}, to be compared with the experimental value \b(B^0 \to \pi^+ \pi^-) = (4.55 \pm 0.44) \times 10^{-6}. The fit implies $|V_{ub}| = (3.62 \pm 0.34) \times 10^{-3}$. Implications for tree-penguin interference in $B^0 \to \pi^+ \pi^-$ and for other charmless $B$ decays are discussed.Comment: 11 pages, LaTeX, 3 figures, to be submitted to Phys. Rev.

Isotropic Dynamic Hierarchical Clustering

We face a need of discovering a pattern in locations of a great number of points in a high-dimensional space. Goal is to group the close points together. We are interested in a hierarchical structure, like a B-tree. B-Trees are hierarchical, balanced, and they can be constructed dynamically. B-Tree approach allows to determine the structure without any supervised learning or a priori knowlwdge. The space is Euclidean and isotropic. Unfortunately, there are no B-Tree implementations processing indices in a symmetrical and isotropical way. Some implementations are based on constructing compound asymmetrical indices from point coordinates; and the others split the nodes along the coordinate hyper-planes. We need to process tens of millions of points in a thousand-dimensional space. The application has to be scalable. Ideally, a cluster should be an ellipsoid, but it would require to store O(n2) ellipse axes. So, we are using multi-dimensional balls defined by the centers and radii. Calculation of statistical values like the mean and the average deviation, can be done in an incremental way. While adding a point to a tree, the statistical values for nodes recalculated in O(1) time. We support both, brute force O(2n) and greedy O(n2) split algorithms. Statistical and aggregated node information also allows to manipulate (to search, to delete) aggregated sets of closely located points. Hierarchical information retrieval. When searching, the user is provided with the highest appropriate nodes in the tree hierarchy, with the most important clusters emerging in the hierarchy automatically. Then, if interested, the user may navigate down the tree to more specific points. The system is implemented as a library of Java classes representing Points, Sets of points with aggregated statistical information, B-tree, and Nodes with a support of serialization and storage in a MySQL database.Comment: 6 pages with 3 example