Parallel dictionaries with local rules on AVL and brother trees

We present a set of local rules to deal with dictionaries, having as a main advantage their possible scheduling in a highly synchronized way to get parallel dictionaries on AVLs. Up to now trees used in massively parallel dictionaries needed to have all the leaves at the same depth, such as 2--3 trees. Therefore, it was possible (in insertions and deletions) to reconstruct the tree bottom-up in a very regular fashion, as a pipeline of plane waves moving up. On AVL trees the situation looks different because leaves can have different depth, therefore any wave in a pipeline is highly irregular. To solve this problem we define {\it virtual} plane waves allowing us to develop an EREW dictionary for $k$ keys with $k$ processors and time $O (\log n + \log k)$. Later on we generalize the sePostprint (published version

A Unified approach to concurrent and parallel algorithms on balanced data structures

Concurrent and parallel algorithms are different. However, in the case of dictionaries, both kinds of algorithms share many common points. We present a unified approach emphasizing these points. It is based on a careful analysis of the sequential algorithm, extracting from it the more basic facts, encapsulated later on as local rules. We apply the method to the insertion algorithms in AVL trees. All the concurrent and parallel insertion algorithms have two main phases. A percolation phase, moving the keys to be inserted down, and a rebalancing phase. Finally, some other algorithms and balanced structures are discussed.Postprint (published version

Fringe analysis of synchronized parallel insertion algorithms on 2--3 trees

The fringe analysis studies the distribution of bottom subtrees or fringe of trees under the assumption of random selection of keys, yielding an average case analysis of the fringe of trees. We are interested in the fringe analysis of the synchronized parallel insertion algorithms of Paul, Vishkin, and Wagener~(PVW) on 2-3 trees. This algorithm inserts k keys with k processors into a tree of size n with time O(log n+log k). As the direct analysis of this algorithm is very difficult we tackle this problem by introducing a new family of algorithms, denoted MacroSplit algorithms, and our main theorem proves that two algorithms of this family, denoted MaxMacroSplit and MinMacroSplit, upper and lower bounds the fringe of the PVW algorithm. Published papers deal with the fringe analysis of sequential algorithms and it was an open problem for parallel algorithms on search trees. We extend the fringe analysis to parallel algorithms and we get a rich mathematical structure giving new interpretations even in the sequential case. We prove that the random selection of keys generates a binomial distribution of them between leaves, that the synchronized insertions of keys can be modeled by a Markov chain, and that the coefficients of the transition matrix of the Markov Chain are related with the expected local behavior of our algorithm. Finally, we show that the coefficients of the power expansion of this matrix over (n+1)^{-1} are the binomial transform of the expected local behavior of the algorithm.Postprint (published version

Efficient Parallel Algorithms and Data Structures Related to Trees

The main contribution of this dissertation proposes a new paradigm, called the parentheses matching paradigm. It claims that this paradigm is well suited for designing efficient parallel algorithms for a broad class of nonnumeric problems. To demonstrate its applicability, we present three cost-optimal parallel algorithms for breadth-first traversal of general trees, sorting a special class of integers, and coloring an interval graph with the minimum number of colors

The Lexiculture Papers: English Words and Culture

The Lexiculture Papers is a collection of scholarship on English words and culture. Each of the 62 chapters was originally authored by a student-scholar in the course, Language and Culture, at Wayne State University, between 2013 and 2020. Each chapter is a short social and historical description of a single English word in its cultural context, principally since 1800. Using a combination of historical linguistics, etymology, corpus linguistics, and discourse analysis, the papers analyze English-speaking social life through the lens of specific words

Creating a Concurrent In-Memory B-Tree Optimized for NUMA Systems

The size of main memory is becoming larger. With the number of Central Processing Unit (CPU) cores ever increasing in modern systems, with each of them being able to access memory, the organization of memory becomes more important. In multicore systems, there are two main architectures for memory organization with respect to the cores - Symmetric Multi-Processor (SMP) and Non-Uniform Memory Architecture (NUMA). Prior work has focused on the improvement of the performance of B-Trees in highly concurrent and distributed environments, as well as in memory, for shared-memory mul- tiprocessors. However, little focus has been given to the performance of main memory B-Trees for NUMA systems. This work focuses on improving the performance of B-Trees contained in main memory of NUMA systems by introducing modifications that consider its storage in the physically distributed main memory of the NUMA system. The work in this thesis makes the following contributions to the development of a distributed B-Tree, specifically in a NUMA environment, modified from a B-Tree originally designed for high concurrency: • It introduces replication of internal nodes of the tree and shows how this can improve its overall performance in a NUMA environment. • It introduces NUMA-aware locking procedures with the aim of managing contention and exploiting locality of lock requests with reference to previous client operation request locations. • It introduces changes in the granularity of locking, starting from the original locking of every node to the locking of certain levels of nodes, showing the tradeoff between the granularity of locking and the performance of the tree based on the workload. • It considers the combination of the different techniques, with the aim of finding the combination which performs well overall for varying read-heavy workloads and number of client threads

The Advocate - April 5, 1958

Original title (1951-1987)--The Advocate: official publication of the Archdiocese of Newark (N.J.)

The Advocate - April 5, 1958

Original title (1951-1987)--The Advocate: official publication of the Archdiocese of Newark (N.J.)

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum