Parallel Merging and Sorting on Linked List

We study linked list sorting and merging on the PRAM model. In this paper we show that n real numbers can be sorted into a linked list in constant time with n2+e processors or in ) time with n2 processors. We also show that two sorted linked lists of n integers in {0, 1, …, m}  can be merged into one sorted linked list in O(log(c)n(loglogm)1/2) time using n/(log(c)n(loglogm)1/2)  processors, where c is an arbitrarily large constant

An Arbitrary CRCW PRAM Algorithm for Sorting Integers Into a LinkedList and Chaining on a Trie

Title from PDF of title page viewed June 1, 2020Thesis advisor: Yijie HanVitaIncludes bibliographical references (pages 22-23)Thesis (M.S.)--School of Computing and Engineering. University of Missouri--Kansas City, 2020The research work comprises of two parts. Part one is using an Arbitrary CRCW PRAM algorithm for sorting integers into a linked list. There are various algorithms and techniques to sort the integers in LinkedList. Arbitrary CRCW PRAM model, being the weakest model is able to sort n integers in a LinkedList in “constant time” using nlogm processors and if we use nt processors, then it can be sorted in O(loglogm/logt) time by converting Arbitrary CRCW PRAM model to Priority CRCW PRAM model. Part two is Chaining on a Trie. This research paper solves the problem of chaining on a Trie by providing more efficient complexity. This Algorithm takes “constant time” using n(logm+1) processors to chain the nodes on a Trie for n input integers on the Arbitrary CRCW PRAM model.Introduction -- Sort integers into a linked list -- Chaining on a Trie --Conclusio

Qualitative Software Engineering and Parallel Sorting Algorithm for Real Numbers

Title from PDF of title page viewed January 30, 2019Thesis advisor: Yijie HanVitaIncludes bibliographical references (pages 24-25)Thesis (M.S.)--School of Computing and Engineering. University of Missouri--Kansas City, 2018The research work consists of two parts. Part one is about qualitative software engineering and Event-B modelling for class and Use case diagrams. Now a days distributed and parallel applications are most popular and are used in applications like telecommunications and aircraft systems with complex computations. It is very important to define the exact properties and features of these systems along with the workflow. UML provides a great opportunity of modelling complex applications but lacks in providing the detailed semantics. In this work, we have provided the importance of implementation of specifications using formal methods like event-B through a simple example and verify its results using ProB. Later, we have defined the UML diagrams like use case and class diagrams in various scenarios and have performed the Event B modeling for these examples. The part one report had been published as a research paper to “The 2018 International Conference on Computational Science and Computational Intelligence 2018, Las Vegas, USA”. The paper was accepted to the conference with Paper Id “CSCI6051”. Part two is on parallel Sorting algorithm on real numbers. There are various best algorithms for sorting integers. The current research work applies the recent important results of serial sorting of real numbers in (n√logn) time to the design of a parallel algorithm for sorting real numbers in O(log¹⁺ᵋn) time and (nlogn/√loglogn) operations. This is the first NC algorithm known to take o(nlogn) operations for sorting real numbers.Introduction -- Qualitative software engineering using Event-B -- A parallel sorting algorithm for real numbers -- Improved parallel sort algorithm -- Conclusio

Searching in a Sorted Linked List and Sort Integers into a Linked List

Title from PDF of title page viewed June 12, 2019Thesis advisor: Yijie HanVitaIncludes bibliographical references (pages 25-27)Thesis (M.S.)--School of Computing and Engineering. University of Missouri--Kansas City, 2019The research work consists of two parts. Part one is about Searching for an integer in a sorted Linked list. A tree is constructed in O(nloglogm/p+loglogm) time with p processors based on the trie with all the given integers. Additional nodes (O(nloglogm) of them) are added to the tree. After the tree is constructed, for any given integer we can find the predecessor and successor of the integer, insert or delete the integer in O(loglogm) time. The result demonstrates for the searching purpose we need not to sort the input numbers into a sorted array for this would need at least O(logn/loglogn) time while this algorithm for constructing the tree can run in O(loglogm) time with n processors. Part two is on sorting integers into a linked list. There are various best algorithms for sorting integers. The current research work applies the recent important results of sorting integers in Ω(logn/loglogn) time. This algorithm takes “constant time” to sort integers into a linked list with nlogm processors and O(loglogm/logt) time using nt processors on the Priority CRCW PRAM model.Introduction -- Searching in a sorted linked list -- Sort integers into a linked list -- Conclusio

Fast Computation of Small Cuts via Cycle Space Sampling

We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the cycle space identifies the cuts of a graph. This leads to simple new linear-time sequential algorithms for finding all cut edges and cut pairs (a set of 2 edges that form a cut) of a graph. In the model of distributed computing in a graph G=(V, E) with O(log V)-bit messages, our approach yields faster algorithms for several problems. The diameter of G is denoted by Diam, and the maximum degree by Delta. We obtain simple O(Diam)-time distributed algorithms to find all cut edges, 2-edge-connected components, and cut pairs, matching or improving upon previous time bounds. Under natural conditions these new algorithms are universally optimal --- i.e. a Omega(Diam)-time lower bound holds on every graph. We obtain a O(Diam+Delta/log V)-time distributed algorithm for finding cut vertices; this is faster than the best previous algorithm when Delta, Diam = O(sqrt(V)). A simple extension of our work yields the first distributed algorithm with sub-linear time for 3-edge-connected components. The basic distributed algorithms are Monte Carlo, but they can be made Las Vegas without increasing the asymptotic complexity. In the model of parallel computing on the EREW PRAM our approach yields a simple algorithm with optimal time complexity O(log V) for finding cut pairs and 3-edge-connected components.Comment: Previous version appeared in Proc. 35th ICALP, pages 145--160, 200