Sort Integers into a Linked List

We show that n integers in {0, 1, …, m-1} can be sorted into a linked list in constant time using nlogm processors on the Priority CRCW PRAM model, and they can be sorted into a linked list in O(loglogm/logt) time using nt processors on the Priority CRCW PRAM model.

FAILURE-SENSITIVE ANALYSIS OF PARALLEL ALGORITHMS WITH CONTROLLED MEMORY ACCESS CONCURRENCY

The abstract problem of using P failure-prone processors to cooperatively update all locations of an N-element shared array is called Write-All. Solutions to Write-All can be used iteratively to construct efficient simulations of PRAM algorithms on failure-prone PRAMS. Such use of Write-All in simulations is abstracted in terms of the iterative Write-All problem. The efficiency of the algorithmic solutions for Write-All and iterative Write-All is measured in terms of work complexity where all processing steps taken by the processors are counted. This paper considers determinitic solutions for the Write-All and iterative Write-All problems in the fail-stop synchronous CRCW PRAM model where memory access concurrency needs to be controlled. A deterministic algorithm of Kanellakis, Michailidis, and Shvartsman [16] efficiently solves the Write-All problem in this model, while controlling read and write memory access concurrency. However it was not shown how the number of processor failures f affects the work efficiency of the algorithm. The results herein give a new analysis of the algorithm [16] that obtain failure-sensitive work bounds, while retaining the known memory access concurrency bounds. Specifically, the new result expresses the work bound as a function of N, Pandf. Another contribution in this paper is the new failure-sensitive analysis for iterative Write-All with controlled memory access concurrency. This result yields tighter bounds on work (vs. [16]) for simulations of PRAM algorithms on fail-stop PRAMS.

TIME OPTIMAL n-SIZE MATCHING PARENTHESES AND BINARY TREE DECODING ALGORITHMS ON A p-PROCESSOR BSR

Time optimal algorithms on an n-processor BSR PRAM for many n-size problems can be found in the literature. They outpace those on EREW, CREW or CRCW PRAM for the same problems. When only p (1 < p < n) processors are available, efficient algorithms on a p-processor BSR for some n-size problems can not be obtained from those on an n-processor BSR, and they have to be reconsidered. In this paper, we discuss and give two algorithms on a p-processor BSR for the two n-size problems of matching parentheses and decoding a binary tree from its bit-string, respectively, and show that they are time optimal.

PARALLEL ALGORITHMS FOR HAMILTONIAN 2-SEPARATOR CHORDAL GRAPHS

In this paper we propose a parallel algorithm to construct a one-sided monotone polygon from a Hamiltonian 2-separator chordal graph. The algorithm requires O( log n) time and O(n) processors on the CREW PRAM model, where n is the number of vertices and m is the number of edges in the graph. We also propose parallel algorithms to recognize Hamiltonian 2-separator chordal graphs and to construct a Hamiltonian cycle in such a graph. They run in O( log 2 n) time using O(mn) processors on the CRCW PRAM model and O( log 2 n) time using O(m) processors on the CREW PRAM model, respectively.

OPTIMALLY FAST CRCW-PRAM TESTING 2D-ARRAYS FOR EXISTENCE OF REPETITIVE PATTERNS

In classical combinatorial string matching repetitions and other regularities play a central role. Besides their theoretical importance, repetitions in strings have been found relevant to coding and automata theory, formal languages, data compression, and molecular biology. An important motivation for developing a 2D pattern matching theory is seen in its relation with pattern recognition, image processing, computer vision and multimedia. Repetitions in 2D arrays have been defined and classified recently.5 In this paper we present an optimally fast CRCW-PRAM algorithm for testing whether a given n × n array contains repetitions of certain type. The algorithm takes optimal O( log log n) time with [Formula: see text] processors.

NC ALGORITHMS FOR THE SINGLE MOST VITAL EDGE PROBLEM WITH RESPECT TO ALL PAIRS SHORTEST PATHS

For a weighted, undirected graph G=(V, E) where |V|=n and |E|=m, we examine the single most vital edge with respect to all-pairs shortest paths (APSP) under two different measurements. The first measurement considers only the impact of the removal of a single edge from the APSP on the shortest distance between each vertex pair. The second considers the total weight of all the edges which make up the APSP, that is, calculate the sum of the distance between each vertex pair after the deletion of any edge belonging to a shortest path. We give a sequential algorithm for this problem, and show how to obtain an NC algorithm running in O( log n) time using mn2 processors and O(mn2) space on the MINIMUM CRCW PRAM. Given the shortest distance between each pair of vertices u and v, the diameter of the graph is defined as the longest of these distances. The Most vital edge with respect to the diameter is the edge lying on such a u–v shortest path which when removed causes the greatest increase in the diameter. We show how to modify the above algorithm to solve this problem using the same time and number of processors. Both algorithms compare favourably with the straightforward solution which simply recalculates the all pairs shortest path information.