PARALLEL RANDOM ACCESS MACHINES WITHOUT BOOLEAN OPERATIONS

1994 ◽  
Vol 04 (01n02) ◽  
pp. 117-124
Author(s):  
JERRY L. TRAHAN ◽  
HOSANGADI BHANUKUMAR
Keyword(s):  
Significant Contribution ◽  
Random Access ◽  
Instruction Set ◽  
Boolean Operations ◽  
Models Of Computation ◽  
Random Access Machine ◽  
Parallel Random Access Machine

The class of problems solved within given time and processor bounds on a Parallel Random Access Machine (PRAM) varies with the instruction set. Previous research has classified the contributions of various instructions, such as multiplication, shifts, and string manipulation operations, to the PRAM. This paper examines the significant contribution of Boolean operations, which play essential roles in many PRAM algorithms and in simulations by the PRAM of other models of computation.

Transforming comparison model lower bounds to the parallel-random-access-machine

1997 ◽  
Vol 62 (2) ◽  
pp. 103-110 ◽  
Author(s):  
Dany Breslauer ◽  
Artur Czumaj ◽  
Devdatt P. Dubhashi ◽  
Friedhelm Meyer auf der Heide
Keyword(s):  
Lower Bounds ◽  
Random Access ◽  
Comparison Model ◽  
Random Access Machine ◽  
Parallel Random Access Machine

scholarly journals Tables should be sorted (on random access machines)

1995 ◽  
Vol 2 (26) ◽  
Author(s):  
Faith Fich ◽  
Peter Bro Miltersen
Keyword(s):  
Random Access ◽  
Binary Search ◽  
Query Time ◽  
Instruction Set ◽  
Element Subset ◽  
Worst Case ◽  
Model Of Computation ◽  
Membership Queries ◽  
Standard Instruction ◽  
Random Access Machine

We consider the problem of storing an n element subset S of a universe<br />of size m, so that membership queries (is x in S?) can be answered<br />efficiently. The model of computation is a random access machine with<br />the standard instruction set (direct and indirect addressing, conditional<br />branching, addition, subtraction, and multiplication). We show that if s<br />memory registers are used to store S, where n <= s <= m/n^epsilon, then query<br />time  Omega(log n) is necessary in the worst case. That is, under these conditions,<br />the solution consisting of storing S as a sorted table and doing<br />binary search is optimal. The condition s <= m/n^epsilon is essentially optimal;<br />we show that if n + m/n^o(1) registers may be used, query time o(log n) is<br />possible.

A Simple Optimal Parallel Algorithm for Reporting Paths in a Tree

1997 ◽  
Vol 07 (01) ◽  
pp. 3-11 ◽  
Author(s):  
Andrzej Lingas ◽  
Anil Maheshwari
Keyword(s):  
Parallel Algorithm ◽  
Random Access ◽  
Input Tree ◽  
Single Pair ◽  
Random Access Machine ◽  
Erew Pram ◽  
Parallel Random Access Machine ◽  
Path Queries

We present optimal parallel solutions to reporting paths between pairs of nodes in an n-node tree. Our algorithms are deterministic and designed to run on an exclusive read exclusive write parallel random-access machine (EREW PRAM). In particular, we provide a simple optimal parallel algorithm for preprocessing the input tree such that the path queries can be answered efficiently. Our algorithm for preprocessing runs in O( log n) time using O(n/ log n) processors. Using the preprocessing, we can report paths between k node pairs in O( log n + log k) time using O(k + (n + S)/ log n) processors on an EREW PRAM, where S is the size of the output. In particular, we can report the path between a single pair of distinct nodes in O( log n) time using O(L/ log n) processors, where L denotes the length of the path.

scholarly journals Transforming Comparison Model Lower Bounds to the PRAM

1995 ◽  
Vol 2 (10) ◽  
Author(s):  
Dany Breslauer ◽  
Devdatt P. Dubhashi
Keyword(s):  
Decision Tree ◽  
Lower Bounds ◽  
Random Access ◽  
Decision Tree Model ◽  
Tree Model ◽  
Machine Model ◽  
Comparison Model ◽  
Random Access Machine ◽  
Input Domain ◽  
Parallel Random Access Machine

This note provides general transformations of lower bounds in Valiant's<br />parallel comparison decision tree model to lower bounds in the priority<br />concurrent-read concurrent-write parallel-random-access-machine model.<br />The proofs rely on standard Ramsey-theoretic arguments that simplify<br />the structure of the computation by restricting the input domain. The<br />transformation of comparison model lower bounds, which are usually easier<br />to obtain, to the parallel-random-access-machine, unifies some known<br />lower bounds and gives new lower bounds for several problems.

ANALYSIS OF PRAM INSTRUCTION SETS FROM A LOG COST PERSPECTIVE

1994 ◽  
Vol 05 (03n04) ◽  
pp. 231-246
Author(s):  
JERRY L. TRAHAN ◽  
SUNDARARAJAN VEDANTHAM
Keyword(s):  
Parallel Machines ◽  
Unit Cost ◽  
Random Access ◽  
Complexity Classes ◽  
Turing Machines ◽  
Instruction Set ◽  
Instruction Sets ◽  
Parallel Random Access Machine ◽  
Bounded Complexity ◽  
Crcw Pram

The log cost measure has been viewed as a more reasonable method of measuring the time complexity of an algorithm than the unit cost measure. The more widely used unit cost measure becomes unrealistic if the algorithm handles extremely large integers. Parallel machines have not been examined under the log cost measure. In this paper, we investigate the Parallel Random Access Machine under the log cost measure. Let the instruction set of a basic PRAM include addition, subtraction, and Boolean operations. We relate resource-bounded complexity classes of log cost PRAMs to complexity classes of Turing machines and circuits. We also relate log cost PRAMs with different instruction sets by simulations that are much more efficient than possible in the unit cost case. Let LCRCWk(CRCWk) denote the class of languages accepted by a log cost (unit cost) basic CRCW PRAM in O( log k n) time with the polynomial in n number of processors. We position the log cost PRAM in the hierarchy of parallel complexity classes as: ACk=CRCWk⊆(NCk+1, LCRCWk+1)⊆ACk+1=CRCWk+1.

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