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 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.

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.

On the use of inaccessible numbers and order indiscernibles in lower bound arguments for random access machines

1988 ◽  
Vol 53 (4) ◽  
pp. 1098-1109 ◽  
Author(s):  
Wolfgang Maass
Keyword(s):  
Mathematical Logic ◽  
Lower Bound ◽  
Computational Model ◽  
Lower Bounds ◽  
Special Interest ◽  
Random Access ◽  
Computation Time ◽  
Test Problems ◽  
Random Access Machine

AbstractWe prove optimal lower bounds on the computation time for several well-known test problems on a quite realistic computational model: the random access machine. These lower bound arguments may be of special interest for logicians because they rely on finitary analogues of two important concepts from mathematical logic: inaccessible numbers and order indiscernibles.

PARALLEL RECOGNITION OF HIGH DIMENSIONAL IMAGES

1992 ◽  
Vol 06 (02n03) ◽  
pp. 285-291 ◽  
Author(s):  
M. NIVAT ◽  
A. SAOUDI
Keyword(s):  
Time Complexity ◽  
Random Access ◽  
Space Complexity ◽  
Recognition Problem ◽  
High Dimensional ◽  
Context Free Grammar ◽  
Random Access Machine ◽  
Parallel Random Access Machine ◽  
Context Free ◽  
Context Free Grammars

We investigate the complexity of the recognition of images generated by a class of context-free image grammars. We show that the sequential time complexity of the recognition of an n × n image as generated by a context-free grammar is O(nM(n)), where M(n) is the time to multiply two boolean n × n matrices. The space complexity of this recognition is O(n3). Using a parallel random access machine (i.e. PRAM), the recognition can be done in O( log 2(n)) time with n7 processors or in O(n log 2(n)) time with n6 processors. We also introduce high dimensional context-free grammars and prove that their recognition problem is polylogarithmic.

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.

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