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 PRAM MEMORY ALLOCATION AND INITIALIZATION

1993 ◽  
Vol 03 (03) ◽  
pp. 291-299 ◽  
Author(s):  
LISA HIGHAM ◽  
ERIC SCHENK
Keyword(s):  
Random Access ◽  
Constant Factor ◽  
The Other ◽  
Memory Allocation ◽  
Random Access Machine ◽  
Erew Pram ◽  
Crew Pram ◽  
Parallel Random Access Machine

Two techniques for managing memory on a parallel random access machine (PRAM) are presented. One is a scheme for an n/log n processor EREW PRAM that dynamically allocates and deallocates up to n records of the same size in O(log n) time. The other is a simulation of a PRAM with initialized memory by one with uninitialized memory. A CREW PRAM variant of the technique justifies the assumption that memory can be assumed to be appropriately initialized with no asymptotic increase in time but a factor of n increase in space. An EREW PRAM solution incurs a factor of O(log n) increase in time but only a constant factor increase in space.

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

PARALLEL ALGORITHMS FOR SOME DOMINANCE PROBLEMS BASED ON THE PRAM MODEL

1993 ◽  
Vol 03 (04) ◽  
pp. 367-382
Author(s):  
I.W. CHAN ◽  
D.K. FRIESEN
Keyword(s):  
Computational Model ◽  
Single Point ◽  
Random Access ◽  
Geometric Algorithms ◽  
Counting Problem ◽  
Erew Pram ◽  
Pram Model ◽  
Input Size ◽  
Parallel Random Access Machine ◽  
Direct Dominance

Two parallel geometric algorithms based on the idea of point domination are presented. The first algorithm solves the d-dimensional isothetic rectangles intersection counting problem of input size N/2d, where d>1 and N is a multiple of 2d, in O( log d−1 N) time and O(N log N) space. The second algorithm solves the direct dominance reporting problem for a set of N points in the plane in O( log N+J) time and O(N log N) space, where J denotes the maximum of the number of direct dominances reported by any single point in the set. Both algorithms make use of the EREW PRAM (Exclusive Read Exclusive Write Parallel Random Access Machine) consisting of O(N) processors as the computational model.

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.

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.

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