Efficient grid based techniques for solving the weighted region least cost path problem on multicomputers.

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by  Ekin, Cengiz.;Zaky, Amr M.

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11 TITLE (IncludeSecuntyClassification)
EFFICIENTGRIDBASEDTECHNIQUESFORSOLVINGTHEWEGHTEDREGIONLEASTCOSTPATHPROBLEMON MULTICOMPUTERS
(UNCLASSIFIED)
mm^^"""^
.engiz
13a. TYP^ C£,FREPORT 13b. TIME COVERED 14 DATE OF REPORT(Year. Month. Day) 15 PAGEHOUNT
Master s Thesis FROM TO December 1992 100
16. SUPPLEMENTARY NOTATioffhe views expressed in this thesis are those ofthe author and do not reflect the ott'icial
policy or position of the Department of Defense or the United States GovemmenL
17, COSATI CODES 18 SUBJECTTERMS(Continueonreverseifnecessaryandidentifybyblocknumber)
Numerical Path Planning, Weigted Regions, Grid Based Techniques,
FIELD GROUP SUB-GROUP
Transputers, Distributed Computing, Parallel Processing,
19. ABSTRACT (Continueonreverseifnecessaryandidentifybyblocknumber)
This thesis explores the possibilities ofdeveloping fast grid-based parallel algorithms to solve the Weighted
Region Least Cost Path problem. Two complementary steps have been undertaken. First, an efficient sequential
algorithm to solve the above problem was developed. The algorithm is a modification of a Gauss-Seidel-like
algorithm for obtaining the minimum costs. The most salient feature of the algorithm is the reduction of the numb(
of nodes and edges in cheaper regions of the grid. The reported experimental results ascertain the superiority of th
algorithm with regard to computer running time at a modest reduction in the accuracy of the obtained solution.
Parallel implementations of grid-based algorithms were studied. A simple grid-based variant was implemented on
network of Transputers. The overall approach employed could be used to develop a parallel version of the above S(
quential algorithm on a Transputer network, combining both advantages ofefficiency and parallelism.
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Efficient GridBased Techniques ForSolving
The WeightedRegion Least CostPath
Problem On Multicomputers
by
Cengiz EKIN
LTJGTurkish Navy
B.S.Turkish Naval WarAcademy,]986
Submitted in partial fulfillment ofthe
requirements for the degree of
MASTER OF SCIENCE IN ENGINEERING SCIENCE
from the
NAVAL POSTGRADUATE SCHOOL
December 1992
ABSTRACT
This thesis explores the possihilities (if developing f;ist grid-lnised p;u;illel iilgoiithms to
solve the Weighted Region Least Cost F'ath pn)hlen). I'wo coiDplenientaiy ste[is have been
nndeitaken, litst. an efficient secjucntial algoiithni to solve the above pioblein was devel-
oped. The algoiithni is a inodification of a Cianss-Seidel-like algoiithin for obtaining the
ininiinnm costs. The most .salient fcatiiie of the algoiithin is the leduction of the luiinber of
nodes and edges in cheaper regions of the grid. I'he leported experiiTiental lesults astcitain
the snperiority ofthis algorithm with regaid to computer running time at a modest reduction
in the accuracy ofthe obtained solution. Parallel implementations of grid-based algorithms
were studied. A simple grid-based variant was implemented on a network of Iianspulers.
The oveiall approach employed could be used to develop a parallel version of the above
se(|ueiitial algorithm on a Transputer network, combining both advantages of efficiency
and parallelism.
Ill
I
.
c.I
TABLE OF CONTENTS
INTRODUCTION
I 1
.
A GENERAL
1
.
B THESIS OUTLINE 2
.
BACKGROUND
I . 3
A. SINGLE SOURCE SHORTEST PATHS (SSSP) 3
1. Dijktra's Algorithm 3
2. Parallelization Of SSSP 5
B RAY TRACING 6
.
1. Snell's Law Of Refraction 6
Implementation
2 7
.
Parallelization
3 8
.
C EDGE SLICING 9
.
Implementation
1 9
2. Parallelization 9
,
D GRID ALGORITHMS .' 9
.
1 The Wavefront Variant 10
.
2 Relaxation-Based Approach 12
.
a. Implementation 13
b. Parallelization 17
5
.
III. A MODIFIED GRID ALGORITHM 21
A INTRODUCTION 21
,
B. VARIABLE GRID SIZE APPROACH 21
C RESULTS 24
.
D DRAWBACKS 2 5
.
IV THE ENVIRONMENT 31
.
A TRANSPUTER 31
.
B . ALSYS ADA 33
Channels
1 . 3 3
2 Harnesses 34
.
C GUIDE TO PROGRAM DEVELOPMENT 34
.
1. MAKE program maintenance Utility 35
2 Checking Tools 35
.
3. Examples in Steps of Instructions 35
V. A MULTICOMPUTER ALGORITHM 40
A IMPLEMENTATION 4
B. A VARIANT ALGORITHM THAT SAVES ON COMMUNICATION ... 43
VI. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH. 4
LIST OF REFERENCES 47
APPENDIX A - SEQUENTIAL ALGORITHM SOURCE CODE 5
APPENDIX B - MODIFIED ALGORITHM SOURCE CODE 58
APPENDIX C - PARALLEL ALGORITHM SOURCE CODE 72
INITIAL DISTRIBUTION LIST 91
LIST OF FIGURES
Figure 1: Dijkstra's Algorithm 3
,
Figure 2: An Example Of The SSSP Algorithm 4
Figure 3: Parallelized SSSP Algorithm Example 6
Figure 4: Snell's Law Of Refraction 7
Figure 5 Ray Tracing 8
:
Figure 6: Edge Slicing (2-P(iint) 10
Figure 7 Neighbors In Grid Algoithm. 11
: . .
Figure 8 Wavefront Technique 12
:
Figure 9; A Node Described With Its Neighbors
And Their Relations 14
Figure 10: Data Structure 15
Figure 11: The Pseudocode For Relaxation-Based Algorithm. 16
Figure 12.a: Example For Relaxation-Based Algorithm
The Values Inside The Nodes Are The
Heights 18
Figure 12.b: Example For Relaxation-Based Algorithm
The Values In The Nodes Are The Initial
Costs From The Source 19
Figure 12.c: Example For Relaxation-Based Algorithm
The Values Inside The Nodes Are The
Minimum Costs From The Source 20
Figure 13: The Pseudocode for Modified Grid Algorithm 22
VI