Thesis: On the development of numerical parallel algorithms for the insetting procedure Master of...
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Transcript of Thesis: On the development of numerical parallel algorithms for the insetting procedure Master of...
Thesis:On the development of numerical
parallel algorithms for the insetting procedure
Master of Science in Communication & Information Systems
Department of Informatics & CommunicationsTEI of Central Macedonia
Christos Christodoulou
Supervisor D.Varsamis Lecturer
Objectives
Find the optimal number of insets
Find insets with numerical Logic
The algorithm can be used not only at maps
Cartography
From Greek χάρτης hartes, "map" and γράφειν graphein, "write") is the study and practice of making maps.
Map construction is one of the oldest human activities.
According to archaeologists older projects have been and could still qualify maps dating to 30,000 years ago
Island Cartography
Deals with special cartographic problems The need of inset map creation for very small islands
sometimes isolated ones
Must be displayed in the main map Key factor for insetting in Island is the “complexity of
land discontinuity”
Example Map Chalkidiki
Existing Method
Algorithm Calculate the Q
correlation Uses standard frames Search step by step all
the map
Example
Step 1
Step 2
Step 3
Numerical Algorithm
Find insets without searching with standard frames Calculate the maximum Q correlation that the
selection area can be maximized Uses only addition of the map pixels
Numerical Algorithm example 1
Example map Rasterized Map
At this example we use a matrix 4 x 8, inset selection 1x1 and q=3.
Numerical Algorithm example 2
Count zeros for each row an increase the row counter
When it finds ones reset the counter until find zero again
Numerical Algorithm example 3
Count the threes for each column an increase the column counter
When it finds different number reset the counter until find three again
Numerical Algorithm example 4
At the final Matrix we just search if it has the q*im = 3
Parallel implementation
Parallel implementation
Implementation Cases
Many ways and execution scenarios SPMD Tasks
Examine two scenarios N ( accuracy ) according to number of workers N (accuracy ) has the maximum value
Case 1 N = Workers
map N Labs Time sec Insets q Inset Dim.
50.tif 8 8 4.442 920 2 50x50
50.tif 16 16 5.506 29 2.297 50x50
50.tif 32 32 7.418 29 2.287 50x50
50.tif 64 64 11.941 29 2.283 50x50
As we can see at the results the time increases as we increase the number of workers instead of reducing. This is happened because we have delay for the communication time.
Workers - Time
Case 2 N stable
map N Labs Time sec Insets q Inset Dim.
50.tif 64 1 20.761 29 2.283 50x50
50.tif 64 4 18.830 29 2.283 50x50
50.tif 64 8 11.369 29 2.283 50x50
50.tif 64 16 8.485 29 2.283 50x50
50.tif 64 32 8.399 29 2.283 50x50
50.tif 64 64 11.359 29 2.283 50x50
Workers-Time ( N stable)
N stable Speed Up - Efficiency
1-core 4-cores 8-cores 16-cores 32-cores 64-
cores
S 1.0000 1.1025 1.8261 2.4467 2.4718 1.8277
E 1.0000 0.2756 0.2282 0.1529 0.0772 0.1848
Workers-Speed Up ( N stable)
Workers-Efficiency N stable
Conclusion
The theoretical computational time of the numerical parallel algorithm is almost the same with the logical parallel algorithm.
The efficiency of the numerical algorithm is in general very good, helping the cartographers who use the algorithm to reduce its execution time in a local machine with multicore processor or to a grid computer.
Future Work
Use different methods for parallel implementation SMPMD Tasks
Transform the algorithm to a web-based application in parallel architecture distributed memory in a network of computers or in a grid computer