Thesis: On the development of numerical parallel algorithms for the insetting procedure Master of Science in Communication & Information Systems Department of Informatics & Communications TEI 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

Numerical Algorithm example 2

Numerical Algorithm example 3

Numerical Algorithm example 4

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 mapNLabsTime secInsetsqInset Dim. 50.tif x50 50.tif x50 50.tif x50 50.tif x50 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 mapNLabsTime secInsetsqInset Dim. 50.tif x50 50.tif x50 50.tif x50 50.tif x50 50.tif x50 50.tif x50

Workers-Time ( N stable)

N stable Speed Up - Efficiency 1-core4-cores8-cores16-cores32-cores64-cores S E

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