Abstract
The tree structured optimization problems encountered in operations research are difficult to parallelize, because the two goals ‘minimization of processor idle times’ and ‘minimization of communication overheads’ cannot both be dealt with efficiently at the same time. We have presented a number of methods to solve the dynamic embedding problem necessary to map the dynamic tree arising during computation onto a distributed computing system.
A number of methods were investigated in more detail. We presented three search schemes with different characteristics:
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a best-first branch & bound search for the Vertex Cover Problem and TSP
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a depth-first branch & bound search with search-frontier splitting for VLSI floor-plan optimization
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an iterative depth-first search with dynamic tree splitting for the N×N puzzle
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an iterative depth-first search with search-frontier splitting for the N×N puzzle
Considerable speedup for all problems even on a large scale computing system connecting 1024 processor could be achieved using the methods presented. The efficiency of the methods was presented by solving small problems. Proving good scalability for these small problems, one can argue that the methods will provide even better scalability features for practical applications using much longer computation times for most cases.
This work was partly supported by the EC Esprit Basic Research Action Nr. 7141 (ALCOM II), the EC Human Capital and Mobility Project: “Efficient Use of Parallel Computers: Architecture, Mapping and Communication (MAP)” and by the EU Human Capital and Mobility Project “Solving combinatorial optimization problems in parallel (SCOOP)”
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Lüling, R., Monien, B., Reinefeld, A., Tschöke, S. (1996). Mapping tree-structured combinatorial optimization problems onto parallel computers. In: Ferreira, A., Pardalos, P. (eds) Solving Combinatorial Optimization Problems in Parallel. Lecture Notes in Computer Science, vol 1054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027120
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