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检索条件"主题词=Polyhedral algorithm"

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Scheduling Independent Tasks under Contiguity Constraint : A polyhedral algorithm Based-Approach for Determining and Comparing all Optimal Solutions 14

Scheduling Independent Tasks under Contiguity Constraint : A...

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14th International Conference on High Performance Computing & Simulation (HPCS)

作者： Salhi, Hajer Mahjoub, Zaher Univ Tunis el Manar Fac Sci Tunis Tunis Tunisia

ISBN: (纸本)9781509020881

We present in this paper a 3-phase approach (3PA) for both determining and comparing all optimal solutions (OSs) of a specific combinatorial optimization problem, namely scheduling independent tasks under contiguity constraint a particular formulation of the general ID Array partitioning problem (1D-APP). The first phase consists in constructing the 1D-APP search space i.e. the set involving all possible solutions. This is done through the design of a specific polyhedral algorithm (PA) i.e. a FOR loop nest with affine loop bounds whose iteration space (IS) is in fact the concerned search space. Since this IS that has to be later scanned may be of large cardinality i.e. exponential in terms of the problem size in the worst case, successive loop bounds tightenings based on the knowledge of an initial OS are applied to the initial PA. This leads to a new PA whose IS is of reduced cardinality that may be restricted, in the best case, to the number of OSs. The second phase consists in extracting all OSs through scanning the new IS. Finally, once precise comparison criteria are specified and sorted, we proceed to the third phase which permits to establish a discriminating comparative study of the OSs according to the chosen criteria. A series of experiments are achieved in order to validate the approach and evaluate its practical interest as well as its robustness.

关键词： ID Array partition problen combinatorial optimization For loop nest iteration space multicriteria analysis optimal solution optimization criterion polyhedral algorithm

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Performance Evaluation of a Parallel algorithm for Determining all Optimal Solutions of the 1D Array Partitioning Problem 14

Performance Evaluation of a Parallel Algorithm for Determini...

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14th IEEE/ACS International Conference on Computer Systems and Applications (AICCSA)

作者： Salhi, Hajer Ben Mabrouk, Bchira Mahjoub, Zaher Univ Tunis El Manar Fac Sci Tunis URAPOP Univ Campus 2092 Manar 2 Tunis Tunisia

ISBN: (纸本)9781538635810

We address the parallelization of the determination of all optimal solutions (DAOS) for the 1D array partitioning problem, an easy combinatorial optimization problem that may be solved by dynamic programming. It turns out that the designed DAOS algorithm is a polyhedral algorithm (PA), i.e. a FOR-loop nest with affine loop bounds, whose iteration space that has to be scanned may be of exponential cardinality in the array size hence too time consuming. Thus, after a cardinality reducing procedure leading to an improved PA (IPA), we propose to parallelize the IPA through a specific approach. This latter first consists in a dependence analysis within the IPA leading to detect that all its loops are parallel. We then apply a loop interchange on the IPA in order to have a new IPA whose first loop has the largest number of parallel iterations. Another alternative consists in moving to the first position the loop whose number of iterations is the closest to the number of available processors. We detail an analysis of the theoretical performances of the derived parallel IPA by proposing several versions fitting the number of available processors and reducing the overhead due to processor synchronizations.

关键词： 1D Array partitioning problem combinatorial optimization loop interchange optimal solution parallelization polyhedral algorithm strip mining

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Performance Evaluation of a Parallel Dynamic Programming algorithm for Solving the Matrix Chain Product Problem 11

Performance Evaluation of a Parallel Dynamic Programming Alg...

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11th IEEE/ACS International Conference on Computer Systems and Applications (AICCSA)

作者： Ben Mabrouk, Bchira Hasni, Hamadi Mahjoub, Zaher Univ Carthage Higher Inst Appl Sci & Technol Mateur 7030 Tunisia Univ Campus Manouba Natl Sch Comp Sci Manouba 2010 Tunisia Univ Tunis El Manar Fac Sci Tunis Tunis 2092 Tunisia

ISBN: (纸本)9781479971008

We address in this paper a particular combinatorial optimization problem (COP) namely the matrix chain product problem (MCPP). We particularly consider the parallelization of the dynamic programming algorithm (DPA) for solving the MCPP which is structured in a DO loop nest of depth 3. Our approach is based on a three-phase procedure. The first consists in transforming the DPA into a perfect loop nest (PLN). The second applies a dependency analysis within the initial PLN permitting the determination of the type of each loop (serial or parallel). As to the third phase, it applies on the initial PLN the loop interchange technique in order to increase the parallelism degree. We focus in this paper on an experimental study achieved on a parallel multicore machine that permits to validate our theoretical contribution.

关键词： combinatorial optimization problem dependence analysis DO loop nest dynamic programming loop interchange matrix chain product multicore machine parallelization performance evaluation polyhedral algorithm

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On a Parallel algorithm for the Determination of Multiple Optimal Solutions for the LCSS Problem 16th

On a Parallel Algorithm for the Determination of Multiple Op...

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16th International Conference on algorithms and Architectures for Parallel Processing (ICA3PP)

作者： Ben Mabrouk, Bchira Hasni, Hamadi Mahjoub, Zaher Univ Tunis El Manar Fac Sci Tunis Univ CampusManar 2 Tunis 2092 Tunisia Higher Sch Technol & Comp Sci Charguia 2 Tunis 2035 Tunisia

ISBN: (纸本)9783319495835;9783319495828

For particular real world combinatorial optimization problems e.g. the longest common subsequence problem (LCSSP) from Bioinformatics, determining multiple optimal solutions (DMOS) is quite useful for experts. However, for large size problems, this may be too time consuming, thus the resort to parallel computing. We address here the parallelization of an algorithm for DMOS for the LCSSP. Considering the dynamic programming algorithm solving it, we derive a generic algorithm for DMOS (A-DMOS). Since the latter is a non perfect DO-loop nest, we adopt a three-step approach. The first consists in transforming the A-DMOS into a perfect nest. The second consists in choosing the granularity and the third carries out a dependency analysis in order to determine the type of each loop i.e. either parallel or serial. The practical performances of our approach are evaluated through experimentations achieved on input benchmarks and random DNA sequences and targeting a parallel multicore machine.

关键词： Bioinformatics Combinatorial optimization problem Dependency analysis Dynamic programming Longest common subsequence Loop nest Multiple optimal solutions Multicore machine Parallelization polyhedral algorithm

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