A Case for Strongly Polynomial Time Sub-Polyhedral Scheduling Using Two-Variable-Per-Inequality Polyhedra

Ramakrishna Upadrasta 1 Albert Cohen 1
1 Parkas - Parallélisme de Kahn Synchrone
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : We make a case for sub-polyhedral scheduling using (Unit-)Two-Variable-Per-Inequality or (U)TVPI Polyhedra. We empirically show that using general convex polyhedra leads to a scalability problem in a widely used polyhedral scheduler. We propose methods in which polyhedral schedulers can beat the scalability challenge by using sub-polyhedral under-aproximations of the polyhedra resulting from the application of the affine form of the Farkas lemma. We propose simple algorithms that under-approximate a general polyhedra into (U)TVPI polyhedra. These algorithms take worstcase polynomial time. We implement the above approximation algorithms in a modified PLuTo, and show that for a majority of the Polybench 2.0 kernels, the above under-approximation yield polyhedra that are non-empty. We also provide preliminary evidence that code generated by our sub-polyhedral parallelization prototype matches the performance of PLuTo-optimized code when the under-approximation preserves feasibility.
Keywords : Approximation Algorithms Complexity Theory Compilers Optimization Geometric Algorithms
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Conference papers
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https://hal.inria.fr/hal-00786832
Contributor : Albert Cohen <>
Submitted on : Sunday, February 10, 2013 - 8:21:28 PM
Last modification on : Wednesday, January 30, 2019 - 11:07:34 AM

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Ramakrishna Upadrasta, Albert Cohen. A Case for Strongly Polynomial Time Sub-Polyhedral Scheduling Using Two-Variable-Per-Inequality Polyhedra. IMPACT 2012 - 2nd Workshop on Polyhedral Compilation Techniques (associated with HiPEAC), Jan 2012, Paris, France. 2012. 〈hal-00786832〉

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