Work

Periodicity is Optimal for Offline and Online Multi-Stage Adjoint Computations

Year: 2015

Type: report

Abstract: We reexamine the work of Aupy et al. on optimal algorithms for multi-stageadjoint computations, where two levels of memories are available. Previousoptimal algorithm had a quadratic execution time. Here, with structuralarguments, namely periodicity, on the optimal solution, we provide an optimalalgorithm in constant time, with appropriate pre-processing. We also provide an asymptotically optimal algorithm for the online problem,when the adjoint graph size is not known before-hand. Again, this algorithmsrely on the proof that the optimal solution for multi-stage adjoint computationsis weakly periodic. We conjecture a closed-form formula for the period. Finally, we experimentallyaccess the convergence speed of the approximation ratio for the online problem,through simulations.

Source: HAL

Authors: Aupy, Guillaume, Herrmann, Julien

Institutions: Pennsylvania State University, Laboratoire de l'Informatique du Parallélisme, ROMA: Optimisation des ressources : modèles, algorithmes et ordonnancement

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2625037576

Cites:

Cited by:

Related to: 10