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Dual-Mode Greedy Algorithms Can Save Energy

Authors Barbara Geissmann , Stefano Leucci , Chih-Hung Liu , Paolo Penna , Guido Proietti



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Author Details

Barbara Geissmann
  • Department of Computer Science, ETH Zürich, Switzerland
Stefano Leucci
  • Department of Algorithms and Complexity, Max Planck Institute for Informatics, Germany
Chih-Hung Liu
  • Department of Computer Science, ETH Zürich, Switzerland
Paolo Penna
  • Department of Computer Science, ETH Zürich, Switzerland
Guido Proietti
  • Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università dell'Aquila, Italy
  • Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti", CNR, Roma, Italy

Acknowledgements

We are grateful to Peter Widmayer for many inspiring discussions.

Cite AsGet BibTex

Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, Paolo Penna, and Guido Proietti. Dual-Mode Greedy Algorithms Can Save Energy. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 64:1-64:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ISAAC.2019.64

Abstract

In real world applications, important resources like energy are saved by deliberately using so-called low-cost operations that are less reliable. Some of these approaches are based on a dual mode technology where it is possible to choose between high-energy operations (always correct) and low-energy operations (prone to errors), and thus enable to trade energy for correctness. In this work we initiate the study of algorithms for solving optimization problems that in their computation are allowed to choose between two types of operations: high-energy comparisons (always correct but expensive) and low-energy comparisons (cheaper but prone to errors). For the errors in low-energy comparisons, we assume the persistent setting, which usually makes it impossible to achieve optimal solutions without high-energy comparisons. We propose to study a natural complexity measure which accounts for the number of operations of either type separately. We provide a new family of algorithms which, for a fairly large class of maximization problems, return a constant approximation using only polylogarithmic many high-energy comparisons and only O(n log n) low-energy comparisons. This result applies to the class of p-extendible system s [Mestre, 2006], which includes several NP-hard problems and matroids as a special case (p=1). These algorithmic solutions relate to some fundamental aspects studied earlier in different contexts: (i) the approximation guarantee when only ordinal information is available to the algorithm; (ii) the fact that even such ordinal information may be erroneous because of low-energy comparisons and (iii) the ability to approximately sort a sequence of elements when comparisons are subject to persistent errors. Finally, our main result is quite general and can be parametrized and adapted to other error models.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • matroids
  • p-extendible systems
  • greedy algorithm
  • approximation algorithms
  • high-low energy

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