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On enhancing the deadlock-preventing object migration automaton using the pursuit paradigm

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Abstract

Probably, the most reputed solution for partitioning, which has applications in databases, attribute partitioning, processor-based assignment and many other similar scenarios, is the object migration automata (OMA). However, one of the known deficiencies of the OMA is that when the problem size is large, i.e., the number of objects and partitions are large, the probability of receiving a reward, which “strengthens” the current partitioning, from the Environment is not significant. This is because of an internal deadlock scenario which is discussed in this paper. As a result of this, it can take the OMA a considerable number of iterations to recover from an inferior configuration. This property, which characterizes learning automaton (LA) in general, is especially true for the OMA-based methods. In spite of the fact that various solutions have been proposed to remedy this issue for general families of LA, overcoming this hurdle is a completely unexplored area of research for conceptualizing how the OMA should interact with the Environment. Indeed, the best reported version of the OMA, the enhanced OMA (EOMA), has been proposed to mitigate the consequent deadlock scenario. In this paper, we demonstrate that the incorporation of the intrinsic properties of the Environment into the OMA’s design leads to a higher learning capacity and to a more consistent partitioning. To achieve this, we incorporate the state-of-the-art pursuit principle utilized in the field of LA by estimating the Environment’s reward/penalty probabilities and using them to further augment the EOMA. We also verify the performance of our proposed method, referred to as the pursuit EOMA (PEOMA), through simulation, and demonstrate a significant increase in the convergence rate, i.e., by a factor of about forty. It also yields a noticeable reduction in sensitivity to the noise in the Environment. The paper also includes some results obtained for a real-world application domain involving faulty sensors.

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Notes

  1. As we shall presently explain, it was specifically designed to learn the underlying clustering by means of “Rewards” and “Penalties” that are inferred from the way the objects are presented to the LA.

  2. The survey of the field of LA, the OPP and the OMA is necessarily brief. A more detailed exegesis is found in the doctoral thesis of the first author [15].

  3. To be consistent with the terminology of LA, we use the terms “action,” “class” and “group” synonymously.

  4. To clarify issues, consider the following example: Consider the query \(\langle 3, 4 \rangle \) in Fig. 1. Since both objects \(O_3\) and \(O_4\) reside in the same group \(G_1\), they will be rewarded and moved deeper toward the most internal state.

  5. The reader will observe that this is the total probability of \(\mathbb {E}\) presenting the pair \(\langle A_i, A_j \rangle \).

  6. In this paper, we consider the “noise” to be uniform in nature. A smaller value of p implies a higher level of noise. This quantity is chosen such that the least amount of information is provided (i.e., one with the maximum entropy) to the partitioning algorithm. Any other distribution would lead to a faster partitioning, inasmuch as pairs referring to the same underlying partition will occur more frequently.

  7. Although this was, indeed, the way that the experiments in [13] were conducted, it was not clearly communicated in that paper.

  8. The description about how the original OMA simulation was carried out is given in [16].

  9. Of course, such an Environment, although ideal, does not exist in a real-world scenario.

  10. The theorems, in and of themselves, are identical to the ones used to incorporate the pursuit paradigm into the OMA [16]. We thus merely state the results and omit the detailed formal proofs.

  11. One might argue that the order of the indices may not necessarily result in a block matrix, but rather in a sparse matrix. However, it can be easily seen that by an appropriate remapping of the indices, in which the elements of the partitioning \(\Omega ^*\) are adjacent, one can obtain such a block matrix.

  12. Extending these results for a non-uniform setting is rather trivial

  13. Of course, these estimates can be obtained using either a Maximum Likelihood or a Bayesian paradigm.

  14. Please note that the matrix can be scrambled and it is rather trivial to group the elements into blocks as it is shown in the picture.

  15. In our current implementation, whenever two objects are to be switched from their boundary states, we decide on the one to be moved by randomly tossing a coin.

  16. The simulations in this paper were performed using the ‘R’ software, and the hardware used was a PC running Windows 10 operating system with Intel Core i5 CPU with 8 GBs of RAM.

  17. The goal is that in the future [18], we will utilize, in an unsupervised manner the readings of the majority of the other remaining sensors, instead of an “Oracle,” to decide on a particular sensor’s “reliability.” After convergence has occurred, we can assume that we do not need the “Oracle” any more!

  18. We are grateful to the anonymous Referee who requested this additional set of experiments.

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Authors and Affiliations

  1. School of Computer Science, Carleton University, Ottawa, K1S 5B6, Canada

    Abdolreza Shirvani & B. John Oommen

  2. University of Agder, Grimstad, Norway

    B. John Oommen

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  1. Abdolreza Shirvani
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  2. B. John Oommen
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Correspondence to B. John Oommen.

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The second author is grateful for the partial support provided by NSERC, the Natural Sciences and Engineering Research Council of Canada. The second author is also an Adjunct Professor at the University of Agder in Grimstad, Norway. A preliminary version of some of the results of this paper was presented at ICTCS’17, the International Conference on New Trends in Computing, Amman, Jordan, in October 2017. We are very grateful for the feedback from the anonymous Referees of the original submission. Their input significantly improved the quality of this final version.

B. J. Oommen: The author is also an Adjunct Professor with University of Agder, Grimstad, Norway.

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Shirvani, A., Oommen, B.J. On enhancing the deadlock-preventing object migration automaton using the pursuit paradigm. Pattern Anal Applic 23, 509–526 (2020). https://doi.org/10.1007/s10044-019-00817-z

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