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Cover Combinatorial Filters and Their Minimization Problem

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Algorithmic Foundations of Robotics XIV (WAFR 2020)

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Abstract

Recent research has examined algorithms to minimize robots’ resource footprints. The class of combinatorial filters (discrete variants of widely-used probabilistic estimators) has been studied and methods for reducing their space requirements introduced. This paper extends existing combinatorial filters by introducing a natural generalization: cover combinatorial filters. In addressing the new —but still NP-complete— problem of minimization of cover filters, we show that multiple concepts previously believed about combinatorial filters (and actually conjectured, claimed, or assumed to be) are in fact false. For instance, minimization does not induce an equivalence relation. We give an exact algorithm for the cover filter minimization problem. Unlike prior work (based on graph coloring) we consider a type of clique-cover problem, involving a new conditional constraint, from which we can find more general relations. In addition to solving the more general problem, the algorithm also corrects flaws present in all prior filter reduction methods. In employing SAT, the algorithm provides a promising basis for future practical development.

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Notes

  1. 1.

    Such bizarre chimera robots are not our invention, e.g., see the Syma X9 Flying Car.

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Acknowledgement

This work was supported by the NSF through awards IIS-1453652 and IIS-1527436.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Texas A&M University, College Station, TX, 77843, USA

    Yulin Zhang & Dylan A. Shell

Authors
  1. Yulin Zhang
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  2. Dylan A. Shell
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Corresponding author

Correspondence to Yulin Zhang .

Editor information

Editors and Affiliations

  1. Center for Ubiquitous Computing, University of Oulu, Oulu, Finland

    Steven M. LaValle

  2. Brendan Iribe Center for Computer Science and Engineering, University of Maryland, College Park, MD, USA

    Ming Lin

  3. Center for Ubiquitous Computing, University of Oulu, Oulu, Finland

    Timo Ojala

  4. Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA

    Dylan Shell

  5. Department of Computer Science, Rutgers University, Piscataway, NJ, USA

    Jingjin Yu

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Zhang, Y., Shell, D.A. (2021). Cover Combinatorial Filters and Their Minimization Problem. In: LaValle, S.M., Lin, M., Ojala, T., Shell, D., Yu, J. (eds) Algorithmic Foundations of Robotics XIV. WAFR 2020. Springer Proceedings in Advanced Robotics, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-030-66723-8_6

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