Cover Combinatorial Filters and their Minimization Problem (Extended Version)
This work addresses the problem of minimizing resource footprints for robots, offering a more general and corrected approach, though it is incremental as it builds on existing combinatorial filter research.
The paper introduces cover combinatorial filters, a generalization of existing combinatorial filters, and presents an exact algorithm for their minimization, which is NP-complete, correcting flaws in prior methods and disproving several previously held beliefs about combinatorial filters.
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 that we dub cover combinatorial filters. In addressing the new -- but still NP-complete -- problem of minimization of cover filters, this paper shows that multiple concepts previously believed to be true 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.