Improper Filter Reduction

TL;DR

This paper introduces the problem of improper filter reduction, aiming to minimize behavioral differences when reducing combinatorial filters to a specified size, and presents algorithms and experimental analysis for this NP-hard problem.

Contribution

It formalizes improper filter reduction, proposes distance metrics, proves NP-hardness, and develops heuristic algorithms with experimental evaluation.

Findings

Improper filter reduction is NP-hard under proposed metrics.

Heuristic algorithms can effectively approximate minimal behavioral differences.

Experimental results demonstrate the algorithms' performance on various filter sets.

Abstract

Combinatorial filters have been the subject of increasing interest from the robotics community in recent years. This paper considers automatic reduction of combinatorial filters to a given size, even if that reduction necessitates changes to the filter's behavior. We introduce an algorithmic problem called improper filter reduction, in which the input is a combinatorial filter F along with an integer k representing the target size. The output is another combinatorial filter F' with at most k states, such that the difference in behavior between F and F' is minimal. We present two metrics for measuring the distance between pairs of filters, describe dynamic programming algorithms for computing these distances, and show that improper filter reduction is NP-hard under these metrics. We then describe two heuristic algorithms for improper filter reduction, one greedy sequential approach, and one randomized global approach based on prior work on weighted improper graph coloring. We have implemented these algorithms and analyze the results of three sets of experiments.