Efficient Stubborn Sets: Generalized Algorithms and Selection Strategies

Abstract

Strong stubborn sets have recently been analyzed and successfully applied as a pruning technique for planning as heuristic search. Strong stubborn sets are defined declaratively as constraints over operator sets. We show how these constraints can be relaxed to offer more freedom in choosing stubborn sets while maintaining the correctness and optimality of the approach. In general, many operator sets satisfy the definition of stubborn sets. We study different strategies for selecting among these possibilities and show that existing approaches can be considerably improved by rather simple strategies, eliminating most of the overhead of the previous state of the art.

Strong Stubborn Sets for Efficient Goal Recognition Design

“…Since we want to minimize wcd, we need to make sure our pruning method is safe, i.e., it is guaranteed that an optimal solution for the given goal recognition design task can still be found in the pruned search tree. Specifically, a successor function is safe if for every non-terminal model R, pr (R) includes at least one operator that starts an optimal solution for R. As described by Wehrle and Helmert (2014), assuming all modifications have non-zero uniform cost, this is a necessary criterion for safety.…”

“…Note that while the original formulation by Wehrle and Helmert (2014) requires non-interfering operators to yield the same state for different orders of application, we only require them to yield the same set of non-distinctive paths which is enough to guarantee both models share the same wcd value. Also, the original formulation of GSSSs considers an envelope of modifications that are sufficient to consider at each node.…”

“…Proof (sketch) The proof, for which the complete version can be found in an extended techincal report (Keren, Gal, and Karpas 2018), shows that under the specified assumptions, for every strongly optimal sequence that is pruned, we can use the method suggested by Wehrle and Helmert (2014) to construct a strongly optimal sequence that is not pruned by pr .…”

“…Our main contribution in this work involves the characterization of a class of GRD models for which an effective pruning of the search space can be done using Strong Stubborn Sets (Valmari 1989;Wehrle and Helmert 2014). Originally suggested in the area of computer aided verifications, Strong Stubborn Sets are used to guarantee that the subset of modifications applied at each node in the search are chosen in a way that preserves completeness.…”

On the Relation between Star-Topology Decoupling and Petri Net Unfolding

“…It maintains concurrent threads separately. Instead of building the forward state space and trying to prune permutative parts as in other methods (e. g. Valmari (1989), Godefroid and Wolper (1991), Wehrle et al (2013), Wehrle and Helmert (2014)), the state variables are not multiplied with each other in the first place. The unfolding process incrementally adds transitions to an acyclic graph, when the transition's input "places" (precondition facts) can be reached jointly.…”