The Relative Pruning Power of Strong Stubborn Sets and Expansion Core

Abstract

In the last years, pruning techniques based on partial order reduction have found increasing attention in the planning community. One recent result is that the expansion core method is a special case of the strong stubborn sets method proposed in model checking. However, it is still an open question if there exist efficiently computable strong stubborn sets with strictly higher pruning power than expansion core. In this paper, we prove that the pruning power of strong stubborn sets is strictly higher than the pruning power of expansion core even for a straight-forward instantiation of strong stubborn sets. This instantiation is as efficiently computable as expansion core. Hence, our theoretical results suggest that strong stubborn sets should be preferred to expansion core. Our empirical evaluation on all optimal benchmarks from the international planning competitions up to 2011 supports the theoretical results.

Efficient Stubborn Sets: Generalized Algorithms and Selection Strategies

“…Strong stubborn sets have been defined in three recent papers on AI planning (Wehrle and Helmert 2012;Alkhazraji et al 2012;Wehrle et al 2013). All three definitions are subtly different, and the definition of generalized strong stubborn sets we present in this section generalizes all of them.…”

“…In the last years, techniques based on partial order reduction have also been investigated for domain-independent planning, including the expansion core method (Chen and Yao 2009) and a direct adaptation of Valmari's strong stubborn sets (Alkhazraji et al 2012). Moreover, the theoretical relationships between different partial order reduction techniques have recently been investigated (Wehrle and Helmert 2012;Wehrle et al 2013). For example, Wehrle et al (2013) have shown that strong stubborn sets strictly dominate the expansion core method in terms of pruning power if the choice points of the strong stubborn set approach are resolved in a suitable way.…”

“…Moreover, the theoretical relationships between different partial order reduction techniques have recently been investigated (Wehrle and Helmert 2012;Wehrle et al 2013). For example, Wehrle et al (2013) have shown that strong stubborn sets strictly dominate the expansion core method in terms of pruning power if the choice points of the strong stubborn set approach are resolved in a suitable way.…”

“…mari 2009; Laarman et al 2013) show that different strategies for computing stubborn sets vary widely in terms of the resulting pruning power. Recent results in planning (Wehrle et al 2013) show that current algorithms for computing strong stubborn sets can offer significant improvements of total performance on a large benchmark suite. However, they also demonstrate a nontrivial performance penalty in cases where little or no pruning occurs, leading to fewer problems solved in 5 out of 44 benchmark domains.…”

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.…”