In this report, we briefly describe our entry to the 2023 ISR competition: Planning Algorithms for Reconfiguring Independent Sets (PARIS 2023). Our solver is a modified version of the 2022 competition submission, which performed extremely well across several of the tracks Soh et al. [2022]. We have adapted the solver given the newly imposed resource limits and implemented a mechanism for the portfolio approach to return the best solution found during the resource limits. We additionally employ a suite of anytime search methods, which may produce better solutions. Careful handling of the time-limits was required to ensure that the solver responds with an answer in time. In the following, we describe the components of our planner and how we combine them for the different tracks.

Binary decision diagrams (BDDs) are widely used to mitigate the state-explosion problem in model checking. A variation of BDDs are Zero-suppressed Decision Diagrams (ZDDs) which omit variables that must be false, instead of omitting variables that do not matter. We use ZDDs to symbolically encode Kripke models used in Dynamic Epistemic Logic, a framework to reason about knowledge and information dynamics in multi-agent systems. We compare the memory usage of different ZDD variants for three well-known examples from the literature: the Muddy Children, the Sum and Product puzzle and the Dining Cryptographers. Our implementation is based on the existing model checker SMCDEL and the CUDD library. Our results show that replacing BDDs with the right variant of ZDDs can significantly reduce memory usage. This suggests that ZDDs are a useful tool for model checking multi-agent systems.

The general approach to all of the solver tracks was to model the ISR problem as one of automated planning, and use a selection of state-of-the-art solvers to solve these instances. Throughout this document, we describe the encoding, solvers, and overall search setup.

Submodular function maximization (SFM) has attracted much attention thanks to its applicability to various practical problems. Although most studies have considered SFM with size or budget constraints, more complex constraints often appear in practice. In this paper, we consider a very general class of SFM with such complex constraints (e.g., an s-t path constraint on a given graph). We propose a novel algorithm that takes advantage of zero-suppressed binary decision diagrams, which store all feasible solutions efficiently thus enabling us to circumvent the difficulty of determining feasibility. Theoretically, our algorithm is guaranteed to achieve (1-c)-approximations, where c is the curvature of a submodular function. Experiments show that our algorithm runs much faster than exact algorithms and finds better solutions than those obtained by an existing approximation algorithm in many instances. Notably, our algorithm achieves better than a 90%-approximation in all instances for which optimal values are available.

Exact cover is the problem of finding subfamilies, S* , of a family of sets, S , over universe U , where S* forms a partition of  U .  It is a popular NP-hard problem appearing in a wide range of computer science studies. Knuth's algorithm DLX, a backtracking-based depth-first search implemented with the data structure called dancing links, is known as state-of-the-art for finding all exact covers. We propose a method to accelerate DLX. Our method constructs a Zero-suppressed Binary Decision Diagram (ZDD) that represents the set of solutions while running depth-first search in DLX. Constructing ZDDs enables the efficient use of memo cache to speed up the search. Moreover, our method has a virtue that it outputs ZDDs; we can perform several useful operations with them. Experiments confirm that the proposed method is up to several orders of magnitude faster than DLX.

The Zero-suppressed Sentential Decision Diagram (ZSDD) is a recentlydiscovered tractable representation of Boolean functions. ZSDD subsumes theZero-suppressed Binary Decision Diagram (ZDD) as a strict subset, andsimilar to ZDD, it can perform several useful operations like model countingand Apply operations. We propose a top-down compilation algorithmfor ZSDD that represents sets of specific graph substructures, e.g.,matchings and simple paths of a graph. We experimentally confirm that theproposed algorithm is faster than other construction methods includingbottom-up methods and top-down methods for ZDDs, and the resulting ZSDDsare smaller than ZDDs representing the same graph substructures. We alsoshow that the size constructed ZSDDs can be bounded by the branch-width of thegraph. This bound is tighter than that of ZDDs.