Listing Maximal Subgraphs Satisfying Strongly Accessible Properties
Alessio Conte, Roberto Grossi, Andrea Marino, Luca Versari · SIAM Journal on Discrete Mathematics · 2019
Algorithms for listing the subgraphs satisfying a given property (e.g., being a clique, a cut, a cycle) fall within the general framework of set systems. A set system $(\mathcal{U}, \mathcal{F})$ consists of a ground set $\mathcal{U}$ (e.g., a network's nodes) and a family $\mathcal{F} \subseteq 2^{\mathcal{U}}$ of subsets of $\mathcal{U}$ that have the required property. For the problem of listing all sets in $\mathcal{F}$ maximal under inclusion, the ambitious goal is to cover a large class of set systems, preserving at the same time the efficiency of the enumeration. Among the existing algorithms, the best-known ones list the maximal subsets in time proportional to their number but may require exponential space. In this paper we improve the state of the art in two directions by introducing an algorithmic framework based on reverse search that, under standard suitable conditions, simultaneously (i) extends the class of problems that can be solved efficiently to strongly accessible set systems and (ii) reduces the additional space usage from exponential in $|\mathcal{U}|$ to stateless, i.e., with no additional memory usage other than that proportional to the solution size, thus accounting for just polynomial space.