# Listing Maximal Subgraphs in Strongly Accessible Set Systems

## TL;DR

This paper introduces an efficient, space-saving algorithmic framework for listing all maximal subsets with a property in strongly accessible set systems, broadening applicability and reducing memory requirements.

## Contribution

It extends efficient enumeration algorithms to strongly accessible set systems and significantly reduces space complexity to linear in the size of the largest maximal set.

## Key findings

- Efficient enumeration in strongly accessible set systems.
- Reduction of space complexity from exponential to linear.
- Broader class of problems solvable efficiently.

## Abstract

Algorithms for listing the subgraphs satisfying a given property (e.g.,being a clique, a cut, a cycle, etc.) fall within the general framework of set systems. A set system (U, F) uses a ground set U (e.g., the network nodes) and an indicator F, subset of 2^U, of which subsets of U have the required property. For the problem of listing all sets in 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 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 |U| to stateless, thus accounting for just O(q) space, where q <= |U| is the largest size of a maximal set in F