# Loose Graph Simulations

## TL;DR

This paper introduces loose graph simulations (LGS), a unified framework that generalizes subgraph isomorphism, regular language pattern matching, and graph simulation, enabling the expression of complex mixed graph problems.

## Contribution

It defines LGS as a unifying concept, proves NP-completeness, and identifies a polynomial subclass, advancing graph pattern matching theory.

## Key findings

- LGS generalizes SGI, RLPM, and GS
- Finding LGS is NP-complete
- A polynomial subclass of LGS is identified

## Abstract

We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly also problems which are "mixed" instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give the representation of a problem which extends both SGI and RLPM. Finally, we identify a subclass of the LGS problem that is polynomial.

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Source: https://tomesphere.com/paper/1705.08241