# Constant Delay Traversal of Grammar-Compressed Graphs with Bounded Rank

## TL;DR

This paper introduces a pointer-based data structure enabling constant-time traversal of edges in grammar-compressed hypergraphs with bounded rank, optimizing navigation efficiency in complex graph representations.

## Contribution

It presents a novel data structure for hypergraph traversal that operates in constant time, specifically tailored for graphs generated by hyperedge-replacement grammars with bounded rank.

## Key findings

- Supports constant-time traversal of hypergraph edges
- Preprocessing requires space proportional to grammar size and parameters
- Applicable to hypergraphs with fixed maximum rank and specific incident edge constraints

## Abstract

We present a pointer-based data structure for constant time traversal of the edges of an edge-labeled (alphabet $\Sigma$) directed hypergraph (a graph where edges can be incident to more than two vertices, and the incident vertices are ordered) given as hyperedge-replacement grammar $G$. It is assumed that the grammar has a fixed rank $\kappa$ (maximal number of vertices connected to a nonterminal hyperedge) and that each vertex of the represented graph is incident to at most one $\sigma$-edge per direction ($\sigma \in \Sigma$). Precomputing the data structure needs $O(|G||\Sigma|\kappa r h)$ space and $O(|G||\Sigma|\kappa rh^2)$ time, where $h$ is the height of the derivation tree of $G$ and $r$ is the maximal rank of a terminal edge occurring in the grammar.