Efficient Graph Rewriting

06/11/2019
by   Graham Campbell, et al.
0

Graph transformation is the rule-based modification of graphs, and is a discipline dating back to the 1970s. The declarative nature of graph rewriting rules comes at a cost. In general, to match the left-hand graph of a fixed rule within a host graph requires polynomial time. To improve matching performance, Dörr proposed to equip rules and host graphs with distinguished root nodes. This model was implemented by Plump and Bak, but unfortunately, is not invertible. We address this problem by defining rootedness using a partial function onto a two-point set rather than pointing graphs with root nodes. We show a new result that the graph class of trees can be recognised by a rooted GT system in linear time, given an input graph of bounded degree. Finally, we define a new notion of confluence modulo garbage and non-garbage critical pairs, showing it is sufficient to require strong joinability of only the non-garbage critical pairs to establish confluence modulo garbage.

READ FULL TEXT
research
11/28/2019

Efficient Recognition of Graph Languages

Graph transformation is the rule-based modification of graphs, and is a ...
research
12/21/2020

Fast Rule-Based Graph Programs

Implementing graph algorithms efficiently in a rule-based language is ch...
research
01/06/2021

Confluence up to Garbage in Graph Transformation

The transformation of graphs and graph-like structures is ubiquitous in ...
research
12/03/2020

A Fast Graph Program for Computing Minimum Spanning Trees

When using graph transformation rules to implement graph algorithms, a c...
research
03/02/2022

Graph Rewriting and Relabeling with PBPO+: A Unifying Theory for Quasitoposes

We extend the powerful Pullback-Pushout (PBPO) approach for graph rewrit...
research
08/21/2023

Computing Optimal Leaf Roots of Chordal Cographs in Linear Time

A graph G is a k-leaf power, for an integer k >= 2, if there is a tree T...
research
11/01/2019

MaxSAT Evaluation 2019 – Benchmark: Identifying Security-Critical Cyber-Physical Components in Weighted AND/OR Graphs

This paper presents a MaxSAT benchmark focused on identifying critical n...

Please sign up or login with your details

Forgot password? Click here to reset