---
_id: '7515'
abstract:
- lang: eng
text: The algebraic approaches to graph transformation are based on the concept
of gluing of graphs corresponding to pushouts in suitable categories of graphs
and graph morphisms. This allows one to give not only an explicit algebraic or
set theoretical description of the constructions but also to use concepts and
results from category theory in order to build up a rich theory and to give elegant
proofs even in complex situations. In the previous chapter we have presented an
overview of the basic notions and problems common to the two algebraic approaches
the double pushout DPO approach and the single pushout SPO approach and their
solutions in the DPO approach. In this chapter we introduce the SPO approach to
graph transformation and some of its main results. We study application conditions
for graph productions and the transformation of more general structures than graphs
in the SPO approach where similar generalizations have been or could be studied
also in the DPO approach. Finally we present a detailed comparison of the DPO
and the SPO approach especially concerning the solutions to the problems discussed
for both approaches in the previous chapter.
author:
- first_name: Hartmut
full_name: Ehrig, Hartmut
last_name: Ehrig
- first_name: Reiko
full_name: Heckel, Reiko
last_name: Heckel
- first_name: Martin
full_name: Korff, Martin
last_name: Korff
- first_name: Michael
full_name: Löwe, Michael
last_name: Löwe
- first_name: Leila
full_name: Ribeiro, Leila
last_name: Ribeiro
- first_name: Annika
full_name: Wagner, Annika
last_name: Wagner
- first_name: Andrea
full_name: Corradini, Andrea
last_name: Corradini
citation:
ama: 'Ehrig H, Heckel R, Korff M, et al. Algebraic Approaches to Graph Transformation,
Part II: Single Pushout Approach and Comparison with Double Pushout Approach.
In: *Handbook of Graph Grammars and Computing by Graph Transformations, Volume
1: Foundations*. Singapore: World Scientific; 1997:247-312.'
apa: 'Ehrig, H., Heckel, R., Korff, M., Löwe, M., Ribeiro, L., Wagner, A., &
Corradini, A. (1997). Algebraic Approaches to Graph Transformation, Part II: Single
Pushout Approach and Comparison with Double Pushout Approach. In *Handbook of
Graph Grammars and Computing by Graph Transformations, Volume 1: Foundations*
(pp. 247–312). Singapore: World Scientific.'
bibtex: '@inbook{Ehrig_Heckel_Korff_Löwe_Ribeiro_Wagner_Corradini_1997, place={Singapore},
title={Algebraic Approaches to Graph Transformation, Part II: Single Pushout Approach
and Comparison with Double Pushout Approach}, booktitle={Handbook of Graph Grammars
and Computing by Graph Transformations, Volume 1: Foundations}, publisher={World
Scientific}, author={Ehrig, Hartmut and Heckel, Reiko and Korff, Martin and Löwe,
Michael and Ribeiro, Leila and Wagner, Annika and Corradini, Andrea}, year={1997},
pages={247–312} }'
chicago: 'Ehrig, Hartmut, Reiko Heckel, Martin Korff, Michael Löwe, Leila Ribeiro,
Annika Wagner, and Andrea Corradini. “Algebraic Approaches to Graph Transformation,
Part II: Single Pushout Approach and Comparison with Double Pushout Approach.”
In *Handbook of Graph Grammars and Computing by Graph Transformations, Volume
1: Foundations*, 247–312. Singapore: World Scientific, 1997.'
ieee: 'H. Ehrig *et al.*, “Algebraic Approaches to Graph Transformation, Part
II: Single Pushout Approach and Comparison with Double Pushout Approach,” in *Handbook
of Graph Grammars and Computing by Graph Transformations, Volume 1: Foundations*,
Singapore: World Scientific, 1997, pp. 247–312.'
mla: 'Ehrig, Hartmut, et al. “Algebraic Approaches to Graph Transformation, Part
II: Single Pushout Approach and Comparison with Double Pushout Approach.” *Handbook
of Graph Grammars and Computing by Graph Transformations, Volume 1: Foundations*,
World Scientific, 1997, pp. 247–312.'
short: 'H. Ehrig, R. Heckel, M. Korff, M. Löwe, L. Ribeiro, A. Wagner, A. Corradini,
in: Handbook of Graph Grammars and Computing by Graph Transformations, Volume
1: Foundations, World Scientific, Singapore, 1997, pp. 247–312.'
date_created: 2019-02-04T22:41:33Z
date_updated: 2019-02-04T22:42:11Z
department:
- _id: '66'
language:
- iso: eng
page: 247-312
place: Singapore
publication: 'Handbook of Graph Grammars and Computing by Graph Transformations, Volume
1: Foundations'
publisher: World Scientific
status: public
title: 'Algebraic Approaches to Graph Transformation, Part II: Single Pushout Approach
and Comparison with Double Pushout Approach'
type: book_chapter
user_id: '52534'
year: '1997'
...