The equivalence of boundary and confluent graph grammars on graph languages of bounded degree

1991 ◽  
pp. 312-322 ◽  
Author(s):  
Franz J. Brandenburg
Keyword(s):  
Graph Grammars ◽  
Bounded Degree ◽  
Graph Languages

Context-free graph languages of bounded degree are generated by apex graph grammars

1994 ◽  
Vol 31 (4) ◽  
pp. 341-378 ◽  
Author(s):  
Joost Engelfriet ◽  
Linda Heyker ◽  
George Leih
Keyword(s):  
Graph Grammars ◽  
Free Graph ◽  
Bounded Degree ◽  
Apex Graph ◽  
Context Free ◽  
Graph Languages

scholarly journals The Bounded Degree Problem for eNCE Graph Grammars

1997 ◽  
Vol 135 (1) ◽  
pp. 15-35 ◽  
Author(s):  
Konstantin Skodinis ◽  
Egon Wanke
Keyword(s):  
Graph Grammars ◽  
Bounded Degree

On the Expressiveness of Context-Sensitive Graph Grammars

2012 ◽  
Vol 23 (7) ◽  
pp. 1635-1655 ◽  
Author(s):  
Yang ZOU ◽  
Jian LÜ ◽  
Chun CAO ◽  
Hao HU ◽  
Wei SONG ◽  
...  
Keyword(s):  
Graph Grammars ◽  
Context Sensitive

scholarly journals A Lower Bound for the Query Phase of Contraction Hierarchies and Hub Labels and a Provably Optimal Instance-Based Schema

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 164
Author(s):  
Tobias Rupp ◽  
Stefan Funke
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Real World ◽  
Road Network ◽  
Upper And Lower Bounds ◽  
Bounded Degree ◽  
Shortest Path Routing ◽  
Graph Classes ◽  
Speed Up ◽  
To Come

We prove a Ω(n) lower bound on the query time for contraction hierarchies (CH) as well as hub labels, two popular speed-up techniques for shortest path routing. Our construction is based on a graph family not too far from subgraphs that occur in real-world road networks, in particular, it is planar and has a bounded degree. Additionally, we borrow ideas from our lower bound proof to come up with instance-based lower bounds for concrete road network instances of moderate size, reaching up to 96% of an upper bound given by a constructed CH. For a variant of our instance-based schema applied to some special graph classes, we can even show matching upper and lower bounds.

scholarly journals Clustered 3-colouring graphs of bounded degree

2021 ◽  
pp. 1-13
Author(s):  
Vida Dujmović ◽  
Louis Esperet ◽  
Pat Morin ◽  
Bartosz Walczak ◽  
David R. Wood
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Bounded Degree ◽  
Bounded Number ◽  
Proper Vertex ◽  
Vertex Colouring

Abstract A (not necessarily proper) vertex colouring of a graph has clustering c if every monochromatic component has at most c vertices. We prove that planar graphs with maximum degree $\Delta$ are 3-colourable with clustering $O(\Delta^2)$ . The previous best bound was $O(\Delta^{37})$ . This result for planar graphs generalises to graphs that can be drawn on a surface of bounded Euler genus with a bounded number of crossings per edge. We then prove that graphs with maximum degree $\Delta$ that exclude a fixed minor are 3-colourable with clustering $O(\Delta^5)$ . The best previous bound for this result was exponential in $\Delta$ .

Schema Compliant Consistency Management via Triple Graph Grammars and Integer Linear Programming

2021 ◽  
Author(s):  
Nils Weidmann ◽  
Anthony Anjorin
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Experimental Evaluation ◽  
Graph Grammars ◽  
Model Driven Engineering ◽  
Rule Based ◽  
Consistency Management ◽  
Model Driven ◽  
Triple Graph Grammars ◽  
Domain Constraints

AbstractIn the field of Model-Driven Engineering, Triple Graph Grammars (TGGs) play an important role as a rule-based means of implementing consistency management. From a declarative specification of a consistency relation, several operations including forward and backward transformations, (concurrent) synchronisation, and consistency checks can be automatically derived. For TGGs to be applicable in realistic application scenarios, expressiveness in terms of supported language features is very important. A TGG tool is schema compliant if it can take domain constraints, such as multiplicity constraints in a meta-model, into account when performing consistency management tasks. To guarantee schema compliance, most TGG tools allow application conditions to be attached as necessary to relevant rules. This strategy is problematic for at least two reasons: First, ensuring compliance to a sufficiently expressive schema for all previously mentioned derived operations is still an open challenge; to the best of our knowledge, all existing TGG tools only support a very restricted subset of application conditions. Second, it is conceptually demanding for the user to indirectly specify domain constraints as application conditions, especially because this has to be completely revisited every time the TGG or domain constraint is changed. While domain constraints can in theory be automatically transformed to obtain the required set of application conditions, this has only been successfully transferred to TGGs for a very limited subset of domain constraints. To address these limitations, this paper proposes a search-based strategy for achieving schema compliance. We show that all correctness and completeness properties, previously proven in a setting without domain constraints, still hold when schema compliance is to be additionally guaranteed. An implementation and experimental evaluation are provided to support our claim of practical applicability.

scholarly journals A short note on conflict‐free coloring on closed neighborhoods of bounded degree graphs

2021 ◽  
Author(s):  
Sriram Bhyravarapu ◽  
Subrahmanyam Kalyanasundaram ◽  
Rogers Mathew
Keyword(s):  
Short Note ◽  
Bounded Degree ◽  
Bounded Degree Graphs

Formal manipulation of Forrester diagrams by graph grammars

1988 ◽  
Vol 18 (6) ◽  
pp. 981-996 ◽  
Author(s):  
J.J. Dolado ◽  
F.J. Torrealdea
Keyword(s):  
Graph Grammars
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