Expressiveness of graph conditions with variables

Habel, Annegret; Radke, Hendrik

doi:10.14279/tuj.eceasst.30.404

Cited by 11 publications

(2 citation statements)

References 23 publications

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“…Additional typical constraints are, e.g., that the output topology should be k-connected, a directed acyclic graph (DAG) or even a tree/forest. In [74,75], Habel and Radke present HR * constraints, a new type of graph constraints that allow to express path-related properties. Fortunately, the constructive approach is applicable to HR * constraints in principle; in future work, we will investigate the applicability of HR * constraints to specify, e.g., connectivity of topologies.…”

Section: Rq4-generalizabilitymentioning

confidence: 99%

A systematic approach to constructing incremental topology control algorithms using graph transformation

Kluge

Stein²,

Varr

et al. 2017

Journal of Visual Languages & Computing

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This document corresponds to the accepted manuscript of the article Kluge, R., Stein, M., Varró, G., Schürr, A., Hollick, M., Mühlhäuser, M.: "A Systematic Approach to Constructing Incremental Topology Control Algorithms using Graph Transformation," in: JVLC 2016. The URL of the formal version is https://dx.Communication networks form the backbone of our society. Topology control algorithms optimize the topology of such communication networks. Due to the importance of communication networks, a topology control algorithm should guarantee certain required consistency properties (e.g., connectivity of the topology), while achieving desired optimization properties (e.g., a bounded number of neighbors). Real-world topologies are dynamic (e.g., because nodes join, leave, or move within the network), which requires topology control algorithms to operate in an incremental way, i.e., based on the recently introduced modifications of a topology. Visual programming and specification languages are a proven means for specifying the structure as well as consistency and optimization properties of topologies. In this paper, we present a novel methodology, based on a visual graph transformation and graph constraint language, for developing incremental topology control algorithms that are guaranteed to fulfill a set of specified consistency and optimization constraints. More specifically, we model the possible modifications of a topology control algorithm and the environment using graph transformation rules, and we describe consistency and optimization properties using graph constraints. On this basis, we apply and extend a well-known constructive approach to derive refined graph transformation rules that preserve these graph constraints. We apply our methodology to re-engineer an established topology control algorithm, kTC, and evaluate it in a network simulation study to show the practical applicability of our approach. Meta-modeling [Sec. 2] WSN meta-model Topology control (TC) Graph constraints [Sec. 3] Structural constraints TC constraints Connectivity Consistency Graph transformation [Sec. 4] TC rules TC algorithm Context event rules Rule refinement [Sec. 5] Rule refinement algorithm Restoring rule applicability Enforcing termination Proving preservation of connectivity Evaluation [Sec. 6] RQ1: Correctness RQ2: Incrementality RQ3: Generalizability RQ4: Performance Figure 1: Overview of the proposed constructive methodology and structure of this paper (i) We characterize the required and desired properties of output topologies of a TC algorithm using graph constraints (as described in [42]).(ii) We use GT rules to describe TC operations, which specify the possible modifications during an execution of a TC algorithm, and context events, which specify the possible modifications by the environment.(iii) We apply and enhance the constructive refinement approach for GT rules presented in [42,43] to TC. Our approach is able to cope with temporarily constraint-violating rules, which contrary to [42,43] may not be restricted.(iv) We ...

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Section: Rq4-generalizabilitymentioning

confidence: 99%

A systematic approach to constructing incremental topology control algorithms using graph transformation

Kluge

Stein²,

Varr

et al. 2017

Journal of Visual Languages & Computing

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“…For this reason, we proved the connectivity of weakly consistent topologies in this paper rather than integrating this property constructively during the development of the TC algorithms. In [30,59], Habel and Radke present HR * constraints, a new type of graph constraints that allow to express path-related properties, which may in principle also serve as input for the constructive approach. Future work should target the question in how far HR * constraints are applicable in our application scenario.…”

Section: Correctness Of Algorithmsmentioning

confidence: 99%

A systematic approach to constructing families of incremental topology control algorithms using graph transformation

et al. 2017

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Verifying Graph Programs with Monadic Second-Order Logic

Wulandari

Plump

2021

Graph Transformation

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To verify graph programs in the language GP 2, we present a monadic second-order logic with counting and a Hoare-style proof calculus. The logic has quantifiers for GP 2's attributes and for sets of nodes or edges. This allows to specify non-local graph properties such as connectedness, k-colourability, etc. We show how to construct a strongest liberal postcondition for a given graph transformation rule and a precondition. The proof rules establish the total correctness of graph programs and are shown to be sound. They allow to verify more programs than is possible with previous approaches. In particular, many programs with nested loops are covered by the calculus.

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Expressiveness of graph conditions with variables

Cited by 11 publications

References 23 publications

A systematic approach to constructing incremental topology control algorithms using graph transformation

A systematic approach to constructing incremental topology control algorithms using graph transformation

A systematic approach to constructing families of incremental topology control algorithms using graph transformation

Verifying Graph Programs with Monadic Second-Order Logic

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