On the Complexity of Local Graph Transformations

Autor:	Scheideler, Christian, Setzer, Alexander
Rok vydání:	2019
Předmět:	Computer Science - Distributed Parallel and Cluster Computing Computer Science - Computational Complexity Computer Science - Networking and Internet Architecture
Druh dokumentu:	Working Paper
Popis:	We consider the problem of transforming a given graph $G_s$ into a desired graph $G_t$ by applying a minimum number primitives from a particular set of local graph transformation primitives. These primitives are local in the sense that each node can apply them based on local knowledge and by affecting only its $1$-neighborhood. Although the specific set of primitives we consider makes it possible to transform any (weakly) connected graph into any other (weakly) connected graph consisting of the same nodes, they cannot disconnect the graph or introduce new nodes into the graph, making them ideal in the context of supervised overlay network transformations. We prove that computing a minimum sequence of primitive applications (even centralized) for arbitrary $G_s$ and $G_t$ is NP-hard, which we conjecture to hold for any set of local graph transformation primitives satisfying the aforementioned properties. On the other hand, we show that this problem admits a polynomial time algorithm with a constant approximation ratio. Comment: This publication is the full version of a paper that appeared at ICALP'19
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1904.11395 Zobrazit plný text záznamu View this record from Arxiv