Graph Editing to a Given Neighbourhood Degree List is Fixed-Parameter Tractable

Nishimura, Nobuya; Subramanya, Vijay

doi:10.1007/978-3-319-71147-8_10

Cited by 3 publications

(3 citation statements)

References 47 publications

(83 reference statements)

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“…In many cases, the barrier to considering the reconfiguration of a problem stems from the difficulty in determining how to define feasible solutions or adjacency. When a solution represents a class of possible graphs, reconfiguration can be used to consider graph editing problems [167]. Particularly challenging are solutions that can be defined as sequences, such as in STRING EDITING; results in the reconfiguration of sequences would permit the reconfiguration of reconfiguration sequences, and hence reconfiguration itself [21].…”

Section: Further Research Directionsmentioning

confidence: 99%

Introduction to Reconfiguration

2018

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Reconfiguration is concerned with relationships among solutions to a problem instance, where the reconfiguration of one solution to another is a sequence of steps such that each step produces an intermediate feasible solution. The solution space can be represented as a reconfiguration graph, where two vertices representing solutions are adjacent if one can be formed from the other in a single step. Work in the area encompasses both structural questions (Is the reconfiguration graph connected?) and algorithmic ones (How can one find the shortest sequence of steps between two solutions?) This survey discusses techniques, results, and future directions in the area.

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Section: Further Research Directionsmentioning

confidence: 99%

Introduction to Reconfiguration

2018

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“…In many cases, the barrier to considering the reconfiguration of a problem stems from the difficulty in determining how to define feasible solutions or adjacency. When a solution represents a class of possible graphs, reconfiguration can be used to consider graph editing problems [166]. Particularly challenging are solutions that can be defined as sequences, such as STRING EDITING; results in the reconfiguration of sequences would permit the reconfiguration of reconfiguration sequences, and hence reconfiguration itself [21].…”

Section: Further Research Directionsmentioning

confidence: 99%

Introduction to Reconfiguration

Nishimura¹

2017

Preprint

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“…However, the prevalence of such topology amongst complex networks in general is unknown. In pure mathematics, Barrus & Donovan independently initiated study of neighbourhood degree lists as a topological invariant more refined than both the degree sequence and joint degree graph matrix 14 , while Nishimura & Subramanya proposed to study neighbourhood degree lists for the combinatorial problem of changing a graph into one with given neighbourhood degrees 15 .…”

Section: Introductionmentioning

confidence: 99%

On neighbourhood degree sequences of complex networks

Smith

2019

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Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in complex networks. We consider how to explicitly characterise important physical concepts such as similarity, heterogeneity and organization in these sequences, as well as updating the notion of hierarchical complexity to reflect previously unnoticed organizational principles. We also point out that neighbourhood degree sequences are related to a powerful subtree kernel for unlabeled graph classification. We study these newly defined sequence properties in a comprehensive array of graph models and over 200 real-world networks. We find that these indices are neither highly correlated with each other nor with classical network indices. Importantly, the sequences of a wide variety of real world networks are found to have greater similarity and organisation than is expected for networks of their given degree distributions. Notably, while biological, social and technological networks all showed consistently large neighbourhood similarity and organisation, hierarchical complexity was not a consistent feature of real world networks. Neighbourhood degree sequences are an interesting tool for describing unique and important characteristics of complex networks.

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Graph Editing to a Given Neighbourhood Degree List is Fixed-Parameter Tractable

Cited by 3 publications

References 47 publications

Introduction to Reconfiguration

Introduction to Reconfiguration

Introduction to Reconfiguration

On neighbourhood degree sequences of complex networks

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