A survey of graph edit distance

Gao, Xinbo; Xiao, Bing; Tao, Dacheng; Li, Xuelong

doi:10.1007/s10044-008-0141-y

Cited by 534 publications

(277 citation statements)

References 56 publications

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“…It is based on heuristics that are experimentally studied without rigorous proofs of approximation guarantees. Similarly, the general problem of graph edit distance [10] also encompasses approximate graph isomorphism. Both graph matchings and graph edit distance give rise to a variety of natural computational problems that are well studied.…”

Section: Introductionmentioning

confidence: 99%

Approximate Graph Isomorphism

Arvind

Köbler

Kuhnert

et al. 2012

Mathematical Foundations of Computer Science 2012

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Abstract. We study optimization versions of Graph Isomorphism. Given two graphs G1, G2, we are interested in finding a bijection π from V (G1) to V (G2) that maximizes the number of matches (edges mapped to edges or non-edges mapped to non-edges). We give an n O(log n) time approximation scheme that for any constant factor α < 1, computes an α-approximation. We prove this by combining the n O(log n) time additive error approximation algorithm of Arora et al. [Math. Program., 92, 2002] with a simple averaging algorithm. We also consider the corresponding minimization problem (of mismatches) and prove that it is NP-hard to α-approximate for any constant factor α. Further, we show that it is also NP-hard to approximate the maximum number of edges mapped to edges beyond a factor of 0.94. We also explore these optimization problems for bounded color class graphs which is a well studied tractable special case of Graph Isomorphism. Surprisingly, the bounded color class case turns out to be harder than the uncolored case in the approximate setting.

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Section: Introductionmentioning

confidence: 99%

Approximate Graph Isomorphism

Arvind

Köbler

Kuhnert

et al. 2012

Mathematical Foundations of Computer Science 2012

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“…1 The majority of the works focuses on how to compare different graph snapshots, and aims to detect those snapshots where the graph structure changes significantly. The research tools developed in this area include novel metrics for graph similarity [48] and graph distance, (see the survey of Gao et al [24]), as well as extending scan-statistics methods for graphs [50], while a number of papers relies on matrix-decomposition methods [5,32].…”

Section: Snapshot-based Community Detectionmentioning

confidence: 99%

Discovering Dynamic Communities in Interaction Networks

Rozenshtein

Tatti

Gionis

2014

Machine Learning and Knowledge Discovery in Databases

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Very often online social networks are defined by aggregating information regarding the interaction between the nodes of the network. For example, a call graph is defined by considering an edge for each pair of individuals who have called each other at least once -or at least k times. Similarly, an implicit social network in a social-media site is defined by considering an edge for each pair of users who have interacted in some way, e.g., have made a conversation, commented to each other's content, etc. Despite the fact that this type of definitions have been used to obtain a lot of insights regarding the structure of social networks, it is obvious that they suffer from a severe limitation: they neglect the precise time that the interaction between network nodes occurs.In this thesis we propose to study interaction networks, where one considers not only the underlying topology of the social network, but also the exact time instances that nodes interact. In an interaction network an edge is associated with a time stamp, and multiple edges may occur for the same pair of nodes. Consequently, interaction networks offer a more fine-grained representation that can be used to reveal otherwise hidden dynamic phenomena in the network.In the context of interaction networks, we study the problem of discovering communities, which are dense in terms of the underlying network structure, and whose edges occur in short time intervals. Such communities represent groups of individuals who interact with each other in some specific time instances, for example, a group of employees who work on a project and whose interaction intensifies before certain project milestones. We prove that the problem we define is NP-hard, and we provide effective algorithms by adapting techniques used to find dense subgraphs. We perform extensive evaluation of the proposed methods on synthetic and real datasets, which demonstrates the validity of our concepts and the good performance of our algorithms.

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“…Hu et al [6], who consider several electronic versions of historical manuscripts. There exists extensive research on reconstructing sequences of operations based on input and output data, but either the entities and operations involved are very simple [5,14,8] or they are tailored to a specific situation [23]. Other approaches require a lot of knowledge, either a formal description of the operations and user requirements on the composite operation (e.g.…”

Section: Related Workmentioning

confidence: 99%

Reconstructing Provenance

Magliacane¹

2012

The Semantic Web – ISWC 2012

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Abstract. Provenance is an increasingly important aspect of data management that is often underestimated and neglected by practitioners. In our work, we target the problem of reconstructing provenance of files in a shared folder setting, assuming that only standard filesystem metadata are available. We propose a content-based approach that is able to reconstruct provenance automatically, leveraging several similarity measures and edit distance algorithms, adapting and integrating them into a multi-signal pipeline. We discuss our research methodology and show some promising preliminary results.

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A survey of graph edit distance

Cited by 534 publications

References 56 publications

Approximate Graph Isomorphism

Approximate Graph Isomorphism

Discovering Dynamic Communities in Interaction Networks

Reconstructing Provenance

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