On structure preserving sampling and approximate partitioning of graphs

Heeswijk, Wouter van; Fletcher, George H. L.; Pechenizkiy, Mykola

doi:10.1145/2851613.2851650

Cited by 7 publications

(7 citation statements)

References 18 publications

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“…Relation to k-bisimulation. k-bisimulation [20,21,22,10] is a type of approximate bisimulation. Given a graph G(V, E, ) and an integer k ≥ 0, node u is simulated by node v via k-bisimulation [21] (i.e., u and v are k-bisimilar) if, and only if, the following conditions hold: (1) (u) = (v); (2) if k > 0, for ∀u ∈ N + G (u), there exists v ∈ N + G (v) s.t.…”

Section: Discussionmentioning

confidence: 99%

“…Reverting to the original definition is as easy as setting w − = 0 in our framework. Additionally, we discussed a variant of approximate bisimulation, namely k-bisimulation [20,21,22,10], and investigated its relation to our framework (Section 4.3). There are other variants that have not yet included in the framework, including bounded simulation [5] and weak simulation [3].…”

Section: Related Workmentioning

confidence: 99%

“…As an interesting future work, we will study to incorporate them in our framework. There are also some algorithms that aim to compute simulation (variants) efficiently and effectively, e.g., a hash-based algorithm in [10], external-memory algorithms in [8,22], a distributed algorithm in [21] and a partition refinement algorithm in [48]. However, all these algorithms compute the "yes-or-no" simulation (or its variant) and cannot provide fractional scores as proposed in this paper.…”

Section: Related Workmentioning

confidence: 99%

“…For example, simulation and degree-preserving simulation are shown to be effective in graph pattern matching [5,1,6,4], and a node in the data graph is considered to be a potential match for a node in the query graph if it simulates the query node. Bisimulation has been applied to compute RDF graph alignment [7] and graph partition [8,9,10]. Generally, two nodes will be aligned or be placed in the same partition if they are in a bisimulation relation.…”

Section: Introductionmentioning

confidence: 99%

“…FSim χ is an iterative framework that computes the fractional χ-simulation scores for all pairs of nodes over two graphs. Furthermore, we show the relations of FSim χ to several well-known concepts, including node similarity measures (i.e., SimRank [18] and RoleSim [19]) and an approximate variant of bisimulation (i.e., k-bisimulation [20,21,22,10]), in Section 4.3.…”

Section: Introductionmentioning

confidence: 99%

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A Framework to Quantify Approximate Simulation on Graph Data

Chen

Lai

et al. 2020

Preprint

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Simulation and its variants (e.g., bisimulation and degree-preserving simulation) are useful in a wide spectrum of applications. However, all simulation variants are coarse "yes-or-no" indicators that simply confirm or refute whether one node simulates another, which limits the scope and power of their utility. Therefore, it is meaningful to develop a fractional χ-simulation measure to quantify the degree to which one node simulates another by the simulation variant χ. To this end, we first present several properties necessary for a fractional χ-simulation measure. Then, we present FSim χ , a general fractional χ-simulation computation framework that can be configured to quantify the extent of all χ-simulations. Comprehensive experiments and real-world case studies show the measure to be effective and the computation framework to be efficient.1 A node u is an out-neighbor of u, if there is an outgoing edge from u to u in G. Similarly, u is an in-neighbor of u, if an edge from u to u presents.

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Section: Discussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Framework to Quantify Approximate Simulation on Graph Data

Chen

Lai

et al. 2020

Preprint

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Efficient Densest Subgraphs Discovery in Large Dynamic Graphs by Greedy Approximation

Han¹

2023

IEEE Access

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Densest subgraph detection has become an important primitive in graph mining tasks when analyzing communities and detecting events in a wide range of application domains. Currently, it is a challenging and practically crucial research issue to develop efficient densest subgraphs mining approaches that can handle both very large and continuously evolving graphs. Although large-scale or dynamic methods have been proposed to find the densest subgraphs, there is still a lack of a promising method to deal with largescale and dynamically evolving graphs. In this paper, the problem is formulated and proved to be NP-Hard, an incremental greedy approximation approach is proposed, and its running time is O(m+n). In order to find the densest subgraph effectively by heuristically merging the local densest subgraphs, firstly, the edge flow of a dynamic graph is divided into several subgraphs in a given period of T . Secondly, a local candidate set is generated by local denser subgraph discovery. Third, the global densest subgraph candidates are collected by heuristically merging. Last, the densest subgraphs are induced from the global densest subgraph candidates with constraints by static densest subgraph discovery algorithm. This incremental approach enables us to scale up the existing densest subgraph discovery algorithms, which focus mainly on small and static graphs and thus can handle very large dynamic graphs. Experiments on real-world networks with billions of nodes for comprehensive evaluations present excellent improvement in efficiency and accuracy: it reduces about 25% running time on average and presents a more accurate estimation of the structure of a graph with more compact subgraphs than the static method.It also performs well when dealing with graphs of varying densities. INDEX TERMSDensest subgraphs, incremental greedy approximation, heuristically merging, local candidate, global densest subgraph candidates.

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