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Abstract
Graphs are widely used to model the relationships of entities in a large spectrum of applications including social networks, world wide web, collaboration networks, and biology. Cohesive subgraph mining, as a fundamental graph problem, extracts highly connected structures from large graphs. Among the cohesive subgraph models, the core model, in which each node from the subgraph subject to a minimum degree constraint, has attracted great attention due to its elegant property and effectiveness in graph analysis. However, the massive graph volume and rapid evolution present huge challenges for core computation, which need highly efficient solutions. In this thesis, we study the problems of core computation in bipartite graphs and multilayer graphs.
Firstly, we study the problem of (α,β)-core computation in bipartite graphs. We present an efficient algorithm for (α,β)-core computation based on a novel index such that the algorithm runs in linear time regarding the result size. We prove that the index only requires O(m) space where m is the number of edges in the bipartite graph. We also devise an efficient algorithm with time complexity O (δ ·m) for index construction where δ is bounded by √m and is much smaller than √m in practice.
Secondly, we study the problem of (α,β)-core maintenance when the bipartite graph is dynamically updated. We show that we can decide whether a node should be updated or not by visiting its neighbours. Based on this locality property, we propose an efficient maintenance algorithm which only needs to visit a local subgraph near the inserted or removed edge. Furthermore, we discuss how to implement our maintenance algorithm in parallel.
Finally, we study the problem of core computation in multilayer graphs, which is challenging due to the various combinations of layers. We propose a novel concept named CoreCube, which records the results of core computation on every combination of layers. We develop efficient algorithms to compute the CoreCube and devise a hybrid storage method that achieves a superior trade-off between the size of CoreCube and the query time. Extensive experiments on real-life datasets demonstrate our algorithms are effective and efficient.