Efficient Enumeration of Bipartite Subgraphs in Graphs

Subgraph enumeration problems ask to output all subgraphs of an input graph that belongs to the specified graph class or satisfy the given constraint. These problems have been widely studied in theoretical computer science. As far, many efficient enumeration algorithms for the fundamental substructures such as spanning trees, cycles, and paths, have been developed. This paper addresses the enumeration problem of bipartite subgraphs. Even though bipartite graphs are quite fundamental and have numerous applications in both theory and application, its enumeration algorithms have not been intensively studied, to the best of our knowledge. We propose the first non-trivial algorithms for enumerating all bipartite subgraphs in a given graph. As the main results, we develop two efficient algorithms: the one enumerates all bipartite induced subgraphs of a graph with degeneracy $k$ in $O(k)$ time per solution. The other enumerates all bipartite subgraphs in $O(1)$ time per solution

Incremental Maintenance of Maximal Bicliques in a Dynamic Bipartite Graph

We consider incremental maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition of edges. When new edges are added to the graph, we seek to enumerate the change in the set of maximal bicliques, without enumerating the set of maximal bicliques that remain unaffected. The challenge is to enumerate the change without explicitly enumerating the set of all maximal bicliques. In this work, we present (1)~Near-tight bounds on the magnitude of change in the set of maximal bicliques of a graph, due to a change in the edge set, and an (2)~Incremental algorithm for enumerating the change in the set of maximal bicliques. For the case when a constant number of edges are added to the graph, our algorithm is change-sensitive , i.e., its time complexity is proportional to the magnitude of change in the set of maximal bicliques. To our knowledge, this is the first incremental algorithm for enumerating maximal bicliques in a dynamic graph, with a provable performance guarantee. Experimental results show that its performance exceeds that of baseline implementations by orders of magnitude

BLADYG: A Graph Processing Framework for Large Dynamic Graphs

International audienceRecently, distributed processing of large dynamic graphs has become very popular , especially in certain domains such as social network analysis, Web graph analysis and spatial network analysis. In this context, many distributed/parallel graph processing systems have been proposed, such as Pregel, PowerGraph, GraphLab, and Trinity. However, these systems deal only with static graphs and do not consider the issue of processing evolving and dynamic graphs. In this paper, we are considering the issues of scale and dynamism in the case of graph processing systems. We present BLADYG, a graph processing framework that addresses the issue of dynamism in large-scale graphs. We present an implementation of BLADYG on top of akka framework. We experimentally evaluate the performance of the proposed framework by applying it to problems such as distributed k-core decomposition and partitioning of large dynamic graphs. The experimental results show that the performance and scalability of BLADYG are satisfying for large-scale dynamic graphs

GraphMineSuite: Enabling High-Performance and Programmable Graph Mining Algorithms with Set Algebra

We propose GraphMineSuite (GMS): the first benchmarking suite for graph mining that facilitates evaluating and constructing high-performance graph mining algorithms. First, GMS comes with a benchmark specification based on extensive literature review, prescribing representative problems, algorithms, and datasets. Second, GMS offers a carefully designed software platform for seamless testing of different fine-grained elements of graph mining algorithms, such as graph representations or algorithm subroutines. The platform includes parallel implementations of more than 40 considered baselines, and it facilitates developing complex and fast mining algorithms. High modularity is possible by harnessing set algebra operations such as set intersection and difference, which enables breaking complex graph mining algorithms into simple building blocks that can be separately experimented with. GMS is supported with a broad concurrency analysis for portability in performance insights, and a novel performance metric to assess the throughput of graph mining algorithms, enabling more insightful evaluation. As use cases, we harness GMS to rapidly redesign and accelerate state-of-the-art baselines of core graph mining problems: degeneracy reordering (by up to >2x), maximal clique listing (by up to >9x), k-clique listing (by 1.1x), and subgraph isomorphism (by up to 2.5x), also obtaining better theoretical performance bounds

Incremental and parallel algorithms for dense subgraph mining

The task of maintaining densely connected subgraphs from a continuously evolving graph is important because it solves many practical problems that require constant monitoring over the continuous stream of linked data often represented as a graph. For example, continuous maintenance of a certain group of closely connected nodes can reveal unusual activity over the transaction network, identification, and evolution of active groups in the social network, etc. On the other hand, mining these structures from graph data is often expensive because of the complexity of the computation and the volume of the structures (the number of densely connected structures can be of exponential order on the number of vertices in the graph). One way to deal with the expensive computations is to consider parallel computation. In this thesis, we advance the state of the art by developing provably efficient algorithms for mining maximal cliques and maximal bicliques; two fundamental dense structures. First, we consider the design of efficient algorithms for the maintenance of maximal cliques and maximal bicliques in an evolving network. We observe that it is important to locate the region of the graph in the event of the update so that we can maintain the structures by computing the changes exactly where it is located. Following this observation, we design efficient techniques that find appropriate subgraphs for identifying the changes in the structures. We prove that our algorithms can maintain dense structures efficiently. More specifically, we show that our algorithms can quickly compute the changes when it is small irrespective of the size of the graph. We empirically evaluate our algorithms and show that our algorithms significantly outperform the state of the art algorithms. Next, we consider parallel computation for efficient utilization of the multiple cores in a multi-core computing system so that the expensive mining tasks can be eased off and we can achieve better speedup than their efficient sequential counterparts. We design shared memory parallel algorithms for the mining of maximal cliques and maximal bicliques and we prove the efficiency of the parallel algorithms through showing that the total work performed by the parallel algorithm is equivalent to the time complexity of the best sequential algorithm for doing the same task. Our experimental study shows that we achieve good speedup over the prior state of the art parallel algorithms and significant speedup over the state of the art sequential algorithms. We also show that our parallel algorithms scale almost linearly with the increase in the processor cores