Given a user-specified minimum degree threshold γ, a γ-quasi-clique is a subgraph g = (Vg, Eg) where each vertex ν ∈ Vg connects to at least γ fraction of the other vertices (i.e., ⌈γ · (|Vg|- 1)⌉ vertices) in g. Quasi-clique is one of the most natural definitions for dense structures useful in finding communities in social networks and discovering significant biomolecule structures and pathways. However, mining maximal quasi-cliques is notoriously expensive. In this paper, we design parallel algorithms for mining maximal quasi-cliques on G-thinker, a distributed graph mining framework that decomposes mining into compute-intensive tasks to fully utilize CPU cores. We found that directly using G-thinker results in the straggler problem due to (i) the drastic load imbalance among different tasks and (ii) the difficulty of predicting the task running time. We address these challenges by redesigning G-thinker's execution engine to prioritize long-running tasks for execution, and by utilizing a novel timeout strategy to effectively decompose long-running tasks to improve load balancing. While this system redesign applies to many other expensive dense subgraph mining problems, this paper verifies the idea by adapting the state-of-the-art quasi-clique algorithm, Quick, to our redesigned G-thinker. Extensive experiments verify that our new solution scalesmore »
Parallel mining of large maximal quasi-cliques
Given a user-specified minimum degree threshold γ, a γ-quasi-clique is a subgraph where each vertex connects to at least γ fraction of the other vertices. Quasi-clique is a natural definition for dense structures, so finding large and hence statistically significant quasi-cliques is useful in applications such as community detection in social networks and discovering significant biomolecule structures and pathways. However, mining maximal quasi-cliques is notoriously expensive, and even a recent algorithm for mining large maximal quasi-cliques is flawed and can lead to a lot of repeated searches. This paper proposes a parallel solution for mining maximal quasi-cliques that is able to fully utilize CPU cores. Our solution utilizes divide and conquer to decompose the workloads into independent tasks for parallel mining, and we addressed the problem of (i) drastic load imbalance among different tasks and (ii) difficulty in predicting the task running time and the time growth with task subgraph size, by (a) using a timeout-based task decomposition strategy, and by (b) utilizing a priority task queue to schedule long-running tasks earlier for mining and decomposition to avoid stragglers. Unlike our conference version in PVLDB 2020 where the solution was built on a distributed graph mining framework called G-thinker, this more »
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G-thinker: a general distributed framework for finding qualified subgraphs in a big graph with load balancingFinding from a big graph those subgraphs that satisfy certain conditions is useful in many applications such as community detection and subgraph matching. These problems have a high time complexity, but existing systems that attempt to scale them are all IO-bound in execution. We propose the first truly CPU-bound distributed framework called G-thinker for subgraph finding algorithms, which adopts a task-based computation model, and which also provides a user-friendly subgraph-centric vertex-pulling API for writing distributed subgraph finding algorithms that can be easily adapted from existing serial algorithms. To utilize all CPU cores of a cluster, G-thinker features (1) a highly concurrent vertex cache for parallel task access and (2) a lightweight task scheduling approach that ensures high task throughput. These designs well overlap communication with computation to minimize the idle time of CPU cores. To further improve load balancing on graphs where the workloads of individual tasks can be drastically different due to biased graph density distribution, we propose to prioritize the scheduling of those tasks that tend to be long running for processing and decomposition, plus a timeout mechanism for task decomposition to prevent long-running straggler tasks. The idea has been integrated into a novelty algorithm for maximum cliquemore »
Cliques and clique-like subgraphs (e.g., quasi-cliques) are important dense structures whose counting or listing are essential in applications like complex network analysis and community detection. These problems are usually solved by divide and conquer, where a task over a big graph can be recursively divided into subtasks over smaller subgraphs whose search spaces are disjoint. This divisible algorithmic paradigm brings enormous potential for parallelism, since different subtasks can run concurrently to drastically reduce the overall running time. In this paper, we explore this potential by proposing a unified framework for counting and listing clique-like subgraphs. We study how to divide and distribute the counting and listing tasks, and meanwhile, to balance the assigned workloads of each thread dynamically. Four applications are studied under our parallel framework, i.e., triangle counting, clique counting, maximal clique listing and quasi-clique listing. Extensive experiments are conducted which demonstrate that our solution achieves an ideal speedup on various real graph datasets.
Quasi-cliques are a type of dense subgraphs that generalize the notion of cliques, important for applications such as community/module detection in various social and biological networks. However, the existing quasi-clique definition and algorithms are only applicable to undirected graphs. In this paper, we generalize the concept of quasi-cliques to directed graphs by proposing $(\gamma_1, \gamma_2)$-quasi-cliques which have density requirements in both inbound and outbound directions of each vertex in a quasi-clique subgraph. An efficient recursive algorithm is proposed to find maximal $(\gamma_1, \gamma_2)$-quasi-cliques which integrates many effective pruning rules that are validated by ablation studies. We also study the finding of top-$k$ large quasi-cliques directly by bootstrapping the search from more compact quasi-cliques, to scale the mining to larger networks. The algorithms are parallelized with effective load balancing, and we demonstrate that they can scale up effectively with the number of CPU cores.
Mining from a big graph those subgraphs that satisfy certain conditions is useful in many applications such as community detection and subgraph matching. These problems have a high time complexity, but existing systems to scale them are all IO-bound in execution. We propose the first truly CPU-bound distributed framework called G-thinker that adopts a user-friendly subgraph-centric vertex-pulling API for writing distributed subgraph mining algorithms. To utilize all CPU cores of a cluster, G-thinker features (1) a highly-concurrent vertex cache for parallel task access and (2) a lightweight task scheduling approach that ensures high task throughput. These designs well overlap communication with computation to minimize the CPU idle time. Extensive experiments demonstrate that G-thinker achieves orders of magnitude speedup compared even with the fastest existing subgraph-centric system, and it scales well to much larger and denser real network data. G-thinker is open-sourced at http://bit.ly/gthinker with detailed documentation.