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Given a user-specified minimum degree threshold $\gamma$, a$\gamma$-quasi-clique is a subgraph $g=(V_g,E_g)$ where each vertex $v\in V_g$connects to at least $\gamma$ fraction of the other vertices (i.e., $\lceil\gamma\cdot(|V_g|-1)\rceil$ vertices) in $g$. Quasi-clique is one of the mostnatural definitions for dense structures useful in finding communities insocial networks and discovering significant biomolecule structures andpathways. However, mining maximal quasi-cliques is notoriously expensive.  In this paper, we design parallel algorithms for mining maximal quasi-cliqueson G-thinker, a recent distributed framework targeting divide-and-conquer graphmining algorithms that decomposes the mining into compute-intensive tasks tofully utilize CPU cores. However, we found that directly using G-thinkerresults in the straggler problem due to (i) the drastic load imbalance amongdifferent tasks and (ii) the difficulty of predicting the task running time andthe time growth with task-subgraph size. We address these challenges byredesigning G-thinker's execution engine to prioritize long-running tasks formining, and by utilizing a novel timeout strategy to effectively decompose themining workloads of long-running tasks to improve load balancing. While thissystem redesign applies to many other expensive dense subgraph mining problems,this paper verifies the idea by adapting the state-of-the-art quasi-cliquealgorithm, Quick, to our redesigned G-thinker. We improve Quick by integratingnew pruning rules, and fixing some missed boundary cases that could lead tomissed results. Extensive experiments verify that our new solution scales wellwith the number of CPU cores, achieving 201$\times$ runtime speedup when mininga graph with 3.77M vertices and 16.5M edges in a 16-node cluster.

Scalable Mining of Maximal Quasi-Cliques: An Algorithm-System Codesign Approach