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1. G-thinker: a general distributed framework for finding qualified subgraphs in a big graph with load balancing

   https://doi.org/10.1007/s00778-021-00688-z  

   Yan, Da ; Guo, Guimu ; Khalil, Jalal ; Özsu, M. Tamer ; Ku, Wei-Shinn ; Lui, John C. ( January 2022 , The VLDB journal)

   Finding 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 »finding (MCF) that adopts a hybrid task decomposition strategy, which significantly improves the running time of MCF on dense and large graphs: The algorithm finds a maximum clique of size 1,109 on a large and dense WikiLinks graph dataset in 70 minutes. 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.« less
2. Scalable Mining of Maximal Quasi-Cliques: An Algorithm-System Codesign Approach

   https://doi.org/10.14778/3436905.3436916  

   Guo, Guimu ; Yan, Da ; Özsu, M. Tamer ; Jiang, Zhe ; Khalil, Jalal ( January 2020 , Proceedings of the VLDB Endowment)

   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 »well with the number of CPU cores, achieving 201× runtime speedup when mining a graph with 3.77M vertices and 16.5M edges in a 16-node cluster.« less
3. Parallel mining of large maximal quasi-cliques

   https://doi.org/10.1007/s00778-021-00712-2  

   Khalil, Jalal ; Guo, Guimu ; Yuan, Lyuheng ( January 2022 , The VLDB journal)

   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, thismore »paper targets a single-machine multi-core environment which is more accessible to an average end user. A general framework called T-thinker is developed to facilitate the programming of parallel programs for algorithms that adopt divide and conquer, including but not limited to our quasi-clique mining algorithm. Additionally, we consider the problem of directly mining large quasi-cliques from dense parts of a graph, where we identify the repeated search issue of a recent method and address it using a carefully designed concurrent trie data structure. Extensive experiments verify that our parallel solution scales well with the number of CPU cores, achieving 26.68× runtime speedup when mining a graph with 3.77M vertices and 16.5M edges with 32 mining threads. Additionally, mining large quasi-cliques from dense parts can provide an additional speedup of up to 89.46×.« less
4. T-thinker: a task-centric distributed framework for compute-intensive divide-and-conquer algorithms

   https://doi.org/10.1145/3293883.3295709  

   Yan, Da ; Guo, Guimu ; Chowdhury, Md Mashiur ; Özsu, M. Tamer ; Lui, John C. ; Tan, Weida ( February 2019 , Proceedings of the 24th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming)

   Many computationally expensive problems are solved by a divide-and-conquer algorithm: a problem over a big dataset can be recursively divided into independent tasks over smaller subsets of the dataset. We present a distributed general-purpose framework called T-thinker which effectively utilizes the CPU cores in a cluster by properly decomposing an expensive problem into smaller independent tasks for parallel computation. T-thinker well overlaps CPU processing with network communication, and its superior performance is verified over a re-engineered graph mining system G-thinker available at http://cs.uab.edu/yanda/gthinker/
5. A Weighted Approach to the Maximum Cardinality Bipartite Matching Problem with Applications in Geometric Settings

   Lahn, Nathaniel ; Raghvendra, Sharath ( June 2019 , Leibniz international proceedings in informatics)

   We present a weighted approach to compute a maximum cardinality matching in an arbitrary bipartite graph. Our main result is a new algorithm that takes as input a weighted bipartite graph G(A cup B,E) with edge weights of 0 or 1. Let w <= n be an upper bound on the weight of any matching in G. Consider the subgraph induced by all the edges of G with a weight 0. Suppose every connected component in this subgraph has O(r) vertices and O(mr/n) edges. We present an algorithm to compute a maximum cardinality matching in G in O~(m(sqrt{w} + sqrt{r} + wr/n)) time. When all the edge weights are 1 (symmetrically when all weights are 0), our algorithm will be identical to the well-known Hopcroft-Karp (HK) algorithm, which runs in O(m sqrt{n}) time. However, if we can carefully assign weights of 0 and 1 on its edges such that both w and r are sub-linear in n and wr=O(n^{gamma}) for gamma < 3/2, then we can compute maximum cardinality matching in G in o(m sqrt{n}) time. Using our algorithm, we obtain a new O~(n^{4/3}/epsilon^4) time algorithm to compute an epsilon-approximate bottleneck matching of A,B subsetR^2 and an 1/(epsilon^{O(d)}}n^{1+(d-1)/(2d-1)}) poly logmore »n time algorithm for computing epsilon-approximate bottleneck matching in d-dimensions. All previous algorithms take Omega(n^{3/2}) time. Given any graph G(A cup B,E) that has an easily computable balanced vertex separator for every subgraph G'(V',E') of size |V'|^{delta}, for delta in [1/2,1), we can apply our algorithm to compute a maximum matching in O~(mn^{delta/1+delta}) time improving upon the O(m sqrt{n}) time taken by the HK-Algorithm.« less