Parallel Batch-Dynamic Graph Connectivity

Acar, Umut A.; Anderson, D. Mark; Blelloch, Guy E.; Dhulipala, Laxman

doi:10.1145/3323165.3323196

Cited by 31 publications

(5 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then, implicit in their paper is the following lemma: Lemma 5.1 (Recent Edge [13]). If F is a minimum spanning forest (MSF) of the edges in the stream so far, where each edge e carries a weight of −τ (e), then any pair of vertices u and v are connected if and only if (1) there is a path between u and v in F and (2) the heaviest edge e * (i.e., the oldest edge) on this path satisfies τ (e * ) ≥ T W , where T W is the τ (•) of the oldest edge in the window.…”

Section: Graph Connectivitymentioning

confidence: 99%

“…To approximate the weight of the MSF, we propose the following: For this problem, assume that the edge weights are between 1 and n O (1) . Using known reductions [11,4,13], the weight of the MSF of G can be approximated up to 1 + ε by tracking the number of connected components in graphs G 0 , G 1 , .…”

Section: Approximate Msf Weightmentioning

confidence: 99%

“…Symmetrically, edge expiration is handled by batch-expiring edges in R instances in parallel. Additionally, at the end of each update operation, we recompute equation (1), which involes R terms and calls to numComponents(). This recomputation step requires O(R) work and O(lg R) = O(lg 2 n) span.…”

Section: Approximate Msf Weightmentioning

confidence: 99%

“…There exists a data structure that maintains the MSF of a weighted undirected graph that can insert a batch of edges into a graph with n vertices in O lg 1 + n work in expectation and O(lg 2 (n)) span w.h.p. 1 in the arbitrary-CRCW PRAM.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Work-efficient Batch-incremental Minimum Spanning Trees with Applications to the Sliding Window Model

Anderson,

Blelloch,

Tangwongsan

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Algorithms for dynamically maintaining minimum spanning trees (MSTs) have received much attention in both the parallel and sequential settings. While previous work has given optimal algorithms for dense graphs, all existing parallel batch-dynamic algorithms perform polynomial work per update in the worst case for sparse graphs. In this paper, we present the first work-efficient parallel batch-dynamic algorithm for incremental MST, which can insert edges in O( lg(1 + n/ )) work in expectation and O(polylog(n)) span w.h.p. The key ingredient of our algorithm is an algorithm for constructing a compressed path tree of an edge-weighted tree, which is a smaller tree that contains all pairwise heaviest edges between a given set of marked vertices. Using our batch-incremental MST algorithm, we demonstrate a range of applications that become efficiently solvable in parallel in the sliding-window model, such as graph connectivity, approximate MSTs, testing bipartiteness, k-certificates, cycle-freeness, and maintaining sparsifiers.

show abstract

Section: Graph Connectivitymentioning

confidence: 99%

Section: Approximate Msf Weightmentioning

confidence: 99%

Section: Approximate Msf Weightmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Work-efficient Batch-incremental Minimum Spanning Trees with Applications to the Sliding Window Model

Anderson,

Blelloch,

Tangwongsan

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Many algorithms were developed under the parallel dynamic model, in which a graph undergoes a series of incoming parallel updates. Next, the parallel batch-dynamic model is a recent development in the area of parallel dynamic graph algorithms [5], [191], [4], [200]. In this model, a graph is modified by updates coming in batches.…”

Section: Parallel Dynamic Graph Algorithmsmentioning

confidence: 99%

Practice of Streaming Processing of Dynamic Graphs: Concepts, Models, and Systems

Besta¹,

Fischer²,

Kalavri³

et al. 2019

Preprint

View full text Add to dashboard Cite

Graph processing has become an important part of various areas of computing, including machine learning, medical applications, social network analysis, computational sciences, and others. A growing amount of the associated graph processing workloads are dynamic, with millions of edges added or removed per second. Graph streaming frameworks are specifically crafted to enable the processing of such highly dynamic workloads. Recent years have seen the development of many such frameworks. However, they differ in their general architectures (with key details such as the support for the parallel execution of graph updates, or the incorporated graph data organization), the types of updates and workloads allowed, and many others. To facilitate the understanding of this growing field, we provide the first analysis and taxonomy of dynamic and streaming graph processing. We focus on identifying the fundamental system designs and on understanding their support for concurrency and parallelism, and for different graph updates as well as analytics workloads. We also crystallize the meaning of different concepts associated with streaming graph processing, such as dynamic, temporal, online, and time-evolving graphs, edge-centric processing, models for the maintenance of updates, and graph databases. Moreover, we provide a bridge with the very rich landscape of graph streaming theory by giving a broad overview of recent theoretical related advances, and by analyzing which graph streaming models and settings could be helpful in developing more powerful streaming frameworks and designs. We also outline graph streaming workloads and research challenges.

show abstract

Accelerated butterfly counting with vertex priority on bipartite graphs

et al. 2022

View full text Add to dashboard Cite

Bipartite graphs are of great importance in many real-world applications. Butterfly, which is a complete $$2 \times 2$$ 2 × 2 biclique, plays a key role in bipartite graphs. In this paper, we investigate the problem of efficient counting the number of butterflies. The most advanced techniques are based on enumerating wedges which is the dominant cost of counting butterflies. Nevertheless, the existing algorithms cannot efficiently handle large-scale bipartite graphs. This becomes a bottleneck in large-scale applications. In this paper, instead of the existing layer-priority-based techniques, we propose a vertex-priority-based paradigm $${\mathsf {BFC}}$$ BFC -$${\mathsf {VP}}$$ VP to enumerate much fewer wedges; this leads to a significant improvement of the time complexity of the state-of-the-art algorithms. In addition, we present cache-aware strategies to further improve the time efficiency while theoretically retaining the time complexity of $${\mathsf {BFC}}$$ BFC -$${\mathsf {VP}}$$ VP . We also show that our proposed techniques can work efficiently in external and parallel contexts. Moreover, we study the butterfly counting problem on batch-dynamic graphs. Specifically, given a bipartite graph G and a batch-update of edges B, we aim to maintain the number of butterflies in G. To tackle this problem, fast vertex-priority-based algorithms are proposed with optimizations for reducing the computation of existing wedges in G. Our extensive empirical studies demonstrate that the proposed techniques significantly outperform the baseline solutions on real datasets.

show abstract

Parallel Batch-Dynamic Graph Connectivity

Cited by 31 publications

References 61 publications

Work-efficient Batch-incremental Minimum Spanning Trees with Applications to the Sliding Window Model

Work-efficient Batch-incremental Minimum Spanning Trees with Applications to the Sliding Window Model

Practice of Streaming Processing of Dynamic Graphs: Concepts, Models, and Systems

Accelerated butterfly counting with vertex priority on bipartite graphs

Contact Info

Product

Resources

About