Efficient computation of the transitive closure size

Tang, Xian; Chen, Ziyang; Li, Kai; Liu, Xiang

doi:10.1007/s10586-018-2278-9

Cited by 4 publications

(11 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Existing works can be divided into two categories:(1) TC size computation [18], [20], which computes the accurate TC size.…”

Section: B Related Workmentioning

confidence: 99%

“…Calculating the accurate TC size using fast binary matrix multiplication [2], [20] has time complexity (| | 2.38 ) and space complexity (| | 2 ), which cannot scale to large graphs due to the expensive computation and space overheads. In [18], Xian Tang et al proposed an algorithm based on pathdecomposition. The result is a set of paths.…”

Section: ) Tc Size Computationmentioning

confidence: 99%

“…Given a directed graph = ( , ), where is the set of nodes and is the set of edges, the transitive closure (TC) of a node is defined as the set of all nodes that can reach in . Obtaining TC size for all nodes in directed graphs is a fundamental graph problem [1]- [18], [21], [23], [24] and has been extensively used in many applications. For example, to efficiently compute transitive reduction [23], [24].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

buTCS: An Optimized Algorithm for Estimating the Size of Transitive Closure

Wang

Zhou

et al. 2021

IEEE Access

View full text Add to dashboard Cite

Given a directed graph and a node , the transitive closure (TC) of is the set of nodes that can reach in the graph. TC size is very important in many applications but the cost of TC size computation is high in both time and space, which makes computing accurate TC size not applicable to the scenario where we need to know the TC size quickly for large graphs. Considering that existing approaches are either inefficient or inaccurate, we propose an algorithm, namely buTCS, to efficiently make more accurate estimation. Our approach works in linear time and space. The basic idea is to compute a node's TC size based on that of its out-neighbors and perform a top-down verification. We further propose two optimizations to improve the estimation accuracy. The experimental results on 13 real datasets show that buTCS achieves better estimation on TC size efficiently.

show abstract

“…Existing works can be divided into two categories:(1) TC size computation [18], [20], which computes the accurate TC size.…”

Section: B Related Workmentioning

confidence: 99%

Section: ) Tc Size Computationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

buTCS: An Optimized Algorithm for Estimating the Size of Transitive Closure

Wang

Zhou

et al. 2021

IEEE Access

View full text Add to dashboard Cite

show abstract

“…The Algorithm: We use Algorithm 2 to compute the partial 2hop distance label, which works in three steps: (1) In line 1, it computes the size of transitive closure T of G by the approach proposed in [23]. (2) In line 3, it sorts all nodes based on degree to get a node processing order.…”

Section: A Partial 2hop Distance Label Constructionmentioning

confidence: 99%

$HT$ : A Novel Labeling Scheme for k-Hop Reachability Queries on DAGs

Anping

Zhou

et al. 2019

IEEE Access

Self Cite

View full text Add to dashboard Cite

Given a directed acyclic graph (DAG), a k-hop reachability query u ?k − → v is used to answer whether there exists a path from u to v with length ≤ k. Answering k-hop reachability queries is a fundamental graph operation and has been extensively studied during the past years. Considering that existing approaches still suffer from inefficiency in practice when processing large graphs, we propose a novel labeling scheme, namely HT, to accelerate k-hop reachability queries answering. HT uses a constrained 2hop distance label to maintain the length of shortest paths between a set of hop nodes and other nodes, and for the remaining reachability information, HT uses a novel topological level to accelerate graph traversal. Further, we propose to enhance HT by two optimization techniques. The experimental results show that compared with the state-of-the-art approaches, HT works best for most graphs when answering k-hop reachability queries with small index size and reasonable index construction time.INDEX TERMS Graph data management, reachability queries processing, k-hop reachability.

show abstract

“…One is computing the size of TC, the other is computing the exact number of reachable queries that can be answered by the partial 2-hop labels, which we call as the coverage size. Considering that TC size computation can be efficiently solved by existing works [27], the difficulty of reachability ratio computation lies in how to efficiently compute the coverage size. The naive way is first generating partial 2-hop labels based on k selected hop-nodes, then getting the coverage size by checking all node pairs using the partial 2-hop labels.…”

Section: Introductionmentioning

confidence: 99%

Efficient Reachability Ratio Computation for 2-hop Labeling Scheme

Zhou¹,

Tang²,

Du³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

As one of the fundamental graph operations, reachability queries processing has been extensively studied during the past decades. Many approaches followed the line of designing 2-hop labels to make acceleration. Considering that the index size cannot be bounded when using all nodes to construct 2-hop labels, researchers proposed to use a part of important nodes to construct 2-hop labels (partial 2-hop labels) to cover as much reachability information as possible. Then, we may achieve better query performance with limited index size and index construction time. However, partial 2-hop labels do not always perform well on different graphs. In this paper, we focus on the problem of how to efficiently compute reachability ratio, such that to help users determine whether partial 2-hop labels should be used to answer reachability queries for the given graph. Intuitively, reachability ratio denotes the ratio of the number of reachable queries that can be answered by partial 2-hop labels over the total number of reachable queries involved in the given graph. We discuss the difficulties of reachability ratio computation, and propose an incremental-partition algorithm for reachability ratio computation. We show by rich experimental results that our algorithm can efficiently get the result of reachability ratio, and show how the overall query performance is affected by different partial 2-hop labels. Based on the experimental results, we give out our findings on whether partial 2-hop labels should be used to the given graph for reachability queries processing.

show abstract

Efficient computation of the transitive closure size

Cited by 4 publications

References 22 publications

buTCS: An Optimized Algorithm for Estimating the Size of Transitive Closure

buTCS: An Optimized Algorithm for Estimating the Size of Transitive Closure

$HT$ : A Novel Labeling Scheme for k-Hop Reachability Queries on DAGs

Efficient Reachability Ratio Computation for 2-hop Labeling Scheme

Contact Info

Product

Resources

About