Fast Computation of Reachability Labeling for Large Graphs

Abstract

There are numerous applications that need to deal with a large graph and need to query reachability between nodes in the graph. A 2-hop cover can compactly represent the whole edge transitive closure of a graph in O(|V | · |E| 1/2 ) space, and be used to answer reachability query efficiently. However, it is challenging to compute a 2-hop cover. The existing approaches suffer from either large resource consumption or low compression rate. In this paper, we propose a hierarchical partitioning approach to partition a large graph G into two subgraphs repeatedly in a top-down fashion. The unique feature of our approach is that we compute 2-hop cover while partitioning. In brief, in every iteration of top-down partitioning, we provide techniques to compute the 2-hop cover for connections between the two subgraphs first. A cover is computed to cut the graph into two subgraphs, which results in an overall cover with high compression for the entire graph G. Two approaches are proposed, namely a node-oriented approach and an edge-oriented approach. Our approach can efficiently compute 2-hop cover for a large graph with high compression rate. Our extensive experiment study shows that the 2-hop cover for a graph with 1,700,000 nodes and 169 billion connections can be obtained in less than 30 minutes with a compression rate about 40,000 using a PC.

Reachability querying: an independent permutation labeling approach

“…In [13], an approximate (greedy) algorithm is proposed. Several heuristic approaches are proposed to compute 2-Hop [23,11,12]. Furthermore, Jin et al propose 3-Hop [20] to improve 2-Hop by utilizing the idea of the chain decomposition as used in Chain-Cover.…”

“…The real applications that need this operation are many and can be found among online social networks, biological networks, ontology, transportation networks, etc. The reachability query has been extensively studied over a decade [1,16,13,23,11,28,7,26,12,8,21,20,29,27,9,10,19,24,31], and the early work can be traced back to 1989 to compute transitive closure (TC) over a graph. However, it is still an unsolved question whether we can do faster to answer reachability queries online over even larger and/or even denser graphs with the possible minimum cost (time/space) for offline precomputing and preparation.…”

“…On the other hand, there are two main ways taken by the LabelOnly approaches. (1) Some works aim at constructing a small index by compressing TC, because it leads to a small index, and therefore reduces query time [1,16,13,28,11,12,8,21,20,27]. (2) Some works aim at constructing an index fast.…”

Coding-based Join Algorithms for Structural Queries on Graph-Structured XML Document

“…In this algorithm, brtree is a RST that supports the following methods: insert(I) and trim (v). insert(I) will insert an interval r [1,9] a1 [1,3] t1 [1,2] d1 [1,1] a3 [4,6] a4 [4,5] d2 [4,4] d3 [7,7] I to the RST; trim(v) will batch delete the intervals in brtree whose y values smaller than v. For example, let's consider running IGMJ on the same example above. x values of a1 and a2( [1,1]) are smaller than d1.…”

“…Many reachability labelling schemes of DAG have been presented, including [9,11,17] and [6]. Vassilis Christophides and Plexousakis [23] presents a survey of labelling schemes on DAG and compare the labelling schemes on the coding of semantic web.…”