Efficient Graph Similarity Search Over Large Graph Databases

Abstract

Since many graph data are often noisy and incomplete in real applications, it has become increasingly important to retrieve graphs g in the graph database D that approximately match the query graph q, rather than exact graph matching. In this paper, we study the problem of graph similarity search, which retrieves graphs that are similar to a given query graph under the constraint of graph edit distance. We propose a systematic method for edit-distance based similarity search problem. Specifically, we derive two lower bounds, i.e., partition-based and branch-based bounds, from different perspectives. More importantly, a hybrid lower bound incorporating both ideas of the two lower bounds is proposed, which is theoretically proved to have higher (at least not lower) pruning power than using the two lower bounds together. We also present a uniform index structure, namely u-tree, to facilitate effective pruning and efficient query processing. Extensive experiments confirm that our proposed approach outperforms the existing approaches significantly, in terms of both the pruning power and query response time.

Semantic locality‐based approximate knowledge graph query

“…Graph queries via structure similarity. Structure similarity based graph pattern match is one commonly used technology to support query over knowledge graph . Zheng et al proposed a instance‐driven mining algorithm to detect diverse structure patterns with equivalent semantic meanings of priori knowledge .…”

“…Zheng et al proposed a instance‐driven mining algorithm to detect diverse structure patterns with equivalent semantic meanings of priori knowledge . On the other hand, graph edit distance is adopted in existing approaches . A graph similarity search over a large number of graphs was defined in the work of Zheng et al In addition, SAGA presented an extension of graph edit distance to allow some special cases of node gaps, node mismatches and graph structural differences.…”

“…The example of ''schema-free'' RDF KG and an example of simple SPARQL expression FIGURE 2 The basic idea of trans-based semantic vector embedding Figure 1. The semantic similarity-based approaches 2,7,[15][16][17] use the concept-level or string edit distance to denote semantics without considering the real knowledge semantics. Moreover, other works 2,18,19 assisted non-expert users by taking prior knowledge to discover more similar answers.…”

Improved local search for graph edit distance

“…The development of heuristics was particularly triggered by the algorithms presented in [5] and [4], which use transformations to the linear sum assignment problem with error correction (LSAPE) [6] -a variant of the linear sum assignment problem (LSAP) where rows and columns may also be inserted and deleted -to compute upper bounds for GED. Further transformations from GED to LSAPE have been proposed in [7,8,9,10,11,12,13,14].…”

NetLSD

“…Heat trace approximation by two Taylor terms and 100 eigenvalues on a random blockmodel[22] graph. (a) Small t (0.5) (b) Medium t (4.5) (c) Large t(55,555) The diagonal of H t at different scales on the Karate club graph; at a large scale, the field reflects node centrality.…”