Incremental graph pattern matching

Abstract

Graph pattern matching has become a routine process in emerging applications such as social networks. In practice a data graph is typically large, and is frequently updated with small changes. It is often prohibitively expensive to recompute matches from scratch via batch algorithms when the graph is updated. With this comes the need for incremental algorithms that compute changes to the matches in response to updates, to minimize unnecessary recomputation. This paper investigates incremental algorithms for graph pattern matching defined in terms of graph simulation, bounded simulation and subgraph isomorphism. (1) For simulation, we provide incremental algorithms for unit updates and certain graph patterns. These algorithms are optimal: in linear time in the size of the changes in the input and output, which characterizes the cost that is inherent to the problem itself. For general patterns we show that the incremental matching problem is unbounded, i.e., its cost is not determined by the size of the changes alone. (2) For bounded simulation, we show that the problem is unbounded even for unit updates and path patterns. (3) For subgraph isomorphism, we show that the problem is intractable and unbounded for unit updates and path patterns. (4) For multiple updates, we develop an incremental algorithm for each of simulation, bounded simulation and subgraph isomorphism. We experimentally verify that these incremental algorithms significantly outperform their batch counterparts in response to small changes, using real-life data and synthetic data.

Time Constrained Continuous Subgraph Search Over Streaming Graphs

“…The research on continuous query processing over highspeed streaming graph data is rather scarce. Fan et al [11] propose an incremental solution for subgraph isomorphism based on repeated search over dynamic graph data, which cannot utilize previously computed results when new data come from the stream since they do not maintain any partial result. To avoid the high overhead in building complicated index, there is some work on approximate solution to subgraph isomorphism.…”

StreamWorks

“…We can search for a pattern repeatedly or we can adopt an incremental approach. The work by Fan et al [7] presents incremental algorithms for graph pattern matching. However, their solution to subgraph isomorphism is based on the repeated search strategy.…”

Network Alignment by Discrete Ollivier-Ricci Flow

“…Given two graphs G 1 and G 2 with approximately the same graph topology, we want to find the correspondence of their nodes -node v in G 1 is mapped to a node f (v) in G 2 such that whenever u, v is connected in G 1 , f (u), f (v) are likely to be connected in G 2 as well. This is called the network alignment problem and has been heavily studied [10] with numerous applications including database schema matching [19], protein interaction alignment [59,9,15,45], ontology matching [58], pattern recognition [48] and social networks [71,23].…”