Abstract
In recent years, we have witnessed an increasing use of graph pattern matching in a wide variety of applications such as social networks analysis, knowledge discovery, software plagiarism detection and many more. It is typically defined in terms of subgraph isomorphism, an NP-Complete problem. To overcome this cost, many extensions of graph simulation have been proposed that allow graph pattern matching to be conducted in cubic-time. However, in emerging applications, more expressive patterns are needed, notably ones with counting quantifiers (CQs) which are not considered by simulation-based approaches. In this article, we propose a simulation-based graph pattern matching approach that supports CQs on edges of graph patterns. We first consider CQs that express numeric aggregates only. We show that our approach is in ptime as earlier extensions of graph simulation by providing a cubic-time quantified matching algorithm, i.e., an algorithm for matching graph patterns that contain CQs. In the second part, we discuss the problem of Label-Repetition Constraints (LRCs). We define a necessary and sufficient condition for the satisfaction of LRCs. Based on this condition, we give an extension of our quantified matching algorithm to deal with LRCs in ptime, together with an optimization technique. Finally, we show that our quantified graph pattern matching approach retains the same complexity bounds when dealing with ratio aggregates. To our knowledge, this is the first effort to deal with numeric aggregates, ratio aggregates, and LRCs on graph patterns in ptime.
Published Version
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