Incremental graph pattern matching

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 recom-pute 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 sim-ulation 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 match-ing problem is unbounded, i.e., its cost is not determined by the size of the changes alone. (2) For bounded simula-tion, 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 exper-imentally verify that these incremental algorithms signifi-cantly outperform their batch counterparts in response to small changes, using real-life data and synthetic data. Categories and Subject Descriptors: F.2 [Analysis of algorithms and problem complexity]: Nonnumerical algo-rithms and problems[pattern matching

Incremental graph pattern matching

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 recom-pute 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 sim-ulation 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 match-ing problem is unbounded, i.e., its cost is not determined by the size of the changes alone. (2) For bounded simula-tion, 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 exper-imentally verify that these incremental algorithms signifi-cantly outperform their batch counterparts in response to small changes, using real-life data and synthetic data. Categories and Subject Descriptors: F.2 [Analysis of algorithms and problem complexity]: Nonnumerical algo-rithms and problems[pattern matching

Incremental Graph Pattern Matching: Data Structures and Initial Experiments

Despite the large variety of existing graph transformation tools, the implementation of their pattern matching engine typically follows the same principle. First a matching occurrence of the left-hand side of the graph transformation rule is searched by some graph pattern matching algorithm. Then potential negative application conditions are checked that might eliminate the previous occurrence. However, when a new transformation step is started, all the information on previous matchings is lost, and the complex graph pattern matching phase is restarted from scratch each time. In the paper, we present the foundational data structures and initial experiments for an incremental graph pattern matching engine which keeps track of existing matchings in an incremental way to reduce the execution time of graph pattern matching

Parallelization of Graph Transformation Based on Incremental Pattern Matching

oai:journal.ub.tu-berlin.de:article/265Graph transformation based on incremental pattern matching explicitly stores all occurrences of patterns (left-hand side of rules) and updates this result cache upon model changes. This allows instantaneous pattern queries at the expense of costlier model manipulation and higher memory consumption. Up to now, this incremental approach has considered only sequential execution despite the inherently distributed structure of the underlying match caching mechanism. The paper explores various possibilities of parallelizing graph transformation to harness the power of modern multi-core, multi-processor computing environments: (i) incremental pattern matching enables the concurrent execution of model manipulation and pattern matching; moreover, (ii) pattern matching itself can be parallelized along caches

Extending graph homomorphism and simulation for real life graph matching

Among the vital problems in a variety of emerging applications is the graph matching problem, which is to determine whether two graphs are similar, and if so, find all the valid matches in one graph for the other, based on specified metrics. Traditional graph matching approaches are mostly based on graph homomorphism and isomorphism, falling short of capturing both structural and semantic similarity in real life applications. Moreover, it is preferable while difficult to find all matches with high accuracy over complex graphs. Worse still, the graph structures in real life applications constantly bear modifications. In response to these challenges, this thesis presents a series of approaches for ef?ciently solving graph matching problems, over both static and dynamic real life graphs. Firstly, the thesis extends graph homomorphism and subgraph isomorphism, respectively, by mapping edges from one graph to paths in another, and by measuring the semantic similarity of nodes. The graph similarity is then measured by the metrics based on these extensions. Several optimization problems for graph matching based on the new metrics are studied, with approximation algorithms having provable guarantees on match quality developed. Secondly, although being extended in the above work, graph matching is defined in terms of functions, which cannot capture more meaningful matches and is usually hard to compute. In response to this, the thesis proposes a class of graph patterns, in which an edge denotes the connectivity in a data graph within a predefined number of hops. In addition, the thesis defines graph pattern matching based on a notion of bounded simulation relation, an extension of graph simulation. With this revision, graph pattern matching is in cubic-time by providing such an algorithm, rather than intractable. Thirdly, real life graphs often bear multiple edge types. In response to this, the thesis further extends and generalizes the proposed revisions of graph simulation to a more powerful case: a novel set of reachability queries and graph pattern queries, constrained by a subclass of regular path expressions. Several fundamental problems of the queries are studied: containment, equivalence and minimization. The enriched reachability query does not increase the complexity of the above problems, shown by the corresponding algorithms. Moreover, graph pattern queries can be evaluated in cubic time, where two such algorithms are proposed. Finally, real life graphs are frequently updated with small changes. The thesis investigates incremental algorithms for graph pattern matching defined in terms of graph simulation, bounded simulation and subgraph isomorphism. Besides studying the results on the complexity bounds, the thesis provides the experimental study verifying that these incremental algorithms significantly outperform their batch counterparts in response to small changes, using real-life data and synthetic data

How and Why is An Answer (Still) Correct? Maintaining Provenance in Dynamic Knowledge Graphs

Knowledge graphs (KGs) have increasingly become the backbone of many critical knowledge-centric applications. Most large-scale KGs used in practice are automatically constructed based on an ensemble of extraction techniques applied over diverse data sources. Therefore, it is important to establish the provenance of results for a query to determine how these were computed. Provenance is shown to be useful for assigning confidence scores to the results, for debugging the KG generation itself, and for providing answer explanations. In many such applications, certain queries are registered as standing queries since their answers are needed often. However, KGs keep continuously changing due to reasons such as changes in the source data, improvements to the extraction techniques, refinement/enrichment of information, and so on. This brings us to the issue of efficiently maintaining the provenance polynomials of complex graph pattern queries for dynamic and large KGs instead of having to recompute them from scratch each time the KG is updated. Addressing these issues, we present HUKA which uses provenance polynomials for tracking the derivation of query results over knowledge graphs by encoding the edges involved in generating the answer. More importantly, HUKA also maintains these provenance polynomials in the face of updates---insertions as well as deletions of facts---to the underlying KG. Experimental results over large real-world KGs such as YAGO and DBpedia with various benchmark SPARQL query workloads reveals that HUKA can be almost 50 times faster than existing systems for provenance computation on dynamic KGs

Investigative Simulation: Towards Utilizing Graph Pattern Matching for Investigative Search

This paper proposes the use of graph pattern matching for investigative graph search, which is the process of searching for and prioritizing persons of interest who may exhibit part or all of a pattern of suspicious behaviors or connections. While there are a variety of applications, our principal motivation is to aid law enforcement in the detection of homegrown violent extremists. We introduce investigative simulation, which consists of several necessary extensions to the existing dual simulation graph pattern matching scheme in order to make it appropriate for intelligence analysts and law enforcement officials. Specifically, we impose a categorical label structure on nodes consistent with the nature of indicators in investigations, as well as prune or complete search results to ensure sensibility and usefulness of partial matches to analysts. Lastly, we introduce a natural top-k ranking scheme that can help analysts prioritize investigative efforts. We demonstrate performance of investigative simulation on a real-world large dataset.Comment: 8 pages, 6 figures. Paper to appear in the Fosint-SI 2016 conference proceedings in conjunction with the 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining ASONAM 201