Graph pattern matching on social network analysis

Graph pattern matching is fundamental to social network analysis. Its effectiveness for identifying social communities and social positions, making recommendations and so on has been repeatedly demonstrated. However, the social network analysis raises new challenges to graph pattern matching. As real-life social graphs are typically large, it is often prohibitively expensive to conduct graph pattern matching over such large graphs, e.g., NP-complete for subgraph isomorphism, cubic time for bounded simulation, and quadratic time for simulation. These hinder the applicability of graph pattern matching on social network analysis. In response to these challenges, the thesis presents a series of effective techniques for querying large, dynamic, and distributively stored social networks. First of all, we propose a notion of query preserving graph compression, to compress large social graphs relative to a class Q of queries. We then develop both batch and incremental compression strategies for two commonly used pattern queries. Via both theoretical analysis and experimental studies, we show that (1) using compressed graphs Gr benefits graph pattern matching dramatically; and (2) the computation of Gr as well as its maintenance can be processed efficiently. Secondly, we investigate the distributed graph pattern matching problem, and explore parallel computation for graph pattern matching. We show that our techniques possess following performance guarantees: (1) each site is visited only once; (2) the total network traffic is independent of the size of G; and (3) the response time is decided by the size of largest fragment of G rather than the size of entire G. Furthermore, we show how these distributed algorithms can be implemented in the MapReduce framework. Thirdly, we study the problem of answering graph pattern matching using views since view based techniques have proven an effective technique for speeding up query evaluation. We propose a notion of pattern containment to characterise graph pattern matching using views, and introduce efficient algorithms to answer graph pattern matching using views. Moreover, we identify three problems related to graph pattern containment, and provide efficient algorithms for containment checking (approximation when the problem is intractable). Fourthly, we revise graph pattern matching by supporting a designated output node, which we treat as “query focus”. We then introduce algorithms for computing the top-k relevant matches w.r.t. the output node for both acyclic and cyclic pattern graphs, respectively, with early termination property. Furthermore, we investigate the diversified top-k matching problem, and develop an approximation algorithm with performance guarantee and a heuristic algorithm with early termination property. Finally, we introduce an expert search system, called ExpFinder, for large and dynamic social networks. ExpFinder identifies top-k experts in social networks by graph pattern matching, and copes with the sheer size of real-life social networks by integrating incremental graph pattern matching, query preserving compression and top-k matching computation. In particular, we also introduce bounded (resp. unbounded) incremental algorithms to maintain the weighted landmark vectors which are used for incremental maintenance for cached results

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

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

Automata-Theoretic Approaches to Planning in Robotics: Combinatorial Filter Minimization, Planning to Chronicle, Temporal Logic Planning With Soft Specifications, and Sensor Selection for Detecting Deviations From a Planned Itinerary

In this dissertation, we present a collection of new planning algorithms that enable robots to achieve complex goals, beyond simple point-to-point path planning, using automata-theoretic methods, and we consider the filter minimization (FM) problem and a variant of it, filter partitioning minimization (FPM) problem, which aims to minimize combinatorial filters, used for filtering and automata-theoretic planning in systems with discrete sensor data. We introduce a new variant of bisimulation, compatibility, and using this notion we identify several classes of filters for which FM or FPM is solvable in polynomial time, and propose several integer linear programming (ILP) formulations of FM and FPM. Then, we consider a problem, planning to chronicle, in which a robot is tasked with observing an uncertain time-extended process to produce a ‘chronicle’ of occurrent events that meets a given specification. This problem is useful in applications where we deploy robots to autonomously make structured videos or documentaries from events occurring in an unpredictable environment. Next, we study two variants of temporal logic planning in which the objective is to synthesize a trajectory that satisfies an optimal selection of soft constraints while nevertheless satisfying a hard constraint expressed in linear temporal logic (LTL). We also extend planning to chronicle with the idea of this problem. Then, we consider the problem of planning where to observe the behavior of an agent to ensure that the agent’s execution within the environment fits a pre-disclosed itinerary. This problem arises in a range of contexts including in validating safety claims about robot behavior, applications in security and surveillance, and for both the conception and the (physical) design and logistics of scientific experiments

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Programming Languages and Systems

This open access book constitutes the proceedings of the 28th European Symposium on Programming, ESOP 2019, which took place in Prague, Czech Republic, in April 2019, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019