Managing and Mining Graph Data is a comprehensive survey book in graph data analytics. It contains extensive surveys on important graph topics such as graph languages, indexing, clustering, data generation, pattern mining, classification, keyword search, pattern matching, and privacy. It also studies a number of domain-specific scenarios such as stream mining, web graphs, social networks, chemical and biological data. The chapters are written by leading researchers, and provide a broad perspective of the area. This is the first comprehensive survey book in the emerging topic of graph data processing. Managing and Mining Graph Data is designed for a varied audience composed of professors, researchers and practitioners in industry. This volume is also suitable as a reference book for advanced-level database students in computer science. About the Editors:Charu C. Aggarwal obtained his B.Tech in Computer Science from IIT Kanpur in 1993 and Ph.D. from MIT in 1996. He has worked as a researcher at IBM since then, and has published over 130 papers in major data mining conferences and journals. He has applied for or been granted over 70 US and International patents, and has thrice been designated a Master Inventor at IBM. He has received an IBM Corporate award for his work on data stream analytics, and an IBM Outstanding Innovation Award for his work on privacy technology. He has served on the executive committees of most major data mining conferences. He has served as an associate editor of the IEEE TKDE, as an associate editor of the ACM SIGKDD Explorations, and as an action editor of the DMKD Journal. He is a fellow of the IEEE, and a life-member of the ACM. Haixun Wang is currently a researcher at Microsoft Research Asia. He received the B.S. and the M.S. degree, both in computer science, from Shanghai Jiao Tong University in 1994 and 1996. He received the Ph.D. degree in computer science from the University of California, Los Angeles in 2000. He subsequently worked as a researcher at IBMuntil 2009. His main research interest is database language and systems, data mining, and information retrieval. He has published more than 100 research papers in referred international journals and conference proceedings. He serves as an associate editor of the IEEE TKDE, and has served as a reviewer and program committee member of leading database conferences and journals.

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Managing and Mining Graph Data

With the prevalence of graph data in a variety of domains, there is an increasing need for a language to query and manipulate graphs with heterogeneous attributes and structures. We propose a query language for graph databases that supports arbitrary attributes on nodes, edges, and graphs. In this language, graphs are the basic unit of information and each query manipulates one or more collections of graphs. To allow for flexible compositions of graph structures, we extend the notion of formal languages from strings to the graph domain. We present a graph algebra extended from the relational algebra in which the selection operator is generalized to graph pattern matching and a composition operator is introduced for rewriting matched graphs. Then, we investigate access methods of the selection operator. Pattern matching over large graphs is challenging due to the NP-completeness of subgraph isomorphism. We address this by a combination of techniques: use of neighborhood subgraphs and profiles, joint reduction of the search space, and optimization of the search order. Experimental results on real and synthetic large graphs demonstrate that our graph specific optimizations outperform an SQL-based implementation by orders of magnitude.

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Graphs-at-a-time: query language and access methods for graph databases

Conventional keyword search engines are restricted to a given data model and cannot easily adapt to unstructured, semi-structured or structured data. In this paper, we propose an efficient and adaptive keyword search method, called EASE, for indexing and querying large collections of heterogenous data. To achieve high efficiency in processing keyword queries, we first model unstructured, semi-structured and structured data as graphs, and then summarize the graphs and construct graph indices instead of using traditional inverted indices. We propose an extended inverted index to facilitate keyword-based search, and present a novel ranking mechanism for enhancing search effectiveness. We have conducted an extensive experimental study using real datasets, and the results show that EASE achieves both high search efficiency and high accuracy, and outperforms the existing approaches significantly.

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EASE: an effective 3-in-1 keyword search method for unstructured, semi-structured and structured data

Graph data have become ubiquitous and manipulating them based on similarity is essential for many applications. Graph edit distance is one of the most widely accepted measures to determine similarities between graphs and has extensive applications in the fields of pattern recognition, computer vision etc. Unfortunately, the problem of graph edit distance computation is NP-Hard in general. Accordingly, in this paper we introduce three novel methods to compute the upper and lower bounds for the edit distance between two graphs in polynomial time. Applying these methods, two algorithms AppFull and AppSub are introduced to perform different kinds of graph search on graph databases. Comprehensive experimental studies are conducted on both real and synthetic datasets to examine various aspects of the methods for bounding graph edit distance. Result shows that these methods achieve good scalability in terms of both the number of graphs and the size of graphs. The effectiveness of these algorithms also confirms the usefulness of using our bounds in filtering and searching of graphs.

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Comparing stars: on approximating graph edit distance

The dramatic proliferation of sophisticated networks has resulted in a growing need for supporting effective querying and mining methods over such large-scale graph-structured data. At the core of many advanced network operations lies a common and critical graph query primitive: how to search graph structures efficiently within a large network? Unfortunately, the graph query is hard due to the NP-complete nature of subgraph isomorphism. It becomes even challenging when the network examined is large and diverse. In this paper, we present a high performance graph indexing mechanism, SPath, to address the graph query problem on large networks. SPath leverages decomposed shortest paths around vertex neighborhood as basic indexing units, which prove to be both effective in graph search space pruning and highly scalable in index construction and deployment. Via SPath, a graph query is processed and optimized beyond the traditional vertex-at-a-time fashion to a more efficient path-at-a-time way: the query is first decomposed to a set of shortest paths, among which a subset of candidates with good selectivity is picked by a query plan optimizer; Candidate paths are further joined together to help recover the query graph to finalize the graph query processing. We evaluate SPath with the state-of-the-art GraphQL on both real and synthetic data sets. Our experimental studies demonstrate the effectiveness and scalability of SPath, which proves to be a more practical and efficient indexing method in addressing graph queries on large networks.

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On graph query optimization in large networks

Query processing over graph-structured data is enjoying a growing number of applications. A top-k keyword search query on a graph finds the top k answers according to some ranking criteria, where each answer is a substructure of the graph containing all query keywords. Current techniques for supporting such queries on general graphs suffer from several drawbacks, e.g., poor worst-case performance, not taking full advantage of indexes, and high memory requirements. To address these problems, we propose BLINKS, a bi-level indexing and query processing scheme for top-k keyword search on graphs. BLINKS follows a search strategy with provable performance bounds, while additionally exploiting a bi-level index for pruning and accelerating the search. To reduce the index space, BLINKS partitions a data graph into blocks: The bi-level index stores summary information at the block level to initiate and guide search among blocks, and more detailed information for each block to accelerate search within blocks. Our experiments show that BLINKS offers orders-of-magnitude performance improvement over existing approaches.

BLINKS: ranked keyword searches on graphs

Graph reachability is fundamental to a wide range of applications, including XML indexing, geographic navigation, Internet routing, ontology queries based on RDF/OWL, etc. Many applications involve huge graphs and require fast answering of reachability queries. Several reachability labeling methods have been proposed for this purpose. They assign labels to the vertices, such that the reachability between any two vertices may be decided using their labels only. For sparse graphs, 2-hop based reachability labeling schemes answer reachability queries efficiently using relatively small label space. However, the labeling process itself is often too time consuming to be practical for large graphs. In this paper, we propose a novel labeling scheme for sparse graphs. Our scheme ensures that graph reachability queries can be answered in constant time. Furthermore, for sparse graphs, the complexity of the labeling process is almost linear, which makes our algorithm applicable to massive datasets. Analytical and experimental results show that our approach is much more efficient than stateof- the-art approaches. Furthermore, our labeling method also provides an alternative scheme to tradeoff query time for label space, which further benefits applications that use tree-like graphs.

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Dual Labeling: Answering Graph Reachability Queries in Constant Time

XML and other types of semistructured data are typically represented by a labeled directed graph. To speed up path expression queries over the graph, a variety of structural indexes have been proposed. They usually work by partitioning nodes in the data graph into equivalence classes and storing equivalence classes as index nodes. A(k)-index introduces the concept of local bisimilarity for partitioning, allowing the trade-off between index size and query answering power. However, all index nodes in A(k)-index have the same local similarity k, which cannot take advantage of the fact that a workload may contain path expressions of different lengths, or that different parts of the data graph may have different local similarity requirements. To overcome these limitations, we propose M(k)- and M*(k)-indexes. The basic M(k)-index is workload-aware: Like the previously proposed D(k)-index, it allows different index nodes to have different local similarity requirements, providing finer partitioning only for parts of the data graph targeted by longer path expressions. Unlike D(k)-index, M(k)-index is never over-refined for irrelevant index or data nodes. However, the workload-aware feature still incurs overrefinement due to over-qualified parent index nodes. Moreover, fine partitions penalize the performance of short path expressions. To solve these problems, we further propose the M*(k)-index. An M*(k)-index consists of a collection of indexes whose nodes are organized in a partition hierarchy, allowing successively coarser partitioning information to co-exist with the finest partitioning information required. Experiments show that our indexes are superior to previously proposed indexes in terms of index size and query performance.

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Multiresolution indexing of XML for frequent queries

Order-based element labeling for tree-structured XML data is an important technique in XML processing. It lies at the core of many fundamental XML operations such as containment join and twig matching. While labeling for static XML documents is well understood, less is known about how to maintain accurate labeling for dynamic XML documents, when elements and subtrees are inserted and deleted. Most existing approaches do not work well for arbitrary update patterns; they either produce unacceptably long labels or incur enormous relabeling costs. We present two novel I/O-efficient data structures, W-BOX and B-BOX that efficiently maintain labeling for large, dynamic XML documents. We show analytically and experimentally that both, despite consuming minimal amounts of storage, gracefully handle arbitrary update patterns without sacrificing lookup efficiency. The two structures together provide a nice tradeoff between update and lookup costs: W-BOX has logarithmic amortized update cost and constant worst-case lookup cost, while B-BOX has constant amortized update cost and logarithmic worst-case lookup cost. We further propose techniques to eliminate the lookup cost for read-heavy workloads.

BOXes: efficient maintenance of order-based labeling for dynamic XML data

Testing reachability between nodes in a graph is a well-known problem with many important applications, including knowledge representation, program analysis, and more recently, biological and ontology databases inferencing as well as XML query processing. Various approaches have been proposed to encode graph reachability information using node labeling schemes, but most existing schemes only work well for specific types of graphs. In this paper, we propose a novel approach, HLSS(Hierarchical Labeling of Sub-Structures), which identifies different types of substructures within a graph and encodes them using techniques suitable to the characteristics of each of them. We implement HLSS with an efficient two-phase algorithm, where the first phase identifies and encodes strongly connected components as well as tree substructures, and the second phase encodes the remaining reachability relationships by compressing dense rectangular submatrices in the transitive closure matrix. For the important subproblem of finding densest submatrices, we demonstrate the hardness of the problem and propose several practical algorithms. Experiments show that HLSS handles different types of graphs well, while existing approaches fall prey to graphs with substructures they are not designed to handle.

http://db.cs.duke.edu/papers/2005-CIKM-hwyy-greach.pdf

Hao He

Papers

BLINKS: ranked keyword searches on graphs

Dual Labeling: Answering Graph Reachability Queries in Constant Time

Multiresolution indexing of XML for frequent queries

BOXes: efficient maintenance of order-based labeling for dynamic XML data

Compact reachability labeling for graph-structured data