Large Graph Databases Research Articles

G-Hash: Towards Fast Kernel-based Similarity Search in Large Graph Databases.

Structured data including sets, sequences, trees and graphs, pose significant challenges to fundamental aspects of data management such as efficient storage, indexing, and similarity search. With the fast accumulation of graph databases, similarity search in graph databases has emerged as an important research topic. Graph similarity search has applications in a wide range of domains including cheminformatics, bioinformatics, sensor network management, social network management, and XML documents, among others.Most of the current graph indexing methods focus on subgraph query processing, i.e. determining the set of database graphs that contains the query graph and hence do not directly support similarity search. In data mining and machine learning, various graph kernel functions have been designed to capture the intrinsic similarity of graphs. Though successful in constructing accurate predictive and classification models for supervised learning, graph kernel functions have (i) high computational complexity and (ii) non-trivial difficulty to be indexed in a graph database.Our objective is to bridge graph kernel function and similarity search in graph databases by proposing (i) a novel kernel-based similarity measurement and (ii) an efficient indexing structure for graph data management. Our method of similarity measurement builds upon local features extracted from each node and their neighboring nodes in graphs. A hash table is utilized to support efficient storage and fast search of the extracted local features. Using the hash table, a graph kernel function is defined to capture the intrinsic similarity of graphs and for fast similarity query processing. We have implemented our method, which we have named G-hash, and have demonstrated its utility on large chemical graph databases. Our results show that the G-hash method achieves state-of-the-art performance for k-nearest neighbor (k-NN) classification. Most importantly, the new similarity measurement and the index structure is scalable to large database with smaller indexing size, faster indexing construction time, and faster query processing time as compared to state-of-the-art indexing methods such as C-tree, gIndex, and GraphGrep.

A classical approach to the graph isomorphism problem using quantum walks

Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such algorithms have been scarce. In this work, we enumerate some important differences between quantum and classical walks, leading to their markedly different properties. We show that for many practical purposes, the implementation of quantum walks can be efficiently achieved using a classical computer. We then develop both classical and quantum graph isomorphism algorithms based on discrete-time quantum walks. We show that they are effective in identifying isomorphism classes of large databases of graphs, in particular groups of strongly regular graphs. We consider this approach to represent a promising candidate for an efficient solution to the graph isomorphism problem, and believe that similar methods employing quantum walks, or derivatives of these walks, may prove beneficial in constructing other algorithms for a variety of purposes.

Out-of-core coherent closed quasi-clique mining from large dense graph databases

Due to the ability of graphs to represent more generic and more complicated relationships among different objects, graph mining has played a significant role in data mining, attracting increasing attention in the data mining community. In addition, frequent coherent subgraphs can provide valuable knowledge about the underlying internal structure of a graph database, and mining frequently occurring coherent subgraphs from large dense graph databases has witnessed several applications and received considerable attention in the graph mining community recently. In this article, we study how to efficiently mine the complete set of coherent closed quasi-cliques from large dense graph databases, which is an especially challenging task due to the fact that the downward-closure property no longer holds. By fully exploring some properties of quasi-cliques, we propose several novel optimization techniques which can prune the unpromising and redundant subsearch spaces effectively. Meanwhile, we devise an efficient closure checking scheme to facilitate the discovery of closed quasi-cliques only. Since large databases cannot be held in main memory, we also design an out-of-core solution with efficient index structures for mining coherent closed quasi-cliques from large dense graph databases. We call this Cocain*. Thorough performance study shows that Cocain* is very efficient and scalable for large dense graph databases.

Decision trees for filtering large databases of graphs

Graphs are a powerful representation formalism for structural data. They are, however, very expensive from the computational point of view. In pattern recognition and intelligent information processing it is often necessary to match an unknown sample against a database of candidate patterns. In this process the size of the database is introduced as an additional factor into the overall complexity of the matching process. To reduce the influence of that factor, an approach based on machine learning techniques is proposed in this paper. Firstly, graphs are represented using feature vectors. Then, based on these vectors, a decision tree is built to index the database. At runtime the decision tree allows one to eliminate a number of graphs from the database to reduce possible matching candidates.

Challenging Complexity of Maximum Common Subgraph Detection Algorithms: A Performance Analysis of Three Algorithms on a Wide Database of Graphs

Graphs are an extremely general and powerful data structure. In pattern recognition and computer vision, graphs are used to represent patterns to be recognized or classified. Detection of maximum common subgraph (MCS) is useful for matching, comparing and evaluate the similarity of patterns. MCS is a well known NP-complete problem for which optimal and suboptimal algorithms are known from the literature. Nevertheless, until now no effort has been done for characterizing their performance. The lack of a large database of graphs makes the task of comparing the performance of different graph matching algorithms difficult, and often the selection of an algorithm is made on the basis of a few experimental results available. In this paper, three optimal and well-known algorithms for maximum common subgraph detection are described. Moreover a large database containing various categories of pairs of graphs (e.g. random graphs, meshes, bounded valence graphs), is presented, and the performance of the three algorithms is evaluated on this database.

A simple geometric structure optimizer for accelerated detection of infeasible zeolite graphs

We describe a geometric structure optimizer that rapidly establishes whether or not SiO 4 units in a hypothetical zeolite framework can exist as minimally-deformed regular tetrahedra. The optimizer, SiGH (Silica General Handler), enables an order of magnitude computational speed gain when processing large databases of zeolite graphs through the early rejection of infeasible graphs.

A large database of graphs and its use for benchmarking graph isomorphism algorithms

Despite of the fact that graph-based methods are gaining more and more popularity in different scientific areas, it has to be considered that the choice of an appropriate algorithm for a given application is still the most crucial task. The lack of a large database of graphs makes the task of comparing the performance of different graph matching algorithms difficult, and often the selection of an algorithm is made on the basis of a few experimental results available. In this paper we present an experimental comparative evaluation of the performance of four graph matching algorithms. In order to perform this comparison, we have built and made available a large database of graphs, which is also described in detail in this article.

Multilevel hierarchical retrieval

As large databases of conceptual graphs are developed for complex domains, efficient retrieval techniques must be developed to manage the complexity of graph-matching while maintaining reasonable space requirements. This paper describes a novel ``the multi-level hierarchical retrieval method that exploits redundancy to improve both space and execution time efficiency. The involves search in multiple partially ordered (by ``more-general-than) hierarchies such that search in a simpler hierarchy reduces the search time in the hierarchy of next complexity. The specific hierarchies used are: the traditional partial order over conceptual graphs; a partial order over node descriptors; a partial order over ``descriptor units; and finally, the simplest partial order is the traditional type hierarchy.