Indices are commonly built into graph databases in order to support fast searches. Any given graph database and the distribution of queries will change over time. Therefore, the cost of processing queries using a static graph index increases because the index is built to optimize old snapshots of the database. There is growing research interest in determining how to update a graph index with the purpose of adapting to database and query changes. Updating features in a graph index is typically an NP-hard problem. In addition, because the features are chosen from a large number of frequent subgraphs, a multi-pass algorithm is not scalable to big datasets. In order to address this issue, we propose a time-efficient one-pass algorithm that is designed to update a graph index by scanning each frequent subgraph at most once. The algorithm replaces a feature with a new subgraph if the latter is ``better" than the former one. We use the branch and bound technique to skip subgraphs that cannot outperform any of the features in the graph index. We further use a decomposed index and reduce the space complexity from O(|G||Q|) to O(|G| + |Q|), where G is database graphs and Q is a query workload. Through the empirical study, we show that the one-pass algorithm is 5--100 times faster than all previous algorithms for updating graph indices. In addition, the one-pass algorithm guarantees the return of a close to optimum solution. Our experiments show that when the one-pass algorithm is used to update an index, the query-processing speed is $1$--$2$ times faster than that of other cutting-edge indices, i.e., the FGindex and the gIndex.

The problem of subgraph search in large graphs has wide applications in both nature and social science. The subgraph search results are typically ordered based on graph similarity score. In this paper, we study the problem of ranking the subgraph search results based on diversification. We design two ranking measures based on both similarity and diversity, and formalize the problem as an optimization problem. We give two efficient algorithms, the greedy selection and the swapping selection with provable performance guarantee. We also propose a novel local search heuristic with at least 100 times speedup and a similar solution quality. We demonstrate the efficiency and effectiveness of our approaches via extensive experiments.

Finding a maximum coverage by k sets from a given collection (Max-k-Cover), finding a minimum number of sets with a required coverage (Partial-Cover) are both important combinatorial optimization problems. Various problems from data mining, machine learning, social network analysis, operational research, etc. can be generalized as a set coverage problem. The standard greedy algorithm is efficient as an in-memory algorithm. However, when we are facing very large-scale dataset or in an online environment, we seek a new algorithm which makes only one pass through the entire dataset. Previous one-pass algorithms for the Max-k-Cover problem cannot be extended to the Partial-Cover problem and do not enjoy the prefix-optimal property. In this paper, we propose a novel one-pass streaming algorithm which produces a prefix-optimal ordering of sets, which can easily be used to solve the Max-k-Cover and the Partial-Cover problems. Our algorithm consumes space linear to the size of the universe of elements. The processing time for a set is linear to the size of this set. We also show with the aid of computer simulation that the approximation ratio of the Max-k-Cover problem is around 0.3. We conduct experiments on extensive datasets to compare our algorithm with existing one-pass algorithms on the Max-k-Cover problem, and with the standard greedy algorithm on the Partial-Cover problem. We demonstrate the efficiency and quality of our algorithm.

Sub graph search is a popular query scenario on graph databases. Given a query graph q, the sub graph search algorithm returns all database graphs having q as a sub graph. To efficiently implement a subgraph search, subgraph features are mined in order to index the graph database. Many subgraph feature mining approaches have been proposed. They are all "mine-at-once" algorithms in which the whole feature set is mined in one run before building a stable graph index. However, due to the change of environments (such as an update of the graph database and the increase of available memory), the index needs to be updated to accommodate such changes. Most of the "mine-at-once" algorithms involve frequent subgraph or subtree mining over the whole graph database. Also, constructing and deploying a new index involves an expensive disk operation such that it is inefficient to re-mine the features and rebuild the index from scratch. We observe that, under most cases, it is sufficient to update a small part of the graph index. Here we propose an "iterative subgraph mining" algorithm which iteratively finds one feature to insert into (or remove from) the index. Since the majority of indexing features and the index structure are not changed, the algorithm can be frequently invoked. We define an objective function that guides the feature mining. Next, we propose a basic branch and bound algorithm to mine the features. Finally, we design an advanced search algorithm, which quickly finds a near-optimum subgraph feature and reduces the search space. Experiments show that our feature mining algorithm is 5 times faster than the popular graph indexing algorithm gIndex, and that features mined by our iterative algorithm have a better filtering rate for the subgraph search problem.