Answering connectivity queries is fundamental to fully dynamic graphs where edges and vertices are inserted and deleted frequently. Existing work proposes data structures and algorithms with worst-case guarantees. We propose a new data structure, the dynamic tree (D-tree), together with algorithms to construct and maintain it. The D-tree is the first data structure that scales to fully dynamic graphs with millions of vertices and edges and, on average, answers connectivity queries much faster than data structures with worst case guarantees.

Graph streams, which refer to the graph with edges being updated sequentially in a form of a stream, have wide applications such as cyber security, social networks and transportation networks. This paper studies the problem of summarizing graph streams. Specifically, given a graph stream G, directed or undirected, the objective is to summarize G as SG with much smaller (sublinear) space, linear construction time and constant maintenance cost for each edge update, such that SG allows many queries over G to be approximately conducted efficiently. Due to the sheer volume and highly dynamic nature of graph streams, summarizing them remains a notoriously hard, if not impossible, problem. The widely used practice of summarizing data streams is to treat each element independently by e.g., hashor sampling-based method, without keeping track of the connections between elements in a data stream, which gives these summaries limited power in supporting complicated queries over graph streams. This paper discusses a fundamentally different philosophy for summarizing graph streams. We present gLava, a probabilistic graph model that, instead of treating an edge (a stream element) as the operating unit, uses the finer grained node in an element. This will naturally form a new graph sketch where edges capture the connections inside elements, and nodes maintain relationships across elements. We discuss a wide range of supported graph queries and establish theoretical error bounds for basic queries.

In practice, data are often found to violate given integrity constraints, e.g., functional dependencies, and are hence inconsistent. To resolve such violations, data are to be restored to a consistent state, known as "repair", while the number of possible repairs may be exponential. Previous works either consider optimal repair computation, to find one single repair that is (nearly) optimal w.r.t. some cost models, or discuss repair sampling, to randomly generate a repair from the space of all possible repairs.This paper makes a first effort to investigate repair diversification problem, which aims at generating a set of repairs by minimizing their costs and maximizing their diversity. There are several motivating scenarios where diversifying repairs is desirable. For example, in the recently proposed interactive repairing approach, repair diversification techniques can be employed to generate several representative repairs that are likely to occur (small cost), and at the same time, that are dissimilar to each other (high diversity). Repair diversification significantly differs from optimal repair computing and repair sampling in its framework and techniques. (1) Based on two natural diversification objectives, we formulate two versions of repair diversification problem, both modeled as bi-criteria optimization problem, and prove the complexity of their related decision problems. (2) We develop algorithms for diversification problems. These algorithms embed repair computation into the framework of diversification, and hence find desirable repairs without searching the whole repair space. (3) We conduct extensive performance studies, to verify the effectiveness and efficiency of our algorithms.

Graph streams, which refer to the graph with edges being updated sequentially in a form of a stream, have wide applications such as cyber security, social networks and transportation networks. This paper studies the problem of summarizing graph streams. Specifically, given a graph stream G, directed or undirected, the objective is to summarize G as S with much smaller (sublinear) space, linear construction time and constant maintenance cost for each edge update, such that S allows many queries over G to be approximately conducted efficiently. Due to the sheer volume and highly dynamic nature of graph streams, summarizing them remains a notoriously hard, if not impossible, problem. The widely used practice of summarizing data streams is to treat each element independently by e.g., hash- or sampling-based method, without keeping track of the connections between elements in a data stream, which gives these summaries limited power in supporting complicated queries over graph streams. This paper discusses a fundamentally different philosophy for summarizing graph streams. We present gLava, a probabilistic graph model that, instead of treating an edge (a stream element) as the operating unit, uses the finer grained node in an element. This will naturally form a new graph sketch where edges capture the connections inside elements, and nodes maintain relationships across elements. We discuss a wide range of supported graph queries and establish theoretical error bounds for basic queries.

A graph stream, which refers to the graph with edges being updated sequentially in a form of a stream, has important applications in cyber security and social networks. Due to the sheer volume and highly dynamic nature of graph streams, the practical way of handling them is by summarization. Given a graph stream G, directed or undirected, the problem of graph stream summarization is to summarize G as SG with a much smaller (sublinear) space, linear construction time and constant maintenance cost for each edge update, such that SG allows many queries over G to be approximately conducted efficiently. The widely used practice of summarizing data streams is to treat each stream element independently by e.g., hash- or sample-based methods, without maintaining the connections (or relationships) between elements. Hence, existing methods can only solve ad-hoc problems, without supporting diversified and complicated analytics over graph streams. We present TCM, a novel generalized graph stream summary. Given an incoming edge, it summarizes both node and edge information in constant time. Consequently, the summary forms a graphical sketch where edges capture the connections inside elements, and nodes maintain relationships across elements. We discuss a wide range of supported queries and establish some error bounds. In addition, we experimentally show that TCM can effectively and efficiently support analytics over graph streams, which demonstrates its potential to start a new line of research and applications in graph stream management.

One of the problems central to data consistency is data repairing. Given a database D violating a set Σ of data dependencies as data quality rules, it aims to modify D for a new relation D' satisfying Σ . When D is a centralized database, a host of methods have been provided to address this problem. In practice, a database may be fragmented and distributed to multiple sites, which is advocated by distributed systems for better scalability and is readily supported by commercial systems. This paper makes a first effort to develop techniques for repairing functional dependency violations in a horizontally partitioned database. (1) Based on a message-passing distributed computing model and two complexity measures (parallel time and data shipment) for distributed algorithms, we study data repairing with equivalence classes in the distributed setting. We show that it is NP-completeto build equivalence classes when the data is horizontally partitioned, and when we aim to minimize either data shipment or parallel computation time. (2) Despite the intractability, we propose efficient distributed algorithms and optimization techniques for data repairing based on equivalence classes. (3) We experimentally verify the effectiveness and efficiency of our algorithms, using both real-life and synthetic data.

In practice, data are often found to violate functional dependencies, and are hence inconsistent. To resolve such violations, data are to be restored to a consistent state, known as “repair”, while the number of possible repairs may be exponential. Previous works either consider optimal repair computation, to find one single repair that is (nearly) optimal w.r.t. some cost model, or discuss repair sampling, to randomly generate a repair from the space of all possible repairs. This paper makes a first effort to investigate repair diversification problem, which aims at generating a set of repairs by minimizing their costs and maximizing their diversity. There are several motivating scenarios where diversifying repairs is desirable. For example, in the recently proposed interactive repairing approach, repair diversification techniques can be employed to generate some representative repairs that are likely to occur (small cost), and at the same time, that are dissimilar to each other (high diversity).Repair diversification significantly differs from optimal repair computing and repair sampling in its framework and techniques. (1) Based on two natural diversification objectives, we formulate two versions of repair diversification problem, both modeled as bi-criteria optimization problem, and prove the complexity of their related decision problems. (2) We develop algorithms for diversification problems. These algorithms embed repair computation into the framework of diversification, and hence find desirable repairs without searching the whole repair space. (3) We conduct extensive performance studies, to verify the effectiveness and efficiency of our algorithms.