To accurately match records it is often necessary to utilize the semantics of the data. Functional dependencies (FDs) have proven useful in identifying tuples in a clean relation, based on the semantics of the data. For all the reasons that FDs and their inference are needed, it is also important to develop dependencies and their reasoning techniques for matching tuples from unreliable data sources. This paper investigates dependencies and their reasoning for record matching. (a) We introduce a class of matching dependencies (MDs) for specifying the semantics of data in unreliable relations, defined in terms of similarity metrics and a dynamic semantics. (b) We identify a special case of MDs, referred to as relative candidate keys (RCKs), to determine what attributes to compare and how to compare them when matching records across possibly different relations. (c) We propose a mechanism for inferring MDs, a departure from traditional implication analysis, such that when we cannot match records by comparing attributes that contain errors, we may still find matches by using other, more reliable attributes. (d) We provide an O(n 2 ) time algorithm for inferring MDs, and an effective algorithm for deducing a set of RCKs from MDs. (e) We experimentally verify that the algorithms help matching tools efficiently identify keys at compile time for matching, blocking or windowing, and that the techniques effectively improve both the quality and efficiency of various record matching methods.

Graph pattern matching is often defined in terms of subgraph isomorphism, an np-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be conducted in cubic-time. However, they fall short of capturing the topology of data graphs, i.e., graphs may have a structure drastically different from pattern graphs they match, and the matches found are often too large to understand and analyze. To rectify these problems, this paper proposes a notion of strong simulation, a revision of graph simulation, for graph pattern matching. (1) We identify a set of criteria for preserving the topology of graphs matched. We show that strong simulation preserves the topology of data graphs and finds a bounded number of matches. (2) We show that strong simulation retains the same complexity as earlier extensions of simulation, by providing a cubic-time algorithm for computing strong simulation. (3) We present the locality property of strong simulation, which allows us to effectively conduct pattern matching on distributed graphs. (4) We experimentally verify the effectiveness and efficiency of these algorithms, using real-life data and synthetic data.

A variety of integrity constraints have been studied for data cleaning. While these constraints can detect the presence of errors, they fall short of guiding us to correct the errors. Indeed, data repairing based on these constraints may not find certain fixes that are absolutely correct, and worse, may introduce new errors when repairing the data. We propose a method for finding certain fixes, based on master data, a notion of certain regions, and a class of editing rules. A certain region is a set of attributes that are assured correct by the users. Given a certain region and master data, editing rules tell us what attributes to fix and how to update them. We show how the method can be used in data monitoring and enrichment. We develop techniques for reasoning about editing rules, to decide whether they lead to a unique fix and whether they are able to fix all the attributes in a tuple, relative to master data and a certain region. We also provide an algorithm to identify minimal certain regions, such that a certain fix is warranted by editing rules and master data as long as one of the regions is correct. We experimentally verify the effectiveness and scalability of the algorithm.

It is increasingly common to find graphs in which edges bear different types, indicating a variety of relationships. For such graphs we propose a class of reachability queries and a class of graph patterns, in which an edge is specified with a regular expression of a certain form, expressing the connectivity in a data graph via edges of various types. In addition, we define graph pattern matching based on a revised notion of graph simulation. On graphs in emerging applications such as social networks, we show that these queries are capable of finding more sensible information than their traditional counterparts. Better still, their increased expressive power does not come with extra complexity. Indeed, (1) we investigate their containment and minimization problems, and show that these fundamental problems are in quadratic time for reachability queries and are in cubic time for pattern queries. (2) We develop an algorithm for answering reachability queries, in quadratic time as for their traditional counterpart. (3) We provide two cubictime algorithms for evaluating graph pattern queries based on extended graph simulation, as opposed to the NP-completeness of graph pattern matching via subgraph isomorphism. (4) The effectiveness, efficiency and scalability of these algorithms are experimentally verified using real-life data and synthetic data.

In a variety of emerging applications one needs to decide whether a graph G matches another Gp, i.e., whether G has a topological structure similar to that of Gp. The traditional notions of graph homomorphism and isomorphism often fall short of capturing the structural similarity in these applications. This paper studies revisions of these notions, providing a full treatment from complexity to algorithms. (1) We propose p-homomorphism (p-hom) and 1-1 p-hom, which extend graph homomorphism and subgraph isomorphism, respectively, by mapping edges from one graph to paths in another, and by measuring the similarity of nodes. (2) We introduce metrics to measure graph similarity, and several optimization problems for p-hom and 1-1 p-hom. (3) We show that the decision problems for p-hom and 1-1 p-hom are NP-complete even for DAGs, and that the optimization problems are approximation-hard. (4) Nevertheless, we provide approximation algorithms with provable guarantees on match quality. We experimentally verify the effectiveness of the revised notions and the efficiency of our algorithms in Web site matching, using real-life and synthetic data.