Uncertain Graph Processing through Representative Instances

Abstract

Data in several applications can be represented as an uncertain graph whose edges are labeled with a probability of existence. Exact query processing on uncertain graphs is prohibitive for most applications, as it involves evaluation over an exponential number of instantiations. Thus, typical approaches employ Monte-Carlo sampling, which (i) draws a number of possible graphs (samples), (ii) evaluates the query on each of them, and (iii) aggregates the individual answers to generate the final result. However, this approach can also be extremely time consuming for large uncertain graphs commonly found in practice. To facilitate efficiency, we study the problem of extracting a single representative instance from an uncertain graph. Conventional processing techniques can then be applied on this representative to closely approximate the result on the original graph. In order to maintain data utility, the representative instance should preserve structural characteristics of the uncertain graph. We start with representatives that capture the expected vertex degrees, as this is a fundamental property of the graph topology. We then generalize the notion of vertex degree to the concept of n -clique cardinality, that is, the number of cliques of size n that contain a vertex. For the first problem, we propose two methods: Average Degree Rewiring (ADR), which is based on random edge rewiring, and Approximate B-Matching (ABM), which applies graph matching techniques. For the second problem, we develop a greedy approach and a game-theoretic framework. We experimentally demonstrate, with real uncertain graphs, that indeed the representative instances can be used to answer, efficiently and accurately, queries based on several metrics such as shortest path distance, clustering coefficient, and betweenness centrality.