Enumerating Subgraph Instances Using Map-Reduce

The theme of this paper is how to find all instances of a given "sample" graph in a larger "data graph," using a single round of map-reduce. For the simplest sample graph, the triangle, we improve upon the best known such algorithm. We then examine the general case, considering both the communication cost between mappers and reducers and the total computation cost at the reducers. To minimize communication cost, we exploit the techniques of (Afrati and Ullman, TKDE 2011)for computing multiway joins (evaluating conjunctive queries) in a single map-reduce round. Several methods are shown for translating sample graphs into a union of conjunctive queries with as few queries as possible. We also address the matter of optimizing computation cost. Many serial algorithms are shown to be "convertible," in the sense that it is possible to partition the data graph, explore each partition in a separate reducer, and have the total computation cost at the reducers be of the same order as the computation cost of the serial algorithm.Comment: 37 page

A New Framework for Join Product Skew

Different types of data skew can result in load imbalance in the context of parallel joins under the shared nothing architecture. We study one important type of skew, join product skew (JPS). A static approach based on frequency classes is proposed which takes for granted the data distribution of join attribute values. It comes from the observation that the join selectivity can be expressed as a sum of products of frequencies of the join attribute values. As a consequence, an appropriate assignment of join sub-tasks, that takes into consideration the magnitude of the frequency products can alleviate the join product skew. Motivated by the aforementioned remark, we propose an algorithm, called Handling Join Product Skew (HJPS), to handle join product skew

On relating CTL to Datalog

CTL is the dominant temporal specification language in practice mainly due to the fact that it admits model checking in linear time. Logic programming and the database query language Datalog are often used as an implementation platform for logic languages. In this paper we present the exact relation between CTL and Datalog and moreover we build on this relation and known efficient algorithms for CTL to obtain efficient algorithms for fragments of stratified Datalog. The contributions of this paper are: a) We embed CTL into STD which is a proper fragment of stratified Datalog. Moreover we show that STD expresses exactly CTL -- we prove that by embedding STD into CTL. Both embeddings are linear. b) CTL can also be embedded to fragments of Datalog without negation. We define a fragment of Datalog with the successor build-in predicate that we call TDS and we embed CTL into TDS in linear time. We build on the above relations to answer open problems of stratified Datalog. We prove that query evaluation is linear and that containment and satisfiability problems are both decidable. The results presented in this paper are the first for fragments of stratified Datalog that are more general than those containing only unary EDBs.Comment: 34 pages, 1 figure (file .eps