Query preserving graph compression

Abstract

It is common to find graphs with millions of nodes and billions of edges in, e.g., social networks. Queries on such graphs are often prohibitively expensive. These motivate us to propose query preserving graph compression, to compress graphs relative to a class Q of queries of users' choice. We compute a small Gr from a graph G such that (a) for any query Q ∈ Q, Q(G) = Q ′ (Gr), where Q ′ ∈ Q can be efficiently computed from Q; and (b) any algorithm for computing Q(G) can be directly applied to evaluating Q ′ on Gr as is. That is, while we cannot lower the complexity of evaluating graph queries, we reduce data graphs while preserving the answers to all the queries in Q. To verify the effectiveness of this approach, (1) we develop compression strategies for two classes of queries: reachability and graph pattern queries via (bounded) simulation. We show that graphs can be efficiently compressed via a reachability equivalence relation and graph bisimulation, respectively, while preserving query answers. (2) We provide techniques for maintaining compressed graph Gr in response to changes ∆G to the original graph G. We show that the incremental maintenance problems are unbounded for the two classes of queries, i.e., their costs are not a function of the size of ∆G and changes in Gr. Nevertheless, we develop incremental algorithms that depend only on ∆G and Gr, independent of G, i.e., we do not have to decompress Gr to propagate the changes. (3) Using real-life data, we experimentally verify that our compression techniques could reduce graphs in average by 95% for reachability and 57% for graph pattern matching, and that our incremental maintenance algorithms are efficient.

Exploiting vertex relationships in speeding up subgraph isomorphism over large graphs

“…The grouping of data vertices into hypernodes in our approach bears some similarity to structural summaries [10,8,2], graph summarization [11,14], and query-preserving graph compression [4]. Structural summaries are designed for path expressions, hence they group vertices sharing the same set of incoming label paths into a hypernode.…”

“…These techniques group vertices into hypernodes based on a variety of statistics, such as node attributes values [16], degree distribution, or user-specified node attributes [14]. More closely related to our work is [4], which proposes a framework for query-preserving graph compression as well as two compression methods that preserve reachability queries and pattern matching queries (based on bounded simulation) respectively. Both methods are based on equivalence relations defined over the vertices of the original graph G, and compress G by merging vertices in the same equivalent class into a single node.…”

Making queries tractable on big data with preprocessing

“…In contrast to lossless compression schemes (e.g., [6,9,17]), query preserving compression is relative to Q, i.e., it generates small Dc that preserves the information only relevant to queries in Q rather than preserving the entire original D. Hence it often achieves a better compression ratio than lossless compression. Indeed, this approach has proven effective in answering graph queries on large social network graphs [16,31,32] and in cryptographic applications [24]. If the compression can be conducted in PTIME [16,31,32] and moreover, queries in Q can be answered in the compressed databases Dc in parallel polylog-time, perhaps by combining with other techniques such as indexing, then Q is Π-tractable, i.e., Q ∈ ΠT 0 Q .…”

“…Indeed, this approach has proven effective in answering graph queries on large social network graphs [16,31,32] and in cryptographic applications [24]. If the compression can be conducted in PTIME [16,31,32] and moreover, queries in Q can be answered in the compressed databases Dc in parallel polylog-time, perhaps by combining with other techniques such as indexing, then Q is Π-tractable, i.e., Q ∈ ΠT 0 Q . (6) Query answering using views.…”

“…In addition to building indices as shown in the example, many more preprocessing strategies have proven effective and are being widely used in practice. These include (i) query-preserving compression schemes that preserve the answers to a class of queries rather than preserving the data itself [16,24,31,32], (ii) building views such that queries can be answered using the views without accessing the original big data [1,23,30]; and (iii) bounded incremental algorithms [35] that, after evaluating queries once on the original data (as preprocessing), incrementally evaluate the queries in response to the changes to the data such that the cost of query evaluation is a function of the size of the changes, rather than the size of the original big data [15,37].…”