Optimizing subgraph queries by combining binary and worst-case optimal joins

Abstract

We study the problem of optimizing subgraph queries using the new worst-case optimal join plans. Worst-case optimal plans evaluate queries by matching one query vertex at a time using multiway intersections. The core problem in optimizing worst-case optimal plans is to pick an ordering of the query vertices to match. We design a cost-based optimizer that (i) picks efficient query vertex orderings for worst-case optimal plans; and (ii) generates hybrid plans that mix traditional binary joins with worst-case optimal style multiway intersections. Our cost metric combines the cost of binary joins with a new cost metric called intersection-cost. The plan space of our optimizer contains plans that are not in the plan spaces based on tree decompositions from prior work. In addition to our optimizer, we describe an adaptive technique that changes the orderings of the worst-case optimal sub-plans during query execution. We demonstrate the effectiveness of the plans our optimizer picks and adaptive technique through extensive experiments. Our optimizer is integrated into the Graphflow DBMS.

Parallel Clique Counting and Peeling Algorithms

“…We additionally compare our counting algorithms to Jain and Seshadhri's PIVOTER algorithm [28], Mhedhbi and Salihoglu's worst-case optimal join algorithm (WCO) [35], Lai et al's implementation of a binary join algorithm (BINARYJOIN) [30], and Pinar et al's ESCAPE algorithm [41]. Note that PIVOTER is designed for counting all cliques, and the latter three algorithms are designed for general subgraph counting.…”

“…We show that on a variety of realworld graphs and different k, our k-clique counting algorithm achieves 1.31-9.88x speedup over the state-of-the-art parallel KCLIST algorithm [15] and self-relative speedups of 13.23-38.99x. We also compared our k-clique counting algorithm to other parallel k-clique counting implementations including Jain and Seshadhri's PIVOTER [28], Mhedhbi and Salihoglu's worst-case optimal join algorithm (WCO) [35], Lai et al's implementation of a binary join algorithm (BINARYJOIN) [30], and Pinar et al's ESCAPE [41], and demonstrate speedups of up to several orders of magnitude.…”

A Schema-Driven Synthetic Knowledge Graph Generation Approach With Extended Graph Differential Dependencies (GDDxs)

“…-Dist A is a probability distribution that is followed by the data value of this attribute. For example, height = ("height", continous, (50,200) -L rt is the name of the relationship type, -S is the source entity type of the relationship type, -T is the target entity type of the relationship type, -Cardinality S = (min card , max card , Dist S ) refers to the number of times instances in S can relate to an instance of T . m/n is the minimal/maximum number of outgoing relationships with the type rt from an instance of S, Dist S is the probability distribution of the number of outgoing relationships with the type rt from an instance of S, -Cardinality T = (min card , max card , Dist T ) refers to the number of times instances in T can relate to an instance of S. m/n is the minimal/maximum number of incoming relationships with the type rt to an instance of T , Dist T is the probability distribution of the number of incoming relationships with the type rt to an instance of T .…”

“…A state-of-the-art algorithm for sub-graph isomorphism, e.g., the Exact Subgraph Matching (ESM) Algorithm [49], is employed to obtain isomorphic sub-graph embeddings (Line 7). A binary and worst-case optimal join combined algorithm [50] is employed to discover homomorphic matches (Line 9). Besides, a minimum k-image based sub-graph matcher is extracted from an efficient sub-graph miner called GraMi [47] to obtain all of the corresponding sub-graph embeddings (Line 11).…”

EdgeFrame

“…We call the algorithm variable-oriented as it allows to enumerate the query result by means of a backtracking depth-first search for possible bindings which requires no intermediate results. Finding the best variable ordering for a wcoj is important [8,13,28] and somewhat analogous to join ordering in query optimization.…”