A Worst-Case Optimal Multi-Round Algorithm for Parallel Computation of Conjunctive Queries

We study the optimal communication cost for computing a full conjunctive query Q over p distributed servers. Two prior results were known. First, for one-round algorithms over skew-free data the optimal communication cost per server is m/p^(1/tau*), where m is the size of the largest input relation, and tau* is the fractional vertex covering number of the query hypergraph. Second, for multi-round algorithms and unrestricted database instances, it was shown that any algorithm requires at least m/p^(1/rho*) communication cost per server, where rho* is the fractional edge covering number of the query hypergraph; but no matching algorithms were known for this case (except for two restricted queries: chains and cycles). In this paper we describe a multi-round algorithm that computes any query with load m/p^(1/rho*) per server, in the case when all input relations are binary. Thus, we prove this to be the optimal load for all queries over binary input relations. Our algorithm represents a non-trivial extension of previous algorithms for chains and cycles, and exploits some unique properties of graphs, which no longer hold for hyper-graphs.