# Algorithms Seminar: Rasums Pagh (ITU Copenhagen)

Date: June 01, 2006 (Thursday) at 14:00

Computing joins—databases meet graph algorithms

Joint work with Anna Pagh. To appear at PODS 2006.

Abstract:

The natural join operation of relational algebra is a cornerstone of relational database systems. Computing a join of k relations can be phrased as the problem of finding all subgraphs of a certain form in a k-partite graph. Not surprisingly, the general problem is NP-hard (reduction to CLIQUE), but special (and typical) cases are tractable.

We consider "acyclic joins", for which the subgraphs to be found are trees with k vertices and show that:

- Previous algorithms have a complexity that grows (at least) linearly with kn (where n is the input size), and

- It is possible to eliminate the dependence on k in most cases, achieving essentially optimal complexity.

Finally, we consider the cyclic case for k<=4 in the I/O model, leaving improvement of the naive approach for k>4 as an intersting open problem.

Room: E:2405

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