## Section: New Results

### Graph Algorithms

We collaborate with the Links project team on graph-based computations and evaluation in databases.

**Dependency Weighted Aggregation on Factorized Databases**
InĀ [17], we study a new class of aggregation
problems, called dependency weighted aggregation. The underlying
idea is to aggregate the answer tuples of a query while accounting
for dependencies between them, where two tuples are considered
dependent when they have the same value on some attribute. The main
problem we are interested in is to compute the dependency weighted
count of a conjunctive query. This aggregate can be seen as a form
of weighted counting, where the weights of the answer tuples are
computed by solving a linear program. This linear program enforces
that dependent tuples are not over represented in the final weighted
count. The dependency weighted count can be used to compute the
s-measure, a measure that is used in data mining to estimate the
frequency of a pattern in a graph database. Computing the dependency
weighted count of a conjunctive query is NP-hard in general. In this
paper, we show that this problem is actually tractable for a large
class of structurally restricted conjunctive queries such as acyclic
or bounded hypertree width queries. Our algorithm works on a
factorized representation of the answer set, in order to avoid
enumerating it exhaustively. Our technique produces a succinct
representation of the weighting of the answers. It can be used to
solve other dependency weighted aggregation tasks, such as computing
the (dependency) weighted average of the value of an attribute in
the answers set.