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Compressed Representation of Dynamic Binary Relations with Applications

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Nieves Brisaboa, Ana Cerdeira-Pena, Guillermo de Bernardo, and Gonzalo Navarro

We introduce a dynamic data structure for the compact representation
of binary relations *R subset-of A x B*. The data
structure is a dynamic variant of the k2-tree, a static compact
representation that takes advantage of clustering in the binary
relation to achieve compression. Our structure can efficiently check
whether two objects *(a,b) in A x B* are related, and list the
objects of *B* related to some *a in A* and vice versa.
Additionally, our structure allows inserting and deleting pairs
*(a,b)* in the relation, as well as modifying the base sets *A*
and *B*. We test our dynamic data structure in different contexts,
including the representation of Web graphs and RDF databases. Our
experiments show that our dynamic data structure achieves good
compression ratios and fast query times, close to those of a static
representation, while also providing efficient support for updates
in the represented binary relation.