Interacting RNA complexes are studied  using a filtration via their topological genus. Our main result is a new bijection for RNA-RNA interaction structures and linear time uniform sampling algorithm for RNA complexes of fixed topological genus. The bijection allows to either reduce the topological genus of an RNA-RNA interaction structure directly, or to loose connectivity by decomposing the complex into a pair of single stranded RNA structures. Our main result is proved bijectively. It provides an explicit algorithm of how to rewire the corresponding complexes  . Using the concept of genus induction, we construct RNA-RNA interaction complexes of fixed topological genus g uniformly in linear time  .
Interacting RNA complexes are studied via bicellular maps using a filtration via their topological genus. Our main result is a new bijection for RNA-RNA interaction structures and linear time uniform sampling algorithm for RNA complexes of fixed topological genus. The bijection allows to either reduce the topological genus of a bicellular map directly, or to lose connectivity by decomposing the complex into a pair of single stranded RNA structures. Our main result is proved bijectively. It provides an explicit algorithm of how to rewire the corresponding complexes and an unambiguous decomposition grammar . Using the concept of genus induction, we construct bicellular maps of fixed topological genus g uniformly in linear time . We present various statistics on these topological RNA complexes and compare our findings with biological complexes. Furthermore we show how to construct loop-energy based complexes using our decomposition grammar .
A
via bicellular maps
R
an RNA-RNA interaction structure
a bicellular map
R
loose
lose
A
and an unambiguous decomposition grammar
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RNA-RNA interaction complexes
bicellular maps
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. We present various statistics on these topological RNA complexes and compare our findings with biological complexes. Furthermore we show how to construct loop-energy based complexes using our decomposition grammar