Before revision:  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  .
After revision:  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 . 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 .