On the Locality of Nash-Williams Forest Decomposition and Star-Forest Decomposition

ABSTRACTGiven a graph G=(V,E) with arboricity a, we study the problem of decomposing the edges of G into (1+ε)a disjoint forests in the distributed LOCAL model. While there is a polynomial time centralized algorithm for a-forest decomposition (e.g. [Imai, J. Operation Research Soc. of Japan '83]), it remains an open question how close we can get to this exact decomposition in the LOCAL model.