We consider the multiple unicast problem under network coding over directed acyclic networks with unit capacity edges. There is a set of n source-terminal (si-ti) pairs that wish to communicate at unit rate over this network. The connectivity between the si-ti pairs is quantified by means of a connectivity level vector, [k1 k2 ... kn] such that there exist ki edge-disjoint paths between si and ti. Our main aim is to characterize the feasibility of achieving this for different values of n and [k1 ... kn]. For 3 unicast connections (n = 3), we characterize several achievable and unachievable values of the connectivity 3-tuple. In addition, in this work, we have found certain network topologies, and capacity characterizations that are useful in understanding the case of general n.
展开▼
