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We consider the "coded cooperative data exchange problem" for general graphs.In this problem, given a graph G=(V,E) representing clients in a broadcastnetwork, each of which initially hold a (not necessarily disjoint) set ofinformation packets; one wishes to design a communication scheme in whicheventually all clients will hold all the packets of the network. Communicationis performed in rounds, where in each round a single client broadcasts a single(possibly encoded) information packet to its neighbors in G. The objective isto design a broadcast scheme that satisfies all clients with the minimum numberof broadcast rounds.  The coded cooperative data exchange problem has seen significant researchover the last few years; mostly when the graph G is the complete broadcastgraph in which each client is adjacent to all other clients in the network, butalso on general topologies, both in the fractional and integral setting. Inthis work we focus on the integral setting in general undirected topologies G.We tie the data exchange problem on G to certain well studied combinatorialproperties of G and in such show that solving the problem exactly or evenapproximately within a multiplicative factor of \log{|V|} is intractable (i.e.,NP-Hard). We then turn to study efficient data exchange schemes yielding anumber of communication rounds comparable to our intractability result. Ourcommunication schemes do not involve encoding, and in such yield bounds on the"coding advantage" in the setting at hand.

Coded Cooperative Data Exchange Problem for General Topologies