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We consider single-source single-sink (ss-ss) multi-hop networks, withslow-fading links and single-antenna half-duplex relays. We identify twofamilies of networks that are multi-hop generalizations of the well-studiedtwo-hop network: K-Parallel-Path (KPP) networks and layered networks. KPPnetworks can be viewed as the union of K node-disjoint parallel relaying paths,each of length greater than one. KPP networks are then generalized to KPP(I)networks, which permit interference between paths and to KPP(D) networks, whichpossess a direct link from source to sink. We characterize the DMT of thesefamilies of networks completely for K > 3. Layered networks are networkscomprising of relaying layers with edges existing only within the same layer orbetween adjacent layers. We prove that a linear DMT between the maximumdiversity d_{max} and the maximum multiplexing gain of 1 is achievable forfully-connected layered networks. This is shown to be equal to the optimal DMTif the number of layers is less than 4. For multi-antenna KPP and layerednetworks, we provide an achievable DMT region.  For arbitrary ss-ss single-antenna directed-acyclic full-duplex networks, weprove that a linear tradeoff between maximum diversity and maximum multiplexinggain is achievable. All protocols in this paper are explicit and use onlyamplify and forward (AF) relaying. We also construct codes with shortblock-lengths based on cyclic division algebras that achieve the optimal DMTfor all the proposed schemes. Two key implications of the results in the paperare that the half-duplex constraint does not entail any rate loss for a largeclass of networks and that simple AF protocols are often sufficient to attainthe optimal DMT.

Multi-hop Cooperative Wireless Networks: Diversity Multiplexing Tradeoff and Optimal Code Design