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A communication network modelled by a directed acyclic graph (DAG) isconsidered, over which a source wishes to send a specified number of bits to adestination node. Each node of the DAG is powered by a separate renewableenergy source, and the harvested energy is used to facilitate the sourcedestination data flow. The challenge here is to find the optimal rate and powerallocations across time for each node on its outgoing edges so as to minimizethe time by which the destination receives a specified number of bits. Anonline setting is considered where an algorithm only has causal informationabout the energy arrivals. Using the competitive ratio as the performancemetric, i.e. the ratio of the cost of the online algorithm and the optimaloffline algorithm, maximized over all inputs, a {\it lazy} online algorithmwith a competitive ratio of $2+\delta$ for any $\delta>0$ is proposed.Incidentally, $2$ is also a lower bound to the competitive ratio of any onlinealgorithm for this problem. Our lazy online algorithm is described and analyzedvia defining a novel max-flow problem over a DAG, where the rate on the subsetof outgoing edges of any node are related/constrained. An optimal algorithm tofind max-flow with these constraints is also provided, which may be ofindependent interest.

Online Energy Harvesting Problem Over An Arbitrary Directed Acyclic Graph Network