Online Energy Harvesting Problem Over An Arbitrary Directed Acyclic Graph Network

TL;DR

This paper introduces a lazy online algorithm for energy harvesting over DAG networks that achieves a competitive ratio close to the theoretical lower bound, optimizing data transmission time with only causal energy information.

Contribution

It proposes a novel lazy online algorithm with a competitive ratio of 2+δ for energy harvesting over DAGs, and develops a max-flow based method for constrained flow optimization.

Findings

Achieves a competitive ratio of 2+δ, close to the lower bound of 2.

Develops a max-flow algorithm for constrained flow in DAGs.

Provides theoretical analysis and optimal algorithms for online energy allocation.

Abstract

A communication network modelled by a directed acyclic graph (DAG) is considered, over which a source wishes to send a specified number of bits to a destination node. Each node of the DAG is powered by a separate renewable energy source, and the harvested energy is used to facilitate the source destination data flow. The challenge here is to find the optimal rate and power allocations across time for each node on its outgoing edges so as to minimize the time by which the destination receives a specified number of bits. An online setting is considered where an algorithm only has causal information about the energy arrivals. Using the competitive ratio as the performance metric, i.e. the ratio of the cost of the online algorithm and the optimal offline algorithm, maximized over all inputs, a {\it lazy} online algorithm with 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 online algorithm for this problem. Our lazy online algorithm is described and analyzed via defining a novel max-flow problem over a DAG, where the rate on the subset of outgoing edges of any node are related/constrained. An optimal algorithm to find max-flow with these constraints is also provided, which may be of independent interest.