# A Quantum-Search-Aided Dynamic Programming Framework for Pareto Optimal Routing in Wireless Multihop Networks

Research paper by D. Alanis, P. Botsinis, Z. Babar, H. V. Nguyen, D. Chandra, S. X. Ng, L. Hanzo

Indexed on: 23 Feb '18Published on: 23 Feb '18Published in: arXiv - Quantum Physics

#### Abstract

Wireless Multihop Networks (WMHNs) have to strike a trade-off among diverse and often conflicting Quality-of-Service (QoS) requirements. The resultant solutions may be included by the Pareto Front under the concept of Pareto Optimality. However, the problem of finding all the Pareto-optimal routes in WMHNs is classified as NP-hard, since the number of legitimate routes increases exponentially, as the nodes proliferate. Quantum Computing offers an attractive framework of rendering the Pareto-optimal routing problem tractable. In this context, a pair of quantum-assisted algorithms have been proposed, namely the Non-Dominated Quantum Optimization (NDQO) and the Non-Dominated Quantum Iterative Optimization (NDQIO). However, their complexity is proportional to $\sqrt{N}$, where $N$ corresponds to the total number of legitimate routes, thus still failing to find the solutions in "polynomial time". As a remedy, we devise a dynamic programming framework and propose the so-called Evolutionary Quantum Pareto Optimization (EQPO) algorithm. We analytically characterize the complexity imposed by the EQPO algorithm and demonstrate that it succeeds in solving the Pareto-optimal routing problem in polynomial time. Finally, we demonstrate by simulations that the EQPO algorithm achieves a complexity reduction, which is at least an order of magnitude, when compared to its predecessors, albeit at the cost of a modest heuristic accuracy reduction.