Non-Dominated Quantum Iterative Routing Optimization for Wireless Multihop Networks

Abstract

Routing in wireless multihop networks (WMHNs) relies on a delicate balance of diverse and often conflicting parameters, when aiming for maximizing the WMHN performance. Classified as a non-deterministic polynomial-time hard problem, routing in WMHNs requires sophisticated methods. As a benefit of observing numerous variables in parallel, quantum computing offers a promising range of algorithms for complexity reduction by exploiting the principle of quantum parallelism (QP), while achieving the optimum full-search-based performance. In fact, the so-called non-dominated quantum optimization (NDQO) algorithm has been proposed for addressing the multiobjective routing problem with the goal of achieving a near-optimal performance, while imposing a complexity of the order of O(N ) and O(N √ N ) in the best and worst case scenarios, respectively. However, as the number of nodes in the WMHN increases, the total number of routes increases exponentially, making its employment infeasible despite the complexity reduction offered. Therefore, we propose a novel optimal quantum-assisted algorithm, namely, the non-dominated quantum iterative optimization (NDQIO) algorithm, which exploits the synergy between the hardware and the QP for the sake of achieving a further complexity reduction, which is on the order of O( √ N ) and O(N √ N ) in the best and worst case scenarios, respectively. In addition, we provide simulation results for demonstrating that our NDQIO algorithm achieves an average complexity reduction of almost an order of magnitude compared with the near-optimal NDQO algorithm, while having the same order of power consumption.INDEX TERMS WMHNs, quantum computing, Pareto optimality, BBHT-QSA, DHA, NDQO.

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

“…In terms of Pareto optimal routing using universal quantum computing [27], the so-called Non-Dominated Quantum Optimization (NDQO) algorithm proposed in [19] succeeded in identifying the entire set of Pareto-optimal routes at the expense of a complexity, which is on the order of O(N √ N ), relying on QP. As an improvement, the so-called Non-Dominated Quantum Iterative Optimization (NDQIO) algorithm was proposed in [30]. Explicitly, the NDQIO algorithm is also capable of identifying the entire set of Pareto-optimal routes, while imposing a parallel complexity and a sequential complexity defined 1 in [30], which is on the order of O(N OPF √ N ) and O(N 2 OPF √ N ), respectively, by relying on the beneficial synergy between QP and Hardware Parallelism (HP).…”

“…As an improvement, the so-called Non-Dominated Quantum Iterative Optimization (NDQIO) algorithm was proposed in [30]. Explicitly, the NDQIO algorithm is also capable of identifying the entire set of Pareto-optimal routes, while imposing a parallel complexity and a sequential complexity defined 1 in [30], which is on the order of O(N OPF √ N ) and O(N 2 OPF √ N ), respectively, by relying on the beneficial synergy between QP and Hardware Parallelism (HP). Note that N OPF corresponds to the number of Pareto-optimal routes.…”

“…By contrast, the sequential complexity does not consider any kind of parallelism. In [30], they are referred to as normalized execution time and normalized power consumption, respectively.…”

“…In the context of this treatise, the model of the networks considered both in [19] and in [30] has been adopted. To elaborate further, the WMHN considered is a fully connected network and it consists of a single Source Node (SN), a single Destination Node (DN) and a cloud of Relay Nodes (RN).…”

“…Therefore, we should point out that this treatise is focused on a centralized protocol. The presence of a cluster-head in possession of a quantum computer is considered at the DN side as in [19] and in [30]. The interference levels experienced by each node are presented in the legend.…”