# Resource Assignment Algorithms for Autonomous Mobile Robots with Task Offloading
## 2 Literature Review
In [26], instead, the model considers offloading mobile robot tasks on edge servers, and the multi-objective MINLP has to minimize travel times and computation workload. Thanks to the weighted-sum method, Pareto-optimal solutions are found that outperform multiple single-objective approaches based on vehicle routing problem-solving methods. Integrated sensing, computing, and communication are optimized in [27], where a fleet of robots exploits a reflective intelligent surface to extend the radio coverage area in potential blockage conditions, and concurrently senses the environment by means of the communication radio signal. The problem is decoupled by minimizing first the computation latency, and then by maximizing transmission rate and sensing accuracy. Thanks to bisection search and alternating optimization algorithms, significant service quality enhancement, latency reduction, and reliability improvement are obtained with respect to other baseline solutions. Service placement is added as a further variable in [28], extending the classical task offloading, sensing, and communication optimization problem. The authors initially focus on minimizing both the latency and the number of deployed services, and then propose a method to optimize the placement of such services on specific edge/cloud servers. The MINLP problem is solved using a sequential fixing algorithm, with long-term and short-term solution strategies. A slightly different problem considered in the literature is the assignment of remote radio units (next to antennas) to baseband signal processing units (in remote computers), for the implementation of virtualized radios in cloud radio access networks (CRAN). In this case, the radio access units are an active part of the optimization problem, since they offload some radio data processing tasks to the remote services. In this sense, some of the solutions devised for CRANs fit well with the problem considered in this paper. For instance, in [29], the optimization of CRAN unit assignment is investigated. The authors aim at energy efficiency improvement, and devise a mixed-integer nonconvex programming problem. Then, they reformulate it as a nonlinear fractional problem and solve it with an iterative algorithm based on the subgradient method. [PERSON] et al. [30] rely on a branch-and-bound solution to optimize the system and lower the complexity thanks to a difference of convex algorithm (DCA) method. The authors of [31] use a queuing model for their system and, thanks to auction theory, solve for the optimum with maximum power, radio allocation, interference, and queuing stability constraints. In [32], the integer linear programming formulation of the problem allows finding several algorithms based on matroids, b-matching, and multiple knapsacks. These algorithms optimize the efficiency of network resource utilization while keeping precise latency requirements. To this purpose, the authors employ a cost function that considers both the front network communication latency and the resources used in edge DCs. [PERSON] and [PERSON] [33] pose the problem as nonconvex and combinatorial, then they propose an approximated solution based on convexification, integer relaxation, and Lagrangian analysis. In summary, many of the reviewed literature works adopt complex models that account for specific issues of the communication aspect (link budget, blockage probability, radio propagation, etc. ), of the computation aspect (requests queue, CPU cycles, energy consumption, etc. ), and of the service aspect (neighbor or edge placement, server selection, requests size, etc.). In our model, instead, all such aspects are simplified by considering stationary conditions in short time windows. Moreover, our proposed solutions do not exploit overly complicated algorithms or advanced machine learning techniques, but rather simple greedy procedures following a straightforward minimization approach.