Abstract-In this paper we consider the problem of constructing a coordinate system in a sensor network where location information is not available. To this purpose we introduce the Virtual Coordinate assignment protocol (VCap) which defines a virtual coordinate system based on hop distances. As compared to other approaches, VCap is simple and have very little requirements in terms of communication and memory overheads. We compare by simulations the performances of greedy routing using our virtual coordinate system with the one using the physical coordinates. Results show that the virtual coordinate system can be used to efficently support geographic routing.

Due to limited functionalities and potentially large number of sensors, existing routing strategies proposed for mobile ad hoc networks are not directly applicable to wireless sensor networks. In this paper, we present a meshed multipath routing (M-MPR) protocol with selective forwarding (SF) of packets and end-to-end forward error correction (FEC) coding. We also describe a meshed multipath searching scheme suitable for sensor networks, which has a reduced signaling overhead and nodal database. Our performance evaluations show that (1) M-MPR achieves a much improved throughput over conventional disjoint multipath routing with comparable power consumption and receiver complexity; (2) to successfully route a message using FEC coding, selective forwarding (SF) consumes much less network resources, such as channel bandwidth and battery power, than packet replication (or limited flooding).

One of the main goals of 5G networks is to support the technological and business needs of various industries (the so-called verticals), which wish to offer to their customers a wide range of services characterized by diverse performance requirements. In this context, a critical challenge lies in mapping in an automated manner the requirements of verticals into decisions concerning the network infrastructure, including VNF placement, resource assignment, and traffic routing. In this paper, we seek to make such decisions jointly, accounting for their mutual interaction, and efficiently. To this end, we formulate a queuingbased model and use it at the network orchestrator to optimally match the vertical's requirements to the available system resources. We then propose a fast and efficient solution strategy, called MaxZ, which allows us to reduce the solution complexity. Our performance evaluation, carried out accounting for multiple scenarios representative of real-world services, shows that MaxZ performs substantially better than state-ofthe-art alternatives and consistently close to the optimum. INTRODUCTION5G networks are envisioned to provide the computational, memory, and storage resources needed to run multiple third parties (referred to as vertical industries or verticals) with diverse communication and computation needs. Verticals provide network operators with the specification of the services they want to provide, e.g., the virtual network functions (VNFs) they want to use to process their data and the associated quality of service.Mobile network operators are in charge of mapping the requirements of the verticals into infrastructure management decisions. This task is part of the network orchestration, and includes making decisions concerning (i) the placement of the VNFs needed by the verticals across the infrastructure; (ii) the assignment of CPU, memory and storage resources to the VNFs; (iii) the routing of data across network nodes.These decisions interact with each other in ways that are complex and often counterintuitive. In this paper, we focus on the allocation of computational and network resources, and make such decisions jointly, accounting for (i) the requirements of each VNF and vertical; (ii) the capabilities of the network operator's infrastructure; (iii) the capacity • S. Agarwal is with IIT Guwahati, India. F. Malandrino and C.-F. Chiasserini are with Politecnico di Torino, Italy and CNR-IEIIT, Italy. S. De is with IIT Delhi, India. • A preliminary version [1] of this work was presented at the IEEE INFOCOM 2018 conference.

Thanks to network slicing, 5G networks will support a variety of services in a flexible and swift manner. In this context, we seek to make high-quality, joint optimal decisions concerning the placement of VNFs across the physical hosts for realizing the services, and the allocation of CPU resources in VNFs sharing a host. To this end, we present a queuing-based system model, accounting for all the entities involved in 5G networks. Then, we propose a fast and efficient solution strategy yielding nearoptimal decisions. We evaluate our approach in multiple scenarios that well represent real-world services, and find it to consistently outperform state-of-the-art alternatives and closely match the optimum.