Connectivity and cooperation are considered important prerequisites to automated driving, as they are crucial elements in increasing the safety of future automated vehicles and their full integration in the overall transport system. Although many European Member States, as part of the C‐Roads Platform, have implemented and are still implementing Road‐side Units (RSUs) for Cooperative Intelligent Transportation Systems (C‐ITS) within pilot deployment projects, the platform aspires a wide extension of deployments in the coming years. Therefore, this paper investigates techno‐economic aspects of C‐ITS RSU deployments from a road authority viewpoint. A two‐phased approach is used, in which firstly the optimal RSU locations are determined, taking into account existing road‐side infrastructure. Secondly, a cost model translates the amount of RSUs into financial results. It was found that traffic density has a significant impact on required RSU density, hence impacting costs. Furthermore, major cost saving can be obtained by leveraging existing road‐side infrastructure. The proposed methodology is valuable for other member states, and in general, to any other country aspiring to roll out C‐ITS road infrastructure. Results can be used to estimate required investment costs based on legacy infrastructure, as well as to benchmark with the envisioned benefits from the deployed C‐ITS services.

In this article we prove bounds for the boundary length of patches with a given set of bounded faces. We assume that with t the number of given triangles, q the number of quadrangles, and p the number of pentagons, the curvature 3t + 2q + p is at most 6 and that at an interior vertex exactly 3 faces meet. There is no restriction on the number of faces with size 6 or larger. We prove that one gets a patch with shortest boundary if one arranges the faces in a spiral order and with increasing size. Furthermore we give explicit formulas that allow to determine all boundary lengths that occur for patches with given numbers p, q and t < 2 and no bounded face larger than 6.The patches studied in this article occur as subgraphs of 3-regular graphs in mathematics as well as models for planar polycyclic hydrocarbons in chemistry where the bounds allow to decide on the (theoretical) existence of molecules for a given chemical formula.

Many real-life problems boil down to a variant of the Minimum Steiner Tree Problem (STP). In telecommunications, Fiber-To-The-Home (FTTH) houses are clustered so they can be connected with fiber as cost-efficiently as possible. The cost calculation of a fiber installment can be formulated as a capacitated STP. Often, STP variants are solved with integer linear programs, which provide excellent solutions, though the running time costs increase quickly with graph size. Some geographical areas require graphs of over 20000 nodes—typically unattainable for integer linear programs. This paper presents an alternative approach. It extends the shortest path heuristic for the STP to a new heuristic that can construct solutions for the capacitated STP: the Capacitated Shortest Path Heuristic (CSPH). It is straightforward to implement, allowing many extensions. In experiments on realistic telecommunications datasets, CSPH finds solutions on average in time O(|V|2), quadratic in the number of nodes, making it possible to solve 50000 node graphs in under a minute.

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