In this paper we consider a set of travelers, starting from likely different locations towards a common destination within a road network, and propose solutions to find the optimal connecting points for them. A connecting point is a vertex of the network where a subset of the travelers meet and continue traveling together towards the next connecting point or the destination. The notion of optimality is with regard to a given aggregated travel cost, e.g., travel distance or shared fuel cost. This problem by itself is new and we make it even more interesting (and complex) by considering affinity factors among the users, i.e., how much a user likes to travel together with another one. This plays a fundamental role in determining where the connecting points are and how subsets of travelers are formed. We propose three methods for addressing this problem, one that relies on a fast and greedy approach that finds a sub-optimal solution, and two others that yield globally optimal solution. We evaluate all proposed approaches through experiments, where collections of real datasets are used to assess the trade-offs, behavior and characteristics of each method.