In this paper we present an algorithm for finding
a distance optimal rendezvous location with respect to both
initial and target locations of the mobile agents. These agents
can be humans or robots, who need to meet and split while
performing a collaborative task. Our aim is to embed the
meeting process within a background activity such that the
agents travel through the rendezvous location while taking the
shortest paths to their respective target locations. We analyze
this problem in a street network scenario with two agents who
are given their individual scheduled routes to complete with an
underlying common goal. The agents are allowed to select any
combination of the waypoints along their routes as long as they
travel the shortest path and pass through the same potential
rendezvous location. The total number of path combinations
that the agents need to evaluate for the shortest path increases
rapidly with the number of waypoints along their routes. We
address this computational cost by proposing a combination of
Euclidean and street network distances for a trade-off between
the number of queries and a distance optimal solution.