Changing lanes on a highway

Paper in proceeding, 2018

We study a combinatorial optimization problem that is motivated by the scenario of autonomous cars driving on a multi-lane highway: some cars need to change lanes before the next intersection, and if there is congestion, cars need to slow down to make space for those who are changing lanes. There are two natural objective functions to minimize: (1) how long does it take for all traffic to clear the road, and (2) the total number of maneuvers. In this work, we present an approximation algorithm for solving these problems in the two-lane case and a hardness result for the multi-lane case.