A garbage collector employs the train algorithm to collect a heap generation incrementally, collecting "car sections" in a collection order. As it updates the "remembered sets" by which it keeps track of where references to objects in respective car sections are located, it also updates oldest- and youngest-car indicators for each car section. The oldest- and youngest-car indicators for a given car section specify limits in the collection sequence beyond which references to objects in the given car have not been found. The garbage collector uses these indicators to identify cars that contain no objects that are reachable except through a reference chain that includes the collection set for the current collection increment. It adds one or more such cars to the collection set, and it collects the thus-expanded collection set without processing the remembered sets associated with the added cars.