An incremental collector can include memory pages, preferably virtual memory (VM) pages containing objects. A bit or byte map is created with one entry corresponding to each VM page. The VM page being collected is first write-protected and then the reachable objects are copied or relocated. Application induced changes to objects that have already been relocated are flagged in the map. Later the collector will suspend the application, scan the map and update the relocated objects that were changed and update the references to these objects. In one embodiment aimed at concurrent collecting, the map is copied to a second map, and the second map is scanned for changes that are propagated as before. The application may be suspended on the last pass through the map for the updating of remaining relocated objects by scanning the first map. The incremental collector can be a Train algorithm.