Map> reverseMap = new HashMap<>();

for (Map.Entry entry : map.entrySet()) {
    if (!reverseMap.containsKey(entry.getValue())) {
        reverseMap.put(entry.getValue(), new ArrayList<>());
    }
    ArrayList keys = reverseMap.get(entry.getValue());
    keys.add(entry.getKey());
    reverseMap.put(entry.getValue(), keys);
}