Map<String, Integer> and Map<Integer ,String> sorting

I am trying to resolve sorting a map , which contains huge data(1000K). Is there any efficient way than this to sorting these maps ? below is the code snippet.

    Map<Integer, String> myMap1 = new HashMap<Integer, String>();
    Map<String,Integer>  myMap2 = new HashMap< String,Integer>();

    List <Entry<Integer,String>> lst1 = new ArrayList<Entry<Integer,String>>(myMap1.entrySet());
    Collections.sort(lst1, new Comparator<Entry<Integer,String>>(){
        @Override
        public int compare(Entry e1, Entry e2)
        {
            return ((String) e1.getValue()).compareTo((String) e2.getValue());
        }}
    );


    List <Entry<String,Integer>> lst2 = new ArrayList<Entry<String,Integer>>(myMap2.entrySet());        
    Collections.sort(lst2, new Comparator<Entry<String,Integer>>(){
        @Override
        public int compare(Entry e1, Entry e2)
        {
            return ((Integer) e1.getValue()).compareTo((Integer) e2.getValue());
        }}
    );

IMO a priority queue can also be a good approach:

Map<Integer, String> myMap1 = new HashMap<Integer, String>();
PriorityQueue<Entry<Integer, String>> pq = new PriorityQueue<Map.Entry<Integer,String>>(myMap1.size(), new Comparator<Entry<Integer, String>>() {
    @Override
    public int compare(Entry<Integer, String> arg0, Entry<Integer, String> arg1) {
        return arg0.getValue().compareTo(arg1.getValue());
    }
});
pq.addAll(myMap1.entrySet());
while (!pq.isEmpty()) {
    System.out.println(pq.poll());
}

Also Google Guava can be a good option as it provides a BiMap implementations which can be inversed, and then just sort on inversed map keys.

 Map<Integer, String> myMap1 = new HashMap<Integer, String>();
    // insert values in myMap
    Map<String,Integer>  myMap2 = myMap1.inverse();
    SortedMap<Integer, Character> sortedInversed = new TreeMap<Integer, Character>(myMap2 );