Finding Key associated with max Value in a Java Map

Basically you'd need to iterate over the map's entry set, remembering both the "currently known maximum" and the key associated with it. (Or just the entry containing both, of course.)

For example:

Map.Entry<Foo, Bar> maxEntry = null;

for (Map.Entry<Foo, Bar> entry : map.entrySet())
{
    if (maxEntry == null || entry.getValue().compareTo(maxEntry.getValue()) > 0)
    {
        maxEntry = entry;
    }
}