Fastest way to remove/hide a lot of elements from a list [closed]

Question

I have a dropdown that contains around 100,000 rows which make up a list.

<input id="search" type="text" />
<ul>
    <li>item 1</li>
    <li>item 2</li>
        ...
    <li>item 100,000</li>
</ul>

I have a text box which acts as a search, so as you type it matches the input to items in the list, removing what does not match. This is the class I wrote to perform the removing of list elements.

See the fiddle (list has about 2000 items)

// requires jQuery
var Search = (function(){

    var cls = function (name) {
        var self = this;

        self.elem = $('#' + name);
        self.list = $('#' + name).next('ul').children();
        self.elem.bind('keyup', function () { self.change(); }); 
    };

    cls.prototype = {
        change: function () {
            var self = this;
            // gets the closest ul list
            var typed = self.elem.val();

            // only do something if there is something typed
            if (typed !== '') {
                // remove irrelevent items from the list
                self.list.each(function () {
                    var item = $(this).html();
                    if (item.indexOf(typed) === -1)  {
                        $(this).addClass('zero');
                        // tried using a class with visibility hidden
                    } else {
                        $(this).removeClass('zero');
                    }
                });
            } else {
                // check what list items are 'hidden' and unhide them
                self.list.each(function () {
                    if ($(this).hasClass('zero')) {
                        $(this).removeClass('zero');
                    }
                });
            }
        }
    };
    return cls;
}());

I am just adding a class which adds a height of 0, and no margin,padding, etc, but I have also tried using visibility:hidden. I have also tried using the detach method in jQuery but this is about the same in terms of speed.

Are their any JavaScript experts who can see any problems with the code, or offer some optimization techniques?