// data in Already Arranged Data (AAD) are sorted by y-position, from y-min to y-max
  // when testing for a new placement, AAD allows to not check for collision with circles that are too far away
  // y-based sorted data are stored in a doubly-linked list
  //   doubly-linked list provides (next) 'above' and (previous) 'below' data

  function AlreadyArrangedData () {
    this._y_min = null; //aad pointing to Math.min(data.y)
    this._y_max = null; //aad pointing to Math.max(data.y)
    this.size = 0 //number of data in the doubly-linked list
    this._idToAad = {}; //direct access to a node of the doubly-linked list
  }

  AlreadyArrangedData.prototype.clear = function () {
    this._y_min = null;
    this._y_max = null;
    this.size = 0;
    this._idToAad = {};
  };

  AlreadyArrangedData.prototype.aad = function (datum){
    return this._idToAad[datum.id];
  };

  AlreadyArrangedData.prototype.addMany = function (data) {
    data.forEach( function (datum, item) {
      this.add(datum);
    }, this)

    //for chaining purpose
    return this;
  };

  AlreadyArrangedData.prototype.add = function (datum){
    //create a new item object, place data in
    var aad = {
      datum: datum,
      above: null,
      below: null
    };

    //insert datum in the y-based doubly-linked list
    if (this.size === 0) { //special case: no items in the list yet
      this._y_min = this._y_max = aad;
    } else if (datum.y <= this._y_min.datum.y) {//special case: new data is the min
      aad.above = this._y_min;
      aad.above.below = aad;
      this._y_min = aad;
    } else if (datum.y >= this._y_max.datum.y) { //special case: new data is the max
      aad.below = this._y_max;
      aad.below.above = aad;
      this._y_max = aad;
    } else {
      //insert the node at the adequate position
      var current = this._y_max;
      //loop to find immediate below
      while (current.datum.y > datum.y) {
        current = current.below;
      }
      aad.below = current;
      aad.above = current.above;
      aad.above.below = aad;
      aad.below.above = aad;
    }

    //direct access to the node
    this._idToAad[datum.id] = aad;

    //update size
    this.size++;

    //for chaining purpose
    return this;
  };

  AlreadyArrangedData.prototype.remove = function (datum) {
    var aad = this.aad(datum);

    //remove datum from doubly-linked list
    if (this.size === 1) { //special case: last item to remove
      this._y_min = this._y_max = null;
    } else if (aad === this._y_min) { //special case: remove y-min
      this._y_min = this._y_min.above;
      this._y_min.below = null;
    } else if (aad === this._y_max) { //special case: remove y-max
      this._y_max = this._y_max.below;
      this._y_max.above = null;
    } else {
      //remove pointers to the noee
      aad.above.below = aad.below;
      aad.below.above = aad.above;
    }

    aad = null // carbage collector
    delete this._idToAad[datum.id]; //remove direct access to the node

    //update size
    this.size--;

    //for chaining purpose
    return this;
  }