pairwise intersections in mongodb

I am new to mongodb, I was wondering if I could get some advice. I have the following collection

{ "_id" : "u1", "item" : [ "a", "b", "c" ] }
{ "_id" : "u2", "item" : [ "b", "d", "e" ] }
{ "_id" : "u3", "item" : [ "a", "c", "f" ] }
{ "_id" : "u4", "item" : [ "c" ] }

I want to create a new collection that will calculate the items’ union and intersection for each pair of users, for example at the end, for user 1 and 2,4 The result will be

{ "_id" : "u12", "intersect_count":1,"union_count":6 }
{ "_id" : "u14", "intersect_count":1,"union_count":4}

I don’t want to do a pairwise operation for each pair, because of inefficiency. Is there any trick to do it more efficiently?

Answers

My solution is this:

map_func = function() {
  self = this;
  ids.forEach(function(id) {
    if (id === self._id) return;
    emit([id, self._id].sort().join('_'), self.item);
  });
};

reduce_func = function(key, vals) {
  return {
    intersect_count: intersect_func.apply(null, vals).length,
    union_count: union_func.apply(null, vals).length
  };
};

opts = {
  out: "redused_items",
  scope: {
    ids: db.items.distinct('_id'),
    union_func: union_func,
    intersect_func: intersect_func
  }
}

db.items.mapReduce( map_func, reduce_func, opts )

If you have N elemets in your collection then map_func will emit N*(N-1) elements for future reduction. Then reduce_func will reduce them into N*(N-1)/2 new elements.

I used scope to pass global variables (ids) and helper methods (union_func, intersect_func) into map_func and reduce_func. Otherwise MapReduce will fail with error, because it evaluates map_func and reduce_func in special environment.

Result of calling MapReduce:

> db.redused_items.find()
{ "_id" : "u1_u2", "value" : { "intersect_count" : 1, "union_count" : 6 } }
{ "_id" : "u1_u3", "value" : { "intersect_count" : 2, "union_count" : 6 } }
{ "_id" : "u1_u4", "value" : { "intersect_count" : 1, "union_count" : 4 } }
{ "_id" : "u2_u3", "value" : { "intersect_count" : 0, "union_count" : 6 } }
{ "_id" : "u2_u4", "value" : { "intersect_count" : 0, "union_count" : 4 } }
{ "_id" : "u3_u4", "value" : { "intersect_count" : 1, "union_count" : 4 } }

I used the following helpers for my tests:

union_func = function(a1, a2) {
  return a1.concat(a2);
};

intersect_func = function(a1, a2) {
  return a1.filter(function(x) {
    return a2.indexOf(x) >= 0;
  });
};

Alternative way is to use mongo cursor instead of global ids object:

map_func = function() {
  self = this;
  db.items.find({},['_id']).forEach(function(elem) {
    if (elem._id === self._id) return;
    emit([elem._id, self._id].sort().join('_'), self.item);
  });
};

opts = {
  out: "redused_items",
  scope: {
    union_func: union_func,
    intersect_func: intersect_func
  }
}

db.items.mapReduce( map_func, reduce_func, opts )

Result will be the same.