The additional metadata added to the IndexEntry as part of SERVER-22399 describes what prefixes of the indexed fields cause the index to be multikey. We can use this information to get tighter bounds by assigning additional predicates to the index.

• It is always safe to assign a predicate on path Y to the index when no prefix of the path Y causes the index to be multikey.
• For any non-$elemMatch predicate on path X already assigned to the index, it isn't safe to assign a predicate on path Y (possibly equal to X) to the index when a shared prefix of the paths X and Y causes the index to be multikey.
• For any $elemMatch predicate on path X already assigned to the index, it isn't safe to assign a predicate on path Y (possibly equal to X) to the index when
  • a shared prefix of the paths X and Y causes the index to be multikey and the predicates aren't joined by the same $elemMatch context, or
  • a shared prefix of the paths X and Y inside the innermost $elemMatch causes the index to be multikey.

Some examples

Can intersect bounds on "a" because it is never an array containing multiple elements.

Index: {a: 1, b: 1}
Document: {a: 5, b: [1, 2, 3]}
⇒ Multikey paths: ["b"]
Query: {a: {$gte: 0, $lt: 10}}
⇒ Bounds on "a": [0, 10)
⇒ Bounds on "b": [MinKey, MaxKey]

Can intersect bounds on "a.b" because neither it nor the "a" field are ever an array containing multiple elements.

Index: {"a.b": 1, "a.c": 1}
Document: {a: {b: 5, c: [7, 8, 9]}}
⇒ Multikey paths: ["a.c"],
Query: {"a.b": {$gte: 0, $lt: 10}, "a.c": 7}
⇒ Bounds on "a.b": [0, 10)
⇒ Bounds on "a.c": [MinKey, MaxKey]

Can compound bounds on "a.b" and "a.c" because the "a" field is never an array containing multiple elements.

Index: {"a.b": 1, "a.c": 1}
Document: {a: {b: [1, 2, 3], c: 5}
⇒ Multikey paths: ["a.b"]
⇒ Index entries: {"": 1, "": 5}, {"": 2, "": 5}, {"": 3, "": 5}
Query: {"a.b": 1, "a.c": 5}
⇒ Bounds on "a.b": [1, 1]
⇒ Bounds on "a.c": [5, 5]

Can compound bounds on "a.b.c" and "a.b.d" because the "a.b" field is never an array containing multiple elements.

Index: {"a.b.c": 1, "a.b.d": 1}
Document: {a: [{b: {c: 1}}, {b: {d: -1}}]}
⇒ Multikey paths: ["a"]
⇒ Index entries {"": 1, "": null}, {"": null, "": -1}
Query: {a: {$elemMatch: {"b.c": 1, "b.d": -1}}}
⇒ Bounds on "a.b.c": [1, 1]
⇒ Bounds on "a.b.d": [-1, -1]