Secret Santa Assignment

You are tasked with developing a function for a Secret Santa gift exchange application. In this exchange, each participant gives a gift to one other participant such that:

• Every participant gives exactly one gift and receives exactly one gift (i.e., the assignment is a one-to-one mapping).
• No participant is assigned to themselves.
• There is a list of forbidden pairs. If a forbidden pair (A, B) is specified, participant A cannot give a gift to participant B.

Your function will receive two inputs:

1. A list of participants (each represented as a unique string).
2. A list of forbidden pairs, where each forbidden pair is represented as a tuple or a list of two strings [giver, receiver].

Your task is to compute a valid Secret Santa assignment, returning the assignment as a mapping (or dictionary) where each key is a giver and the corresponding value is the receiver. If there are multiple valid assignments, you may return any one of them. If no valid assignment exists, return an empty mapping.

Example:

Given participants:

participants = ["Alice", "Bob", "Charlie", "Diana"]

and forbidden pairs:

forbidden = [("Alice", "Bob"), ("Bob", "Alice")]

One possible valid assignment might be:

{
  "Alice": "Charlie",
  "Bob": "Diana",
  "Charlie": "Bob",
  "Diana": "Alice"
}

Note: Your solution should consider the possibility of small lists of participants (e.g., less than 20), and you can assume that the input lists are valid and contain unique participants. Think carefully about the approach you take to efficiently explore valid assignments given the constraints.