Create algorithm to minimise total number of transactions

[IsaacCheng9]

Summary

• Created an algorithm to minimise the total number of transactions.
  • This recalculates the transactions required to reach a zero-state in debts every time there is an update to the debts (expense added/debt settled).
• As the underlying problem is np-complete, this algorithm is a heuristic.
  • It runs in O(k * n log n), where k is the number of debts and n is the number of users.
  • The algorithm calculates the total net debt for each user, then creates two min-heaps (one for debt and one for credit).
  • It pops from the min-heaps and creates the transaction between the two popped users until it reaches a zero-state in debt.
• In the future, we could optimise the algorithm to O(n log n) by denormalising the user debts.
  • The algorithm currently spends O(k) time going through all debts and calculating the net debt for each user.
  • If we store this in a separate collection and update it every time a debt pair is updated, we'll save repeated work.

Note that this hasn't been implemented in the front-end yet – we should add a switch that allows the user to turn this on (and a hint explaining what it does), as it may otherwise cause confusion. I've created issue #59 to track this.

Related Issues

Fixes issue #8.

Resources

• Algorithm behind bill splitting app
• What algorithm to use to determine minimum number of actions required to get the system to "Zero" state?
• Algorithm to simplify a weighted directed graph of debts

Example

Originally six transactions -> four transactions after algorithm applied:

[
  {
    _id: new ObjectId("6308be56359b0cfb02ccb0c3"),
    from: 'user4',
    to: 'user2',
    amount: 2000,
    __v: 0
  },
  {
    _id: new ObjectId("6308c0ef359b0cfb02ccb0d9"),
    from: 'user1',
    to: 'user4',
    amount: 2000,
    __v: 0
  },
  {
    _id: new ObjectId("6308cc75bc58e8af84d40c7f"),
    from: 'user1',
    to: 'user3',
    amount: 1000,
    __v: 0
  },
  {
    _id: new ObjectId("6308ccc7bc58e8af84d40c8b"),
    from: 'user4',
    to: 'user5',
    amount: 2000,
    __v: 0
  },
  {
    _id: new ObjectId("6308ccdebc58e8af84d40c9b"),
    from: 'user6',
    to: 'user5',
    amount: 3000,
    __v: 0
  },
  {
    _id: new ObjectId("6308ccf3bc58e8af84d40cad"),
    from: 'user5',
    to: 'user1',
    amount: 4000,
    __v: 0
  }
]
-------------------------------------------------------------
Map(6) {
  'user4' => 2000,
  'user2' => -2000,
  'user1' => -1000,
  'user3' => -1000,
  'user5' => -1000,
  'user6' => 3000
}
Heap {
  cmp: [Function (anonymous)],
  nodes: [
    { username: 'user4', amount: 2000 },
    { username: 'user6', amount: 3000 }
  ]
}
Heap {
  cmp: [Function (anonymous)],
  nodes: [
    { username: 'user1', amount: 1000 },
    { username: 'user5', amount: 1000 },
    { username: 'user3', amount: 1000 },
    { username: 'user2', amount: 2000 }
  ]
}




Heap {
  cmp: [Function (anonymous)],
  nodes: [
    { username: 'user4', amount: 1000 },
    { username: 'user6', amount: 3000 }
  ]
}
Heap {
  cmp: [Function (anonymous)],
  nodes: [
    { username: 'user3', amount: 1000 },
    { username: 'user5', amount: 1000 },
    { username: 'user2', amount: 2000 }
  ]
}




Heap {
  cmp: [Function (anonymous)],
  nodes: [ { username: 'user6', amount: 3000 } ]
}
Heap {
  cmp: [Function (anonymous)],
  nodes: [
    { username: 'user5', amount: 1000 },
    { username: 'user2', amount: 2000 }
  ]
}




Heap {
  cmp: [Function (anonymous)],
  nodes: [ { username: 'user6', amount: 2000 } ]
}
Heap {
  cmp: [Function (anonymous)],
  nodes: [ { username: 'user2', amount: 2000 } ]
}




Heap { cmp: [Function (anonymous)], nodes: [] }
Heap { cmp: [Function (anonymous)], nodes: [] }

[gkSideProjects]

This is great stuff, everything working as expected!