Branch and bound, or "BnB," is a cryptocurrency trading technique designed to reduce trading fees.
Technically, a single, whole cryptocurrency (for example, one bitcoin) is not comprised of a single bundle of code. It is comprised of multiple "chunks" of data called "unspent transaction outputs" (UTXOs) - unused fragments of bitcoin left over from previous transactions.
Sometimes, a user may try to send an amount of bitcoin made up of a cluster of UTXOs that is so small, the value they are trying to send is exceeded by the fees required to carry out the transaction.
The term "dust" is used to describe UTXOs of bitcoin so small, they aren't worth spending - what's the point of using bitcoin to buy a pack fo gum that costs $1.50 if you need to spend an additional $3 in mining and transaction fees just to make the payment?
How BnB works
BnB is an algorithm designed to avoid this problem. It does so by choosing the best combination of existing UXTOs from the sender's bitcoin wallet to see if there is a combination that rounds out to as close as possible to exactly the amount a user wishes to send.