Best-fit bin packing

Best-fit is an online algorithm for bin packing. Its input is a list of items of different sizes. Its output is a packing - a partition of the items into bins of fixed capacity, such that the sum of sizes of items in each bin is at most the capacity. Ideally, we would like to use as few bins as possible, but minimizing the number of bins is an NP-hard problem. The best-fit algorithm uses the following heuristic:

• It keeps a list of open bins, which is initially empty.
• When an item arrives, it finds the bin with the maximum load into which the item can fit, if any. The load of a bin is defined as the sum of sizes of existing items in the bin before placing the new item.
  • If such a bin is found, the new item is placed inside it.
  • Otherwise, a new bin is opened and the coming item is placed inside it.