Bin packing problem

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The bin packing problem is an optimization problem, in which items of different sizes must be packed into a finite number of bins or containers, each of a fixed given capacity, in a way that minimizes the number of bins used. The problem has many applications, such as filling up containers, loading trucks with weight capacity constraints, creating file backups in media, splitting a network prefix into multiple subnets, and technology mapping in FPGA semiconductor chip design. Computationally, the problem is NP-hard, and the corresponding decision problem, deciding if items can fit into a specified number of bins, is NP-complete. Despite its worst-case hardness, optimal solutions to very large instances of the problem can be produced with sophisticated algorithms. In addition, many approximation algorithms exist. For example, the first fit algorithm provides a fast but often non-optimal solution, involving placing each item into the first bin in which it will fit. It requires Θ(n log n)...

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