A fast solver for the 0/1-knapsack problem with multiple knapsacks
(C) Martin Väth (martin at mvath.de)- This project is distributed under the terms of the GNU General Public License v2.
This program was written rather quickly to train myself. It was later rewritten in a more general and efficient way.
It uses a dynamic programming type approach to the 0/1 knapsack problem (in the bound or unbound form) for multiple knapsacks.
In practice, one typically runs into this problem if one wants to distribute files of certain sizes to e.g. one or several USB-Sticks or CD-Roms: One is looking for a distribution of the files onto the media (knapsack) such that the amount of data is maximized. In some cases, the value of the data is differs from its filesize. Therefore, it is convenient that one can give values independently of the size. For example, if one gives some extremely high values to some files, one makes sure that the solution eventually found contains at least these files.
Some notes on the algorithm: The classical dynamic programming approach based on arrays requires an enormous amount of memory if the weights are huge: Especially for the above mentioned application, this classical approach would need more memory for calculation than what matches on all considered media togethher.
In contrast, the algorithm of this library uses hashing and a recursive approach to calculate less data and require less memory, in general. There are some cases (e.g. if you have an unlimited number of files of size 1 bytes to distribute) in which also this algorithm will require too much memory, but in "typical" cases it should be relative fast and low in memory consumption. After all, the full problem is NP-complete, so by current state of research, one cannot expect a "perfect" solution.
The program consists of a library which can be used independently:
knapsack.h: The main generic class implementing the algorithm. The output functions have to be overloaded.
The library is consumed by:
knapsack.cc: A simple CLI to the library
The library needs the boost library for advanced hash functions.
Since boost is needed anyway, also
boost::format is used for convenience
(the CLI additionally uses
If the requirement is fulfilled, compilation of the CLI should be simple:
make (as user) and
make install (as root)
Look at the
Makefile if you need to adapt paths.
To use the libraries, just include them (with the appropriate path);
the description how to use the library is in the file
To use the zsh completion file, make sure that it is in you zsh's
To get help for the CLI, type