MDCKP

Multiple Disjunctively Constrained Knapsak problem: definition and an approximation algorithm implementation.

The problem is formally explained in this document. In this repo you can find also an implementation in C++ of a naive algorithm for a simple solution.

• How to use
• Use it in your project
• Input and output file formats

How to use

• Build the software:

mkdir build
cd build
cmake ..
make -j4

• (from the root) Run the algorithm:

build/app/mdckp-cli/mdckp-cli < data/input_test_1

Tested on Ubuntu 19.10 CMake version 3.13.4.

Example:

• Test it with:

build/app/mdckp-cli/mdckp-cli < data/input_test_2

It should print:

71
1 5 9 13
2 3 4
0 12
6 7 10

See output format for more details.

For the source of this example, look at examples/mdckp.cpp.

Input and output file formats

Input format

N M
c1 c2 c3 ... cm
p1 w1
p2 w2
...
pn wn
e11 e12
e21 e22
...

where:

N = number of items
M = number of knapsacks
pi = profit of item i
wi = weight of item i
cj = capacity of knapsack j
ex ey = pair of items id that are not compatible

• Example (data/input_test_1):

2 1
10
20 5
10 5
0 1

• There are 2 items and 1 knapsack
• The knapsack has capacity 10
• item 0 has profit 20 and weight 5
• item 1 has profit 10 and weight 5
• item 0 and item 1 are incompatible.

Output format

S
x11 x21 ...
...
x1m x2m ...

where:

S = total score
x1j x2j ... = ids of items assigned to knapsack j

• Example:

20
0

• The total profit of the following assignment is 20;
• To the first knapsack (knapsack 0) has been assigned the item 0

Try it out:

/build/app/mdckp-cli/mdckp-cli < data/input_test_1