Linked Questions

4 votes
5 answers
10k views

"Greater than" condition in integer linear program with a binary variable

How can one model the following condition in an integer linear program? $$A = \begin{cases} 1 & \text{if } B > C\\ 0 & \text{otherwise}\end{cases}$$ where $A \in \{0,1\}$ and $B, C \in \...
Salah's user avatar
  • 91
40 votes
4 answers
24k views

Why is linear programming in P but integer programming NP-hard?

Linear programming (LP) is in P and integer programming (IP) is NP-hard. But since computers can only manipulate numbers with finite precision, in practice a computer is using integers for linear ...
Sasha the Noob's user avatar
15 votes
3 answers
3k views

Cast to boolean, for integer linear programming

I want to express the following constraint, in an integer linear program: $$y = \begin{cases} 0 &\text{if } x=0\\ 1 &\text{if } x\ne 0. \end{cases}$$ I already have the integer variables $x,...
D.W.'s user avatar
  • 160k
2 votes
3 answers
249 views

Integer linear programming formulation of formula in DNF

I have multiple sets, e.g., $$\{1, 2\}, \{2, 3, 4\}, \{1, 4\}$$ Each variable $1, 2, 3, 4$ is binary. I need to represent the following condition without additional variables $$(1 \land 2) \lor (2 \...
Tom's user avatar
  • 185
14 votes
2 answers
698 views

Does every NP problem have a poly-sized ILP formulation?

Since Integer Linear Programming is NP-complete, there is a Karp reduction from any problem in NP to it. I thought this implied that there is always a polynomial-sized ILP formulation for any problem ...
andy's user avatar
  • 253

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