# Tag Info

### Can you generate random linear programming problems?

Sure, of course you can create random linear programming problems. Why not? Yes, in general, you can usually verify the solution to a linear programming problem faster than you can find the solution....
Accepted

### Are some Integer programming formulations completely useless for relaxation?

Yes, some IP formulations are less useful than others. The technique used to show that an LP relaxation can only be so good is showing integrality gaps. For a minimization problem, an integrality gap ...
Accepted

### Why can't we round results of linear programming to get integer programming?

If there are only constraints that place a lower bound on the number of trucks, but no constraints that place an upper limit on the number of trucks, then of course you can round up. That will still ...
Accepted

### Finding a minimal width strip which encloses a set of points in the plane

Take the convex hull of your set of points. Then use "rotating calipers" to find the optimal strip. What is needed here to make this work is a lemma that characterizes a potentially optimal solution: ...
Accepted

### Converting If-else condition to Linear Programming

This can be expressed with just the equation $X=Y$. Since $X,Y$ are zero-or-one variables, the only possible assignments that are consistent with your condition are $X=Y=0$ and $X=Y=1$. See Express ...

### Why does this not prove $P\neq NP$?

What you're proposing isn't "a linear program for TSP", so it doesn't come into the scope of the proof. You've observed that, if $\mathrm{P=NP}$, then TSP can be reduced to polynomial-sized linear ...
Accepted

### Fractional vertex cover number may not be feasible? Very confusing!

The linear program defining the minimum fractional vertex cover always has an optimal solution. The fact that some linear programs are infeasible or unbounded doesn’t mean that every linear program is ...
Accepted

### Reducing linear programming to positive linear programming

You can add a variable $y$ and a linear equality $y=c^Tx+c_0$ for some $c_0$. Then, the original problem is equivalent to maximizing $y$ in the new system. Except for the condition $y\geq 0$. That ...