# Questions tagged [integrality-gap]

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### Greedy vs LP Approximation

I wanted to know whether Greedy approximation algorithms can outperform LP relaxation and rounding based algorithms. Specifically, can it beat the integrality gap of a 'reasonable' LP relaxation, (e.g....
135 views

### Exactly solvable but non-trivial integrality gap

Are there interesting polynomial time solvable problems that we know of for which the natural convex relaxation has a non-trivial integrality gap? Note: Maximum matching doesn't qualify because I ...
1k views

### Difference between Multiple Knapsack problem and Multidimensional Knapsack Problem

What is the difference between Multiple Knapsack problem and Multidimensional Knapsack Problem? (http://en.wikipedia.org/wiki/List_of_knapsack_problems#Multiple_constraints) According to the ...
262 views

### What does “no integrality gap” imply?

I'm currently working on a linear time heuristic for the rectangle decomposition of a binary matrix. This problem has a polynomial time solution, which in our case is too slow for large-scale ...
850 views

### Does zero integrality gap imply zero duality gap for certain problems?

We know that if the gap between the values of an integer program and its dual (the "duality gap") is zero, then the linear programming relaxations of the integer program and the dual of the relaxation,...
1k views

### Max-cut via linear programming or sdp

I am looking for a linear programming formulation for the max-cut problem. My interest is to know about the primal - dual algorithm for max-cut. It would be nice if someone can tell me that what is ...
867 views

### Why is Metric TSP's best possible achieved approximation ratio believed to be 4/3?

Is it just that integrality gaps (LP/IP) for specific instances do not give more than 4/3? Thanks in priori.
1k views

### Integrality gap and approximation ratio

When we consider an approximation algorithm for a minimization problem, the integrality gap of an IP formulation for this problem gives a lower bound of an approximation ratio for certain class of ...
817 views

### Which Integer Linear Programs are easy?

While trying to solve a problem, I ended up expressing part of it as the following integer linear program. Here $\ell,m,n_{1},n_{2},\ldots,n_{\ell},c_{1},c_{2},\ldots,c_{m},w$ are all positive ...