# The Hardness of Approximating Poset Dimension

@article{Hegde2007TheHO, title={The Hardness of Approximating Poset Dimension}, author={Rajneesh Hegde and Kamal Jain}, journal={Electronic Notes in Discrete Mathematics}, year={2007}, volume={29}, pages={435-443} }

- Published 2007 in Electronic Notes in Discrete Mathematics
DOI:10.1016/j.endm.2007.07.084

The dimension of a partially ordered set (poset) is the minimum integer k such that the partial order can be expressed as the intersection of k total orders. We prove that there exists no polynomial-time algorithm to approximate the dimension of a poset on N elements with a factor of O(N0.5− ) for any > 0, unless NP = ZPP. The same hardness of approximation holds for the fractional version of poset dimension, which was not even known to be NP-hard.

#### Citations

##### Publications citing this paper.

Showing 1-10 of 19 extracted citations

## Graph Products Revisited: Tight Approximation Hardness of Induced Matching, Poset Dimension and More

View 6 Excerpts

Highly Influenced

## Boxicity and Poset Dimension

View 3 Excerpts

Highly Influenced

## The Hardness of Approximating the Threshold Dimension , Boxicity and Cubicity of a Graph

View 5 Excerpts

Highly Influenced

## Dimension Preserving Contractions and a Finite List of 3-Irreducible Posets

View 3 Excerpts

Highly Influenced

## Hitting Families of Schedules for Asynchronous Programs

View 2 Excerpts

## Succinct Posets

View 1 Excerpt

#### References

##### Publications referenced by this paper.

Showing 1-10 of 19 references

## Dimension, Graph and Hypergraph Coloring

View 1 Excerpt

## Zero Knowledge and the Chromatic Number

View 1 Excerpt

## Partial orders

## On the hardness of approximating minimization problems

View 1 Excerpt

## Brightwell and Edward R . Scheinerman . Fractional dimension of partial orders

## Combinatorics and partially ordered sets. Johns Hopkins Series in the Mathematical Sciences

View 1 Excerpt

## Fractional dimension of partial orders

View 2 Excerpts