Topic
Interval order
About: Interval order is a research topic. Over the lifetime, 301 publications have been published within this topic receiving 5188 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, it was shown that it is NP-hard to determine if a partial order has dimension 3, and several other related dimension-type problems are shown to be NP-complete.
Abstract: The dimension of a partial order P is the minimum number of linear orders whose intersection is P. There are efficient algorithms to test if a partial order has dimension 1 or 2. We prove that it is NP-complete to determine if a partial order has dimension 3. As a consequence, several other related dimension-type problems are shown to be NP-complete.
494 citations
TL;DR: This work proposes a method to build admissible orders in terms of two aggregation functions and proves that some of the most used examples of total orders that appear in the literature are specific cases of this construction.
326 citations
AT&T1
TL;DR: Two invariants of the family of interval orders that agree with an interval graph are established, namely magnitude, which affects end-point placements, and the property of having the lengths of all representing intervals between specified bounds.
275 citations
TL;DR: It is shown that the dimension of a tree is at most three and the forbidden subposet characterization of two-dimensional trees is given and given to the graph-theoretic sense.
125 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 3 |
| 2019 | 8 |
| 2018 | 2 |
| 2017 | 11 |
| 2016 | 7 |