# Recognition Algorithms for Orders of Small Width and Graphs of Small Dilworth Number

@article{Felsner2003RecognitionAF, title={Recognition Algorithms for Orders of Small Width and Graphs of Small Dilworth Number}, author={Stefan Felsner and Vijay Raghavan and Jeremy P. Spinrad}, journal={Order}, year={2003}, volume={20}, pages={351-364} }

Partially ordered sets of small width and graphs of small Dilworth number have many interesting properties and have been well studied. Here we show that recognition of such orders and graphs can be done more efficiently than by using the well-known algorithms based on bipartite matching and matrix multiplication. In particular, we show that deciding deciding if an order has width k can be done in O(kn2) time and whether a graph has Dilworth number k can be done in O(k2n2) time.For very small k…

## 56 Citations

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An algorithm based on the notion of frontier antichains, generalizing the standard notion of right-most maximum antichain of a directed acyclic graph, which is faster than all existing MPC algorithms and shows that some basic problems on DAGs get faster algorithms as immediate corollaries of this result.

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- Mathematics, Computer ScienceArXiv
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A characterization result reminiscent of the proof of Dilworth's theorem is proved, which yields as a byproduct a flow-based algorithm for computing such a minimal decomposition of sets and sequences of intervals.

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