Mining Posets from Linear Orders
2009) Mining Posets from Linear Orders . Technical Report TR-09-16, Computer Science, Virginia Tech. (
There has been much research on the combinatorial problem of generating the linear extensions of a given poset. This paper focuses on the reverse of that problem, where the input is a set of linear orders, and the goal is to construct a poset or set of posets that generates the input. Such a problem ﬁnds applications in computational neuroscience, systems biology, paleontology, and physical plant engineering. In this paper, several algorithms are presented for efficiently ﬁnding a single poset that generates the input set of linear orders. The variation of the problem where a minimum set of posets that cover the input is also explored. It is found that the problem is polynomially solvable for one class of simple posets (kite(2) posets) but NP-complete for a related class (hammock(2,2,2) posets).
|Item Type:||Departmental Technical Report|
|Keywords:||partial orders, posets, linear extensions|
|Subjects:||Computer Science > Algorithms and Data Structure|
|Deposited By:||Administrator, Eprints|
|Deposited On:||29 July 2009|