# Entropy and Sorting Seminars/Workshops

Speaker: | Jeong Han Kim |
---|---|

Time: | 1999-10-25 10:30:00 |

Place: | Rm.1403, CS Bldg./KAIST |

### Abstract

We reconsider the old problem of sorting under partial
information, and give polynomial time algorithms for the following
tasks.

(1) Given a partial order $P$, find (adaptively) a sequence of
comparisons (questions of the form, ``is $x<y$?") which {\em
sorts} (i.e. finds an unknown linear extension of) $P$ using
$O(\log(e(P)))$ comparisons in worst case (where $e(P)$ is the
number of linear extensions of $P$).

(2) Compute (on line) answers to any comparison algorithm for
sorting a partial order $P$ which force the algorithm to use
$\Omega(\log(e(P)))$ comparisons.

(3) Given a partial order $P$ of size $n$, estimate $e(P)$ to
within a factor exponential in $n$. (We give upper and lower
bounds which differ by the factor $n^n/n!$.)

Our approach, based on entropy of the comparability graph of $P$
and convex minimization via the ellipsoid method, is completely
different from earlier attempts to deal with these questions.

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