Discrete & Computational Geometry
Fredman-Kolmo´s bounds and information theory
SIAM Journal on Algebraic and Discrete Methods
New bounds for perfect hashing via information theory
European Journal of Combinatorics
Optimal separations between concurrent-write parallel machines
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
A random polynomial time algorithm for approximating the volume of convex bodies
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
On Assigning Prefix Free Codes to the Vertices of a Graph
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Recovering Set Systems and Graph Entropy
Combinatorics, Probability and Computing
Sorting and selection in posets
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Fundamenta Informaticae
Characterizing isometries on the order polytope with an application to the theory of fuzzy measures
Information Sciences: an International Journal
Adjacency on the order polytope with applications to the theory of fuzzy measures
Fuzzy Sets and Systems
Sorting and Selection in Posets
SIAM Journal on Computing
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Fundamenta Informaticae
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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 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 &OHgr;(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 nn/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.