Book Chapter10.1007/978-3-642-40273-9_12
On Generalized Comparison-Based Sorting Problems
Jean Cardinal,Samuel Fiorini +1 more
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TL;DR: Recent algorithms for partial order production and sorting under partial information are outlined and the complementarity of the two problems is emphasized and the common aspects of the algorithms are emphasized.
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Abstract: We survey recent results on comparison-based sorting problems involving partial orders. In particular, we outline recent algorithms for partial order production and sorting under partial information. We emphasize the complementarity of the two problems and the common aspects of the algorithms. We also include open questions on two other related problems, namely partial order identification and sorting with forbidden comparisons.
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Citations
Sorting under Forbidden Comparisons
Indranil Banerjee,Dana Richards +1 more
- 01 Jan 2016
TL;DR: This paper proposes the first non-trivial deterministic algorithm which makes O((q + n)*log(n)) comparisons with a total complexity of O(n^2 + q^(omega/2)), where omega is the exponent in the complexity of matrix multiplication.
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Efficient Algorithms for Sorting in Trees
Jishnu Roychoudhury,Jatin Yadav +1 more
TL;DR: This work considers the problem of sorting in trees, a particular case of partial orders, and parametrize the complexity with respect to d, the maximum degree of an element in the tree, as d is usually much smaller than w in trees.
2
Universal Sorting: Finding a DAG using Priced Comparisons
Mayank Goswami,Riko Jacob +1 more
TL;DR: In this paper , Huang et al. gave a randomized algorithm with a O( polylog n ) competitive ratio for the generalized sorting problem with priced information, which is the first algorithm with competitive ratio lower bound for generalized sorting.
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•Posted Content
Information-theoretic lower bounds for quantum sorting.
TL;DR: It is proved that the quantum query complexity of sorting under partial information is not asymptotically smaller than the classical information-theoretic lower bound, and this holds for a wide class of partially ordered sets.
Selecting Multiple Order Statistics with a Graphics Processing Unit
Jeffrey D. Blanchard,Erik Opavsky,Emircan Uysaler +2 more
- 20 Jul 2016
TL;DR: An algorithm, bucketMultiSelect, for simultaneously selecting multiple order statistics with a graphics processing unit (GPU), which significantly reduces computation time by eliminating a large portion of the unnecessary operations involved in sorting.
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Graham Brightwell,Peter Winkler +1 more
TL;DR: The problem of counting the number of linear extensions of a partially ordered set is #P-complete as discussed by the authors, which is the state-of-the-art algorithm for this problem.
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How good is the information theory bound in sorting
TL;DR: If X and Y are n element sets of real numbers, then the n 2 element set X + Y can be sorted with O ( n 2 ) comparisons, improving upon the n2 log 2 n bound established by Harper et al.
215
Entropy splitting for antiblocking corners and -perfect graphs
TL;DR: Pairs of convex sets A, B in thek-dimensional space with the property that every probability distribution has a repsesentationpi=al.bi, a∃A, b∃B are characterized, closely related to a new entropy concept.
Entropy and sorting
Jeff Kahn,Jeong Han Kim +1 more
- 01 Jul 1992
TL;DR: The old problem of sorting under partial information is reconsidered, and polynomial time algorithms for the following tasks are given, based on entropy of the comparability graph of P and convex minimization via the ellipsoid method.
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