361,065 research outputs found
Twenty-Five Comparators is Optimal when Sorting Nine Inputs (and Twenty-Nine for Ten)
This paper describes a computer-assisted non-existence proof of nine-input
sorting networks consisting of 24 comparators, hence showing that the
25-comparator sorting network found by Floyd in 1964 is optimal. As a
corollary, we obtain that the 29-comparator network found by Waksman in 1969 is
optimal when sorting ten inputs.
This closes the two smallest open instances of the optimal size sorting
network problem, which have been open since the results of Floyd and Knuth from
1966 proving optimality for sorting networks of up to eight inputs.
The proof involves a combination of two methodologies: one based on
exploiting the abundance of symmetries in sorting networks, and the other,
based on an encoding of the problem to that of satisfiability of propositional
logic. We illustrate that, while each of these can single handed solve smaller
instances of the problem, it is their combination which leads to an efficient
solution for nine inputs.Comment: 18 page
The case for absolute ligand discrimination : modeling information processing and decision by immune T cells
Some cells have to take decision based on the quality of surroundings
ligands, almost irrespective of their quantity, a problem we name "absolute
discrimination". An example of absolute discrimination is recognition of
not-self by immune T Cells. We show how the problem of absolute discrimination
can be solved by a process called "adaptive sorting". We review several
implementations of adaptive sorting, as well as its generic properties such as
antagonism. We show how kinetic proofreading with negative feedback implements
an approximate version of adaptive sorting in the immune context. Finally, we
revisit the decision problem at the cell population level, showing how
phenotypic variability and feedbacks between population and single cells are
crucial for proper decision
An In-Place Sorting with O(n log n) Comparisons and O(n) Moves
We present the first in-place algorithm for sorting an array of size n that
performs, in the worst case, at most O(n log n) element comparisons and O(n)
element transports.
This solves a long-standing open problem, stated explicitly, e.g., in [J.I.
Munro and V. Raman, Sorting with minimum data movement, J. Algorithms, 13,
374-93, 1992], of whether there exists a sorting algorithm that matches the
asymptotic lower bounds on all computational resources simultaneously
Analisis Faktor Penyebab Tandan Buah Segar (TBS) Busuk Dan Bahaya Kecelakaan Menggunakan Fishbone Chart (Studi Kasus Pada Bagian Sortasi di PT Sutopo Lestari Jaya)
At the PT Sutopo Lestari Jaya sorting work station it was seen that the sorting work environment had an open working environment so that when hot weather operators quickly experienced fatigue and the oil content in FFB would shrink, during the rain the work floor sorting would be slippery caused by FFB oil so makes the operator slip and the loader operator is difficult to drive then FFB quickly decays. So improvements are needed by finding the root cause of the problem experienced by using a fishbone diagram. The results obtained are that the sorting work station needs to be repaired by installing a roof in the sorting work environment. With the roof in the sorting work environment, the company can minimize the losses that occur and can eliminate the causes of problems that exist in the sorting work station
Information-theoretic lower bounds for quantum sorting
We analyze the quantum query complexity of sorting under partial information.
In this problem, we are given a partially ordered set and are asked to
identify a linear extension of using pairwise comparisons. For the standard
sorting problem, in which is empty, it is known that the quantum query
complexity is not asymptotically smaller than the classical
information-theoretic lower bound. We prove that this holds for a wide class of
partially ordered sets, thereby improving on a result from Yao (STOC'04)
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