Berge Sorting

In 1966, Claude Berge proposed the following sorting problem. Given a string of $n$ alternating white and black pegs on a one-dimensional board consisting of an unlimited number of empty holes, rearrange the pegs into a string consisting of $\lceil\frac{n}{2}\rceil$ white pegs followed immediately by $\lfloor\frac{n}{2}\rfloor$ black pegs (or vice versa) using only moves which take 2 adjacent pegs to 2 vacant adjacent holes. Avis and Deza proved that the alternating string can be sorted in $\lceil\frac{n}{2}\rceil$ such {\em Berge 2-moves} for $n\geq 5$. Extending Berge's original problem, we consider the same sorting problem using {\em Berge $k$-moves}, i.e., moves which take $k$ adjacent pegs to $k$ vacant adjacent holes. We prove that the alternating string can be sorted in $\lceil\frac{n}{2}\rceil$ Berge 3-moves for $n\not\equiv 0\pmod{4}$ and in $\lceil\frac{n}{2}\rceil+1$ Berge 3-moves for $n\equiv 0\pmod{4}$, for $n\geq 5$. In general, we conjecture that, for any $k$ and large enough $n$, the alternating string can be sorted in $\lceil\frac{n}{2}\rceil$ Berge $k$-moves. This estimate is tight as $\lceil\frac{n}{2}\rceil$ is a lower bound for the minimum number of required Berge $k$-moves for $k\geq 2$ and $n\geq 5$.Comment: 10 pages, 2 figure

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

Fish sorting assessments of Clarias gariepinus fingerlings raised in fish tanks

Fish sorting assessments of Clarias gariepinus fingerlings stocked and raised in fish tanks were undertaken for a 6-month culture period: Sorting was undertaken from the first, second, and third months of stocking the fish fingerlings while the control was not sorted at all. The sorting assessments revealed that the twice sorting of fish fingerlings stocked with a Marginal Rate of Return (MRR) of 3.44 was significantly different (p>0.05) from those sorted once with MRR of 0.912, and three times with MRR of 2.65 respectively, thus making twice sorting most advisable for fish farmers utilizing Clarias gariepinus fingerlings for tank aquacultur

Sorting networks implemented as νMOS circuits

A new realisation for n-input sorters is presented. Resorting to the neuron-MOS (νMOS) concept and to an adequate electrical scheme, a compact and efficient implementation is obtained.Comisión Interministerial de Ciencia y Tecnología TIC95-0094, TIC97-064