Abstract:
This paper deals with sorting a list of items. Sorting within a linear time is always desirable. We have many sorting algorithms. But the complexities of almost all of them are not linear. Here we have proposed a sorting algorithm named K-Index-Sort whose time complexity is O(n). We have used a temporary character array that will hold a track character against every input number. This is an interesting thing of that method as the input list is being sorted with the help of a character array. For every input k, a track symbol (like ‘-‘, ‘$`, ‘#`, any symbol) is placed to that character array to an index of k. After collecting the index numbers sequentially from that where the track symbol is residing we will get sorted list. Distinct integer numbers are a prerequisite of that algorithm. This algorithm will perform better performance for k=O(n) where k is the maximum number and n is the number of input items.

Abstract:
The index map after vector quantization has a strong statistical correlation.That means the neighboring indices are the same or the offset between them is very small.Codebook sorting can,according to some criteria,enhance the correlation among neighboring indices.Based on the squared Euclidean distance between code words,a new codebook sorting method is proposed.Compared with the conventional mean-ordered codebook,the distance-ordered codebook has a much higher correlations between neighboring indices and the offset become even smaller.As a result,distance-ordered codebook can also significantly improve the compression efficiency of the AICS (adaptive index coding scheme) algorithm.

Abstract:
In a totally ordered set the notion of sorting a finite sequence is defined through a suitable permutation of the sequence's indices. In this paper we prove a simple formula that explicitly describes how the elements of a sequence are related to those of its sorted counterpart. As this formula relies only on the minimum and maximum functions we use it to define the notion of sorting for lattices. A major difference of sorting in lattices is that it does not guarantee that sequence elements are only rearranged. However, we can show that other fundamental properties that are associated with sorting are preserved.

Abstract:
A kind of heap sorting method based on array sorting was proposed. Some advantages and disadvantages of it were discussed. It was compared with the traditional method of direct application. In the method, the ordered keywords in the array are put into the heap one by one after building an empty heap. This method needs relatively less space and is fit for ordered sequence.

Abstract:
A common query against large protein and gene sequence data sets is to locate targets that are similar to an input query sequence.The current set popular search tools,such as BLAST,employ heuristics to improve the speed of such searches.However,such heuristics can sometimes miss targets,which in many cases is undesirable.The alterna- tive to BLAST is to use an accurate algorithm,Such as Smith-Waterman(S-W) algorithm.However,these accurate al- gorithms are computationaUy very expensive.Recently,a new technique,OASIS,has been proposed to improve the ef- ficiency and accuracy by employing dynamical programming during traversing suffix tree and its speed is comparable to BLAST.But its main drawback is too much memory consuming.We propose an efficient and accurate algorithm for lo- cally aligning genome sequences.We construct a block sorting index structure for the large sequence.The index struc- ture is less than the suffix tree index and can be fit for large data size.Experimental results show that our algorithm has better performance than OASIS.

Abstract:
Chemical analysis of acid-insoluble fractions in loess and paleosols shows that concentrations of Fe and Mg were under control of wind sorting and post-depositional weathering-pedogenesis. The former caused Fe and Mg concentrated in the finer grain-size fractions, displaying synchronous variations, while the latter made Fe and Mg separated, leading to Fe retained in the weathered section and Mg leached out. Therefore, Fe/Mg ratios in the acid insoluble fraction of loess and paleosols can eliminate the effect of wind sorting and serve as an excellent proxy record on intensity of weathering-pedogenesis. Based on calculation, leaching percentage of Mg in the paleosol S1 from the Luochuan, Xifeng and Huanxian sections is 15%, 11% and 2%, respectively, and on average 9% for the paleosols S2–S14 from the Luochuan section, with the highest value amounting to 22% in S5-1, suggesting the strongest weathering-pedogenesis.

Abstract:
Previous compact representations of permutations have focused on adding a small index on top of the plain data $<\pi(1), \pi(2),...\pi(n)>$, in order to efficiently support the application of the inverse or the iterated permutation. In this paper we initiate the study of techniques that exploit the compressibility of the data itself, while retaining efficient computation of $\pi(i)$ and its inverse. In particular, we focus on exploiting {\em runs}, which are subsets (contiguous or not) of the domain where the permutation is monotonic. Several variants of those types of runs arise in real applications such as inverted indexes and suffix arrays. Furthermore, our improved results on compressed data structures for permutations also yield better adaptive sorting algorithms.

Abstract:
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 $n\geq 5$.

Abstract:
The objective of this paper is to review the folklore knowledge seen in research work devoted on synthesis, optimization, and effectiveness of various sorting algorithms. We will examine sorting algorithms in the folklore lines and try to discover the tradeoffs between folklore and theorems. Finally, the folklore knowledge on complexity values of the sorting algorithms will be considered, verified and subsequently converged in to theorems.

Abstract:
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors and applied problems with data streams, sorting changed its face. This changes and generalizations are the subject of investigation in the research below.