Cost Of Sorting Research Articles

Genomic sorting with length-weighted reversals.

Current algorithmic studies of genome rearrangement ignore the length of reversals (or inversions); rather, they only count their number. We introduce a new cost model in which the lengths of the reversed sequences play a role, allowing more flexibility in accounting for mutation phenomena. Our focus is on sorting unsigned (unoriented) permutations by reversals; since this problem remains difficult (NP-hard) in our new model, the best we can hope for are approximation results. We propose an efficient, novel algorithm that takes (a monotonic function f of) length into account as an optimization criterion and study its properties. Our results include an upper bound of O(fn lg2n) for any additive cost measure f on the cost of sorting any n-element permutation, and a guaranteed approximation ratio of O(lg2n) times optimal for sorting a given permutation. Our work poses some interesting questions to both biologists and computer scientists and suggests some new bioinformatic insights that are currently being studied.

COEVOLUTIONARY EVENTS IN THE HISTORY OF ASSOCIATION BETWEEN JERBOAS (RODENTIA: DIPODIDAE) AND THEIR FLEA PARASITES

We studied historical patterns of the association between fleas and jerboas using Brooks parsimony analysis (BPA), tree reconciliation analysis, general parsimony analysis (TreeFitter), and the ParaFit method. A phylogenetic host tree reconstructed by BPA was incongruent with the known host phylogeny and most characters were homoplasious. The optimization of the recoded flea tree on the jerboa tree suggested that the common evolutionary history of fleas and jerboas was characterized mainly by inertia, host switching, and sorting events. There was a geographic pattern in parasite-based jerboa trees. Species with common geographic distribution and/or habitat preferences or common geographic origin tended to cluster together. The fit of the phylogenetic trees of jerboas and their fleas by reconciliation did not need cospeciation, but mainly suggested sorting events. Optimal reconstruction by TreeFitter revealed a significant phylogenetic effect only when the costs of host switching and linear sorting were as...

How good is the critical factor concept in estimating the average number of character comparisons per item in string sorting?

In this paper, we present a new approach for determining the cost of sorting a string item, in terms of the average number character comparisons. The approach is based on the critical factor (CF) concept which refers to the first character at which strings Si and Sj disagree. The research assumptions of the study were tested using samples from Arabic and English. The results indicate that the technique described, in this paper, to estimate the time cost of string sorting provides a measure that seems to offer figures that are closer to the real average cost than what is offered by the measures suggested before. The results also show some differences between the sorting costs of Arabic and English string objects.

On RAM Priority Queues

Priority queues are some of the most fundamental data structures. For example, they are used directly for task scheduling in operating systems. Moreover, they are essential to greedy algorithms. We study the complexity of integer priority queue operations on a RAM with arbitrary word size, modeling the possibilities in standard imperative programming languages such as C. We present exponential improvements over previous bounds, and we show tight relations to sorting. Our first result is a RAM priority queue supporting find-min in constant time and insert and delete-min in time O(log log n), where n is the current number of keys in the queue. This is an exponential improvement over the $O(\sqrt{\log n})$ bound of Fredman and Willard [ Proceedings of the 22nd ACM Symposium on the Theory of Computing, Baltimore, MD, pp. 1--7]. Plugging this priority queue into Dijkstra's algorithm gives an O(mlog log m) algorithm for the single source shortest path problem on a graph with m edges, as compared with the previous $O(m\sqrt{\log m})$ bound based on Fredman and Willard's priority queue. The above bounds assume $O(n 2^{{\varepsilon} w})$ space, where w is the word length and ${\varepsilon}>0$. They can, however, be achieved in linear space using randomized hashing. Our second result is a general equivalence between sorting and priority queues. A priority queue is monotone if the minimum is nondecreasing over time, as in many greedy algorithms. We show that on a RAM, the amortized operation cost of a monotone priority queue is equivalent to the per-key cost of sorting. For example, the equivalence implies that the single source shortest paths problem on a graph with m edges is no harder than that of sorting m keys. With the current RAM sorting, this gives an O(m log log m) time bound, as above, but the relation holds regardless of the future developments in RAM sorting. From the equivalence result, for any fixed ${\varepsilon}>0$, we derive a randomized monotone $O(\sqrt{\log n}^{1+{\varepsilon}})$ priority queue with expected constant time decrease-key. Plugging this into Dijkstra's algorithm gives an $O(n\sqrt{\log n}^{1+{\varepsilon}}+m)$ algorithm for the single source shortest path problem on a graph with n nodes and m edges, complementing the above O(mlog log m) algorithm if $m\gg n$. This improves the O(nlog n/log log n + m) bound by Fredman and Willard [Proceedings of the 31st IEEE Symposium on the Foundations of Computer Science, St. Louis, MO, 1990, pp. 719--725], based on their O(log n/log log n) priority queue with constant decrease-key.

Suffix Trees on Words

We discuss an intrinsic generalization of the suffix tree, designed to index a string of length n which has a natural partitioning into m multicharacter substrings or words . This word suffix tree represents only the m suffixes that start at word boundaries. These boundaries are determined by delimiters , whose definition depends on the application. Since traditional suffix tree construction algorithms rely heavily on the fact that all suffixes are inserted, construction of a word suffix tree is nontrivial, in particular when only O(m) construction space is allowed. We solve this problem, presenting an algorithm with O(n) expected running time. In general, construction cost is Ω(n) due to the need of scanning the entire input. In applications that require strict node ordering, an additional cost of sorting O(m') characters arises, where m' is the number of distinct words. In either case, this is a significant improvement over previously known solutions. Furthermore, when the alphabet is small, we may assume that the n characters in the input string occupy o(n) machine words. We illustrate that this can allow a word suffix tree to be built in sublinear time.

Associative random access machines and data-parallel multiway binary-search join

Rapid advances in semiconductor technology have made it possible to build massively parallel processors. In addition, optical 3D storage and optical interconnections open a new opportunity due to inherent massive parallelism and non-interference of light beams. The approaches used in current parallel database research cannot take advantage of massive parallelism which can be provided by the emerging technologies, due to speedup and scaleup limitations. In this paper, we present a computational paradigm for database machines which takes advantage of the opening opportunity for massive parallelism and discuss the validity and feasibility of the paradigm. The approach we take is based on associative computing and fine grained data parallelism which allow unlimited speedup and scaleup. Additionally, an asymptotically fast data-parallel join algorithm, which can efficiently deal with the joins in which multiple relations share a common join field, is presented. The algorithm is based on parallel sorting and parallel binary search, and performs a multiway join in O( Σs + Σ log r) where s is the cost of sorting an intermediate relation and r is the size of an input relation. The cost s of sorting is kept minimum by the algorithm.

Optimal Clustering of Relations to Improve Sorting and Partitioning for Joins

The sorting or partitioning of relations is very common in relational database systems. Implementations of the join operation include the sort-merge join algorithm, which sorts both relations, and the hash join algorithm, which usually partitions both relations. We describe how clustering records using an optimal multi-attribute hash (MAH) file, taking the query pattern and distribution into account, reduces the average cost of sorting or partitioning. We demonstrate that maintaining multiple copies of a data file, each with a different clustering organization, further reduces the average cost of sorting or partitioning. We describe an inexpensive method for determining a good partitioning index (MAH file organization). Our analysis and experiments show that the partitioning indexes we find are usually optimal and can often partition a relation more than ten times faster than by not using any clustering. We also show that a significant change in the query pattern or distribution is required before a reorganization of a data file is necessary, and that such a reorganization is, in general, an inexpensive operation.

Yield strength of low-density polyethylene-polypropylene blends

Polymer waste recycling is becoming a major problem, because huge amounts of synthetic polymers are manufactured every year for many different purposes. Polymer scraps are gathered from the Municipal Solid Waste (MSW). Within those wastes there are several different polyolefins—such as polyethylene, polypropylene, and polystyrene—all incompatible with each other. In order to recycle these polymers, compatibilization of these polyolefins is needed to avoid high sorting costs and unacceptably low market-value products. In this work, the compatibilization of low-density polyethylene with polypropylene is accomplished through the addition of maleated polyethylene and maleated polypropylene. Prediction of the tensile properties of these blends is attempted, using a model based on continuity of phases in a two-components mixture of thermoplastics. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 275–281, 1997

An Economic Analysis of Highgrading in ITQ Fisheries Regulation Programs

ITQ management programs can provide incentives to discard low valued fish so that individual quota can be used for relatively more valuable fish. Such can also occur where there are other constraints on harvest, such as hold capacity. This paper compares and contrasts the exact conditions under which highgrading will occur with ITQ and other harvest constraints. Considering all costs, highgrading can be efficient with physical constraints but it is an unfortunate artifact of ITQs. Whether or not highgrading will occur depends upon the price differential between high and low valued fish, the cost of sorting and discarding and the cost of re-harvest. Policies for correcting or reducing ITQ highgrading should it occur, are described.

Separation technology of used polymers

The technology of separating plastics from the municipal waste stream for reuse is reviewed, with emphasis on the key role played by the bottle sorting step. Experience gained in the first year's operation of two large commercial recycling plants provides a better understanding of practical problems encountered, their relative importance, and technical advances needed for improved operation. It is concluded that purity of feedstock and processing rate are two critical independent variables requiring technical and business understanding and management. Hypothetical examples illustrate the interplay of these with dependent variables of yield and sorting cost.

Two levels are as good as any

The asymptotic expected efficiency of distributive sorting is studied showing that for “smooth” key distributions it suffices to consider 2-level methods. The expected cost of sorting n such keys satisfies asymptotically: C( n) ⩽ Kn, where K does not depend on the distribution.

Why sort-merge gives the best implementation of the natural join

To join two relations efficiently, they must not only be clustered but mutually clustered . Sorting is the only known way to achieve mutual clustering. Once the relations are sorted, merging is the obvious way to implement the join. If the relations are known to be sorted appropriately, the most costly part of the process can be omitted. To know that a relation is sorted already, it is best to remember that we sorted it. Otherwise detecting that the relation is sorted requires inspection of each tuple, a cost comparable in many cases to the cost of sorting. Detecting any other form of mutual clustering is bound to be a combinatorial process of much greater cost than sorting. Cheaper forms of detection may be possible using sampling, but these are heuristics at best and there is no reliable foundation for them.It is assumed that the sizes of the relations are large compared with the RAM memory available or, equivalently, compared with the number of processors available. Our conclusion that sort-merge is best is thus applicable to single-processor computers or to multiple-processor database machines. Discussing the cost of joining relations without making this assumption is outside the subject of databases.

INFORMATIONAL ASYMMETRIES, FINANCIAL STRUCTURE, AND FINANCIAL INTERMEDIATION

NUMEROUS MARKETS ARE characterized by informational differences between buyers and sellers. In financial markets, informational asymmetries are particularly pronounced. Borrowers typically know their collateral, industriousness, and moral rectitude better than do lenders; entrepreneurs possess "inside" information about their own projects for which they seek financing. Lenders would benefit from knowing the true characteristics of borrowers. But moral hazard hampers the direct transfer of information between market participants. Borrowers cannot be expected to be entirely straightforward about their characteristics, nor entrepreneurs about their projects, since there may be substantial rewards for exaggerating positive qualities. And verification of true characteristics by outside parties may be costly or impossible. Without information transfer, markets may perform poorly. Consider the financing of projects whose quality is highly variable. While entrepreneurs know the quality of their own projects, lenders cannot distinguish among them. Market value, therefore, must reflect average project quality. If the market were to place an average value greater than average cost on projects, the potential supply of low quality projects may be very large, since entrepreneurs could foist these upon an uninformed market (retaining little or no equity) and make a sure profit. But this argues that the average quality is likely to be low, with the consequence that even projects which are known (by the entrepreneur) to merit financing cannot be undertaken because of the high cost of capital resulting from low average project quality. Thus, where substantial information asymmetries exist and where the supply of poor projects is large relative to the supply of good projects, venture capital markets may fail to exist. For projects of good quality to be financed, information transfer must occur. We have argued that moral hazard prevents direct information transfer. Nonetheless, information on project quality may be transferred if the actions of entrepreneurs ("which speak louder than words") can be observed. One such action, observable because of disclosure rules, is the willingness of the person(s) with inside information to invest in the project or firm. This willingness to invest may serve as a signal to the lending market of the true quality of the project; lenders will place a value

Reducing Letter Delays in Post Offices

This paper reports a number of mathematical models and experiments that have been designed for the analysis and evaluation of delays of first-class letter mail in a post office. The flow pattern of mail consists of a number of serial and parallel processing stages. A letter takes a particular path through this flow network, which depends on its final destination, consequently, the delay of letter mail depends on its address as well as the inventories of other mail and the processing rates met enroute. While mail flow into a post office may contain many random elements, it is generally the case that input rates are predictable and strongly time-dependent. Scheduling policies must take into account the peak flows that temporarily exceed available processing rates and, in addition, must observe certain specified restrictions on the cost of processing, sorting, and storage operations. The effect of various transportation facilities between processing stages and from one post office to another must also be considered. The mathematical analysis deals with the minimization of letter delay through a network of processing and storage stages where there are capacity restrictions on individual and/or serial and parallel stage combinations. Analytical and graphical procedures are developed and numerical results are reported. The paper also reports a series of full-scale experiments performed at one of the larger United States Post Offices where theoretical procedures and decision rules were applied and tested. Delay reductions for first-class letter mail are believed to be of the order of 25 per cent.

Mechanical sorting of cinchona seeds.

Tests have shown that the usual method of sorting cinchona seed by hand in transmitted light is unreliable. A machine constructed for winnowing the seed in a slow current of air proved quite satisfactory. A good correlation was obtained between number of seeds per gram and germination capacity of the winnowed seed. The cost of mechanical sorting was very much lower than that of hand sorting and the percentage of good seed to waste seed was considerably higher.-W. Java exp. Stat., Buitenzorg. (Abstract retrieved from CAB Abstracts by CABI’s permission)