Showing papers on "Sorting published in 1996"

Genome Rearrangements and Sorting by Reversals

Abstract: Sequence comparison in molecular biology is in the beginning of a major paradigm shift---a shift from gene comparison based on local mutations (i.e., insertions, deletions, and substitutions of nucleotides) to chromosome comparison based on global rearrangements (i.e., inversions and transpositions of fragments). The classical methods of sequence comparison do not work for global rearrangements, and little is known in computer science about the edit distance between sequences if global rearrangements are allowed. In the simplest form, the problem of gene rearrangements corresponds to sorting by reversals, i.e., sorting of an array using reversals of arbitrary fragments. Recently, Kececioglu and Sankoff gave the first approximation algorithm for sorting by reversals with guaranteed error bound 2 and identified open problems related to chromosome rearrangements. One of these problems is Gollan's conjecture on the reversal diameter of the symmetric group. This paper proves the conjecture. Further, the problem of expected reversal distance between two random permutations is investigated. The reversal distance between two random permutations is shown to be very close to the reversal diameter, thereby indicating that reversal distance provides a good separation between related and nonrelated sequences in molecular evolution studies. The gene rearrangement problem forces us to consider reversals of signed permutations, as the genes in DNA could be positively or negatively oriented. An approximation algorithm for signed permutation is presented, which provides a performance guarantee of ${3 \over 2}$. Finally, using the signed permutations approach, an approximation algorithm for sorting by reversals is described which achieves a performance guarantee of ${7 \over 4}$.

How Much Does Sorting Increase Inequality

Abstract: Social commentators from William Julius Wilson to Charles Murray have argued that increased sorting people into internally homogeneous neighborhoods, schools, and marriages is spurring long- run inequality. Calibration of a formal model suggests that these fears are misplaced.

Filtered document retrieval with frequency-sorted indexes

Abstract: Ranking techniques are effective at finding answers in document collections but can be expensive to evaluate. We propose an evaluation technique that uses early recognition of which documents are likely to be highly ranked to reduce costs ; for our test data, queries are evaluated in 2% of the memory of the standard implementation without degradation in retrieval effectiveness. Cpu time and disk traffic can also be dramatically reduced by designing inverted indexes explicitly to support the technique. The principle of the index design is that inverted lists are sorted by decreasing within-document frequency rather than by document number, and this method experimentally reduces cpu time and disk traffic to around one third of the original requirement. We also show that frequency sorting can lead to a net reduction in index size, regardless of whether the index is compressed.

System and method for reading package information

Abstract: A system for reading package information includes an imaging system and a label decoding system. The imaging system captures an image of a package surface that includes a machine readable code such as a bar code and an alphanumeric destination address. The label decoding system locates and decodes the machine readable code and uses OCR techniques to read the destination address. The destination address is validated by comparing the decoded address to a database of valid addresses. If the decoded address is invalid, an image of the destination address is displayed on a workstation and an operator enters the correct address. The system forms a unified package record by combining the decoded bar code data and the correct destination address data. The unified package record is used for subsequently sorting and tracking the package and is stored in a database and applied to a label that is affixed to the package.

Fast Sorting by Reversal

Abstract: Analysis of genomes evolving by inversions leads to a combinatorial problem of sorting by reversals studied in detail recently. Following a series of work recently, Hannenhalli and Pevzner developed the first polynomial algorithm for the problem of sorting signed permutations by reversals and proposed an O(n4) implementation of the algorithm. In this paper we exploit a few combinatorial properties of the cycle graph of a permutation and propose an O(n2α(n)) implementation of the algorithm where α is the inverse Ackerman function. Besides making this algorithm practical, our technique improves implementations of the other rearrangement distance problems.

Improved algorithms and data structures for solving graph problems in external memory

Abstract: Recently, the study of I/O-efficient algorithms has moved beyond fundamental problems of sorting and permuting and into wider areas such as computational geometry and graph algorithms. With this expansion has come a need for new algorithmic techniques and data structures. In this paper, we present I/O-efficient analogues of well-known data structures that we show to be useful for obtaining simpler and improved algorithms for several graph problems. Our results include improved algorithms for minimum spanning trees, breadth-first search, and single-source shortest paths. The descriptions of these algorithms are greatly simplified by their use of well-defined I/O-efficient data structures with good amortized performance bounds. We expect that I/O efficient data structures such as these will be a useful tool for the design-of I/O-efficient algorithms.

Method and apparatus for span and subspan sorting rendering system

Abstract: The invention provides for a data shifting capability that permits sorting the data in addition to searching for obtaining real-time performance in color, with high quality imagery through a simple search of a spatial database based on a rectangularly shaped search region or range search (fig. 13). A sorting Magnitude Comparison Content Addressable Memory (SMCCAM) performs a range search, introducing a conservative approximation of the ideal Occluding Region, and provides a MCCAM wherein the data words stored in the fields is shifted to corresponding fields in an adjacent word, based on the magnitude comparisons (fig. 7). The 3D graphics method stores the parameters of a polygon span in a spatial database (804-814) and a query operation is performed on the database to determine which of those spans, or portions of spans, are visible (816 and 818), and applies a rule for comparing new span portion to an old span portion on a subspan-by-subspan basis, thereby providing additional polygon edge information within a raster line, providing anti-aliasing.

Fundamental techniques for order optimization

Abstract: Decision support applications are growing in popularity as more business data is kept on-line. Such applications typically include complex SQL queries that can test a query optimizer's ability to produce an efficient access plan. Many access plan strategies exploit the physical ordering of data provided by indexes or sorting. Sorting is an expensive operation, however. Therefore, it is imperative that sorting is optimized in some way or avoided all together. Toward that goal, this paper describes novel optimization techniques for pushing down sorts in joins, minimizing the number of sorting columns, and detecting when sorting can be avoided because of predicates, keys, or indexes. A set of fundamental operations is described that provide the foundation for implementing such techniques. The operations exploit data properties that arise from predicate application, uniqueness, and functional dependencies. These operations and techniques have been implemented in IBM's DB2/CS.

Faster deterministic sorting and searching in linear space

Abstract: We present a significant improvement on linear space deterministic sorting and searching. On a unit-cost RAM with word size w, an ordered set of n w-bit keys (viewed as binary strings or integers) can be maintained in O(min{[/spl radic/(logn)][logn/logw+loglogn][logwloglogn]}) time per operation, including insert, delete, member search, and neighbour search. The cost for searching is worst-case while the cost for updates is amortized. As an application, n keys can be sorted in linear at O(n/spl radic/(logn)) worst-case cost. The best previous method for deterministic sorting and searching in linear space has been the fusion trees which supports updates and queries in O(logn/loglogn) amortized time and sorting in O(nlogn/loglogn) worst-case time. We also make two minor observations on adapting our data structure to the input distribution and on the complexity of perfect hashing.

A high speed mass flow food sorting apparatus for optically inspecting and sorting bulk food products

Abstract: A high speed mass flow food sorting apparatus (10) and method comprises a product conveyor (12) for receiving and conveying a laterally-distributed stream of bulk food articles (14) past a product diverter (72). A camera (28) is positioned to view the stream of food articles upstream of a product diverter (72). A sorting system downstream of a camera (28) including a product diverter (72) is configured to divert undesirable product in response to optically detected undesirable characteristics pursuant to an automated control system. The automated control system connects to the optical inspection system and the sorting system and includes an operator control console. Preferably, the operator control console displays a graphical user interface (32) via a computer (27) on which the control system is implemented and includes a software application pack (30) specifically configured for processing a particular type of food article having corresponding desirable features.

Query execution techniques for caching expensive methods

Abstract: Object-Relational and Object-Oriented DBMSs allow users to invoke time-consuming ("expensive") methods in their queries. When queries containing these expensive methods are run on data with duplicate values, time is wasted redundantly computing methods on the same value. This problem has been studied in the context of programming languages, where "memoization" is the standard solution. In the database literature, sorting has been proposed to deal with this problem. We compare these approaches along with a third solution, a variant of unary hybrid hashing which we call Hybrid Cache. We demonstrate that Hybrid Cache always dominates memoization, and significantly outperforms sorting in many instances. This provides new insights into the tradeoff between hashing and sorting for unary operations. Additionally, our Hybrid Cache algorithm includes some new optimization for unary hybrid hashing, which can be used for other applications such as grouping and duplicate elimination. We conclude with a discussion of techniques for caching multiple expensive methods in a single query, and raise some new optimization problems in choosing caching techniques.

Fast parallel sorting under LogP: experience with the CM-5

Abstract: In this paper, we analyze four parallel sorting algorithms (bitonic, column, radix, and sample sort) with the LogP model. LogP characterizes the performance of modern parallel machines with a small set of parameters: the communication latency (L), overhead (o), bandwidth (g), and the number of processors (P). We develop implementations of these algorithms in Split-C, a parallel extension to C, and compare the performance predicted by LogP to actual performance on a CM-5 of 32 to 512 processors for a range of problem sizes. We evaluate the robustness of the algorithms by varying the distribution and ordering of the key values. We also briefly examine the sensitivity of the algorithms to the communication parameters. We show that the LogP model is a valuable guide in the development of parallel algorithms and a good predictor of implementation performance. The model encourages the use of data layouts which minimize communication and balanced communication schedules which avoid contention. With an empirical model of local processor performance, LogP predictions closely match observed execution times on uniformly distributed keys across a broad range of problem and machine sizes. We find that communication performance is oblivious to the distribution of the key values, whereas the local processor performance is not; some communication phases are sensitive to the ordering of keys due to contention. Finally, our analysis shows that overhead is the most critical communication parameter in the sorting algorithms.

Automatic order selection system and method of operating

Abstract: An order selection system is disclosed together with a method of operating the system for retrieving multiple types of items stored in preselected storage locations and delivering retrieved items in an orderly sequence to a plurality of packing stations in accordance with the specific requirements of different orders. The order selection system comprises: a dispenser; a conveyor; a dispensing control system; a sorter; a plurality of stacking devices; and identifying means to identify the end of each order. The steps in the method of operating the system are: arranging the multiple types of items in the preselected storage locations; determining the requirements of orders to be filled; dispensing the items stored in the preselected storage locations in an alternating order sequence in accordance with the requirements of sequential orders; receiving the dispensed items on the conveyor in the alternating order sequence; transporting the dispensed items on the conveyor toward the packing stations; sorting the items so as to divert every other item toward separate packing stations; stacking the sorted items into discrete continuous stacks conforming with the specific requirements of the orders; and identifying the end of each order.

Deterministic sorting and randomized median finding on the BSP model

Abstract: We present new BSP algorithms for deterministic sorting and rmdomized median finding. We sort n general keys by using a partitioning scheme that achieves the requirements of efficiency (one-optimality) and insensitivity against data skew (the accuracy of the splitting keys depends solely on the step distance, which can be adapted to meet the worstcase requirements of our application). Although we employ sampling in order to realize efficiency, we can give a precise worst-case estimation of the maximum imbalance which might occur. We also investigate optimal randomized BSP algorithms for the problem of finding the median of n elements that require, with high-probability, 3rz/(2p) + o(n/p) number of comparisons, for a wide range of values of n and p. Experimental results for the two algorithms are also presented

Method and apparatus for sorting information

Abstract: A sorting technique in which a computer system or other data processing device interacts with a user to develop a spatial structure to represent information, such as a set of documents, according to a particular user's viewpoint. As a result of developing the spatial structure, and based on the structure, the system is able to sort other information, including its placement with respect to the other information in the spatial structure. The spatial structure also enables retrieval, searching and filtering information.

A sorting image sensor: an example of massively parallel intensity-to-time processing for low-latency computational sensors

Abstract: The need for low-latency vision systems is growing: high speed visual servoing and vision-based human computer interface. In this paper we present a new intensity-to-time processing paradigm suitable for low-latency massively parallel global computation over fine-grained data such as images. As an example of a low-latency global computation, we have developed a VLSI sorting computational sensor-a sensor which sorts all pixels of an input image by their intensities, as the image is being sensed. The first sorting sensor prototype is a 21 by 26 array of cells. It detects an image focused thereon and computes the image of indices as well as the image's cumulative histogram, before the intensity data are readout. The image of indices never saturates and has uniform histogram. Under user's control, the chip can perform other operations including simple segmentation and labeling.

Multilingual storage and retrieval

Abstract: A single processor/storage device provides multilingual support for a computer system. Information is divided into two parts. The first part is initially stored in a first character set, e.g., the character set in which it was created. A tag, identifying the character set, is associated with the first part. The second part is stored in a universal character set. The first part is converted to another character set only when requested. Indices may be generated from the second part using specified language sorting rules.

Method for flexibly sorting particles

Abstract: This invention relates to a method and apparatus for flexibly controlling sorting decisions for a flow cytometer or similar instrument at a purity vs. yield ratio of sorted particles, particularly at high event rates. The system monitors distances between sequential objects to determine if they are in close enough proximity to be within a single resolution unit of the sorting device. The "friend" or "foe" status of neighboring events is considered by this system in dealing with detected "coincident" events. The system operates on information of the desirability to sort the object, i.e. droplet, based upon the properties of the individual object. A storage and retrieval method is provided for making the information available at the time a sort operation based on a sorting logic condition is performed. Accordingly, an easily reconfigurable mode of operation control is provided to allow customized sorting strategies, based on the needs of individual applications or experiments. This system may be included as an integral part of a flow cytometer/cell sorter or similar instrument and may also be provided as an outboard module to such systems.

To cut…or not to cut (applications of comparative physical maps in molecular evolution)

Abstract: Studies of genomes evolving by rearrangements lead to cornbinatorial problem of sorting permutation by reversals. Kececioglu and Sankoff conjectured that for every permutation there exists an optimal sorting by reversals which does not cut long strips in the permutation. We prove this conjecture and further study the problem of sorting by reversals for permutations without strips of size one, called singletons. We give a polynomial algorithm for sorting such permutations, thus demonstrating that singletons present the major obstacle on the way towards an efficient algorithm for sorting by reversals. Using this result, we prove the strong Kecedoglu-Sankoff conjecture: for every permutation there exists an optimal sorting by reversals that never increases the number of breakpoints. Finally we present a new algorithm for sorting by reversals based on the notion of the spin of a permutation. For permutations with O(log n) singletons the algorithm runs in polynomial time and suggests a desired trade-off of resolution for cross-hybridization physical mapping in molecular evolution studies. We describe applications of this algorithm to analyze rearrangements in maize and green algae, in particular we find a most parsimonious rearrangement scenario for Chlamydomonas moewusii versus Chlamydomonas reinhardtii representing the most complicated known case of rearrangements inmore » organelles.« less

Coin classification using a novel technique for learning characteristic decision trees by controlling the degree of generalization

Abstract: A novel method for learning characteristic decision trees is applied to the problem of learning the decision mechanism of coin-sorting machines. Decision trees constructed by ID3-like algorithms are unable to detect instances of categories not present in the set of training examples. Instead of being rejected, such instances are assigned to one of the classes actually present in the training set. To solve this problem the algorithm must learn characteristic, rather than discriminative, category descriptions. In addition, the ability to control the degree of generalization is identified as an essential property of such algorithms. A novel method using the information about the statistical distribution of the feature values that can be extracted from the training examples is developed to meet these requirements. The central idea is to augment each leaf of the decision tree with a subtree that imposes further restrictions on the values of each feature in that leaf. (Less)

Device and method for sorting objects using buffer receptacles at sorting outlets

Abstract: The device for sorting objects, for example mail items, includes a conveyor (1) that directs the objects to be sorted to sorting output receptacles (7) associated with corresponding sorting outputs and in which the sorted objects are stored. A buffer receptacle (11) is provided at each sorting output. Each buffer receptacle (11) has a retractable bottom (12) and temporarily stores sorted objects before they are transferred into a sorting output receptacle and/or while that sorting output receptacle is replaced by an empty receptacle. Because of these buffer receptacles, the throughput of the sorting device may remain constant while sorting output receptacles are replaced.

Database system with improved methods for radix sorting

Abstract: System and methods are described for improved sorting of information records. The system provides radix sorting on native data types--that is, without the resource-expensive approach of converting data types into character representations. A correct interpretation of a group of bits under examination is provided by the system at the point of examination by a radixsort engine. "Sort plan" information is provided to the radixsort engine instructing it how a particular set of bits should be interpreted for purposes of comparison. The knowledge includes a "comparison type" for a set of bits under exam. This is employed by the engine to determine an appropriate "weighting" of each group of bits--how each group should be treated at the point of comparison. The engine itself operates generically: it simply operates on the set of bits as specified by the sort plan entries, regardless of the particular data types which comprise the bits or the one or more keys from which the bits are derived. In this manner, the system can enable the radixsort engine to properly interpret groups of bits, for undertaking a comparison operation for different types, thereby avoiding the undesirable task of converting data types into character representations.

Parallel algorithms for personalized communication and sorting with an experimental study (extended abstract)

Abstract: A fundamental challenge for parallel computing is to obtain high-level, architecture independent, algorithms which execute efficiently on general-purpose parallel machines. With the emergence of message passing standards such as MPI, it has become easier to design efficient and portable parallel algorithms by making use of these communication primitives. While existing primitives allow an assortment of collective communication routines, they do not handle an important communication event when most or all processors have nonuniformly sized personalized messages to exchange with each other. We first present an algorithm for the h-relation personalized communication whose efficient implementation will allow high performance implementations of a large class of algorithms. We then consider how to effectively use these communication primitives to address the problem of sorting. Previous schemes for sorting on general-purpose parallel machines have had to choose between poor load balancing and irregular communication or multiple rounds of all-to-all personalized communication. In this paper, we introduce a novel variation on sample sort which uses only two rounds of regular all-to-all personalized communication in a scheme that yields very good load balancing with virtually no overhead. Another variation using regular sampling for choosing the splitters has similar performance with deterministic guaranteed bounds on the memory and communication requirements. Both of these variations efficiently handle the presence of duplicates without the overhead of tagging each element. The personalized communication and sorting algorithms presented in this paper have been coded in SPLIT-C and run on a variety of platforms, including the Thinking Machines CM-5, IBM SP-2, Gray Research T3D, Meiko Scientific CS-2, and the Intel Paragon. Our experimental results are consistent with the theoretical analyses and illustrate “ The support by NASA Graduate Student Researcher Fellowship No NGT-50951 is gratefully acknowledged tsupported in part by NSF grant No cCR-91113135 and NSF HPCC/GCAG grant No. BIR-9318183, Permission to make digital/bard copies of all or part of this material for personal or classroom use is granted without fee provided that the copies are not made or $stributed for profit or commercial advantage, tbe copyn,ght notice, the .Utle,of the publication and Its date appear, and notice is given that copymght M by pernmwon of the ACM, Inc. To copy otherwise, to republish, to post on servers or to redistribute to Iista, requires specific permission and/or fee. SPAA’96, Padua, Italy 01996 ACM 0-89791-809-6/96/06 ..$3.50 the scalability and efficiency of our algorithms across different platforms. In fact, they seem to outperform all similar algorithms known to the authors on these platforms, ancl performance is invariant over the set of input distributions unlike previous efficient algorithms. Our sorting results also compare favorably with those reported for the simpler ranking problem posed by the NAS Integer Sorting ( 1S) Benchmark.

Sorting on a parallel pointer machine with applications to set expression evaluation

Abstract: We present optimal algorithms for sorting on parallel CREW and EREW versions of the pointer machine model. Intuitively, one can view our methods as being based on a parallel mergesort using linked lists rather than arrays (the usual parallel data structure). We also show how to exploit the “locality” of our approach to solve the set expression evaluation problem, a problem with applications to database querying and logic-programming in O(log n) time using O(n) processors. Interestingly, this is an asymptotic improvement over what seems possible using previous techniques.

The block distributed memory model

Abstract: We introduce a computation model for developing and analyzing parallel algorithms on distributed memory machines. The model allows the design of algorithms using a single address space and does not assume any particular interconnection topology. We capture performance by incorporating a cost measure for interprocessor communication induced by remote memory accesses. The cost measure includes parameters reflecting memory latency, communication bandwidth, and spatial locality. Our model allows the initial placement of the input data and pipelined prefetching. We use our model to develop parallel algorithms for various data rearrangement problems, load balancing, sorting, FFT, and matrix multiplication. We show that most of these algorithms achieve optimal or near optimal communication complexity while simultaneously guaranteeing an optimal speed-up in computational complexity. Ongoing experimental work in testing and evaluating these algorithms has thus far shown very promising results.