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82-474: BWT may refer to the Burrows–Wheeler transform , an algorithm used in file compression BWT , an Austrian wastewater company Bridgwater railway station , station code Bob Willis Trophy , English cricket competition Burnie Airport , IATA airport code "BWT" See also [ edit ] .bwt files, produced by BlindWrite Topics referred to by

164-399: A bottleneck in a system – a component that is the limiting factor on performance. In terms of code, this will often be a hot spot  – a critical part of the code that is the primary consumer of the needed resource – though it can be another factor, such as I/O latency or network bandwidth. In computer science, resource consumption often follows

246-447: A type safe alternative in many cases. In both cases, the inlined function body can then undergo further compile-time optimizations by the compiler, including constant folding , which may move some computations to compile time. In many functional programming languages, macros are implemented using parse-time substitution of parse trees/abstract syntax trees, which it is claimed makes them safer to use. Since in many cases interpretation

328-479: A complete rewrite if they need to be changed. Thus optimization can typically proceed via refinement from higher to lower, with initial gains being larger and achieved with less work, and later gains being smaller and requiring more work. However, in some cases overall performance depends on performance of very low-level portions of a program, and small changes at a late stage or early consideration of low-level details can have outsized impact. Typically some consideration

410-536: A different order. The bijective transform is computed by factoring the input into a non-increasing sequence of Lyndon words ; such a factorization exists and is unique by the Chen–Fox–Lyndon theorem , and may be found in linear time and constant space. The algorithm sorts the rotations of all the words; as in the Burrows–Wheeler transform, this produces a sorted sequence of n strings. The transformed string

492-497: A few, Burrows–Wheeler transform is used in algorithms for sequence alignment , image compression , data compression , etc. The following is a compilation of some uses given to the Burrows–Wheeler Transform. The advent of next-generation sequencing (NGS) techniques at the end of the 2000s decade has led to another application of the Burrows–Wheeler transformation. In NGS, DNA is fragmented into small pieces, of which

574-481: A filtering program will commonly read each line and filter and output that line immediately. This only uses enough memory for one line, but performance is typically poor, due to the latency of each disk read. Caching the result is similarly effective, though also requiring larger memory use. Optimization can reduce readability and add code that is used only to improve the performance . This may complicate programs or systems, making them harder to maintain and debug. As

656-575: A form of power law distribution, and the Pareto principle can be applied to resource optimization by observing that 80% of the resources are typically used by 20% of the operations. In software engineering, it is often a better approximation that 90% of the execution time of a computer program is spent executing 10% of the code (known as the 90/10 law in this context). More complex algorithms and data structures perform well with many items, while simple algorithms are more suitable for small amounts of data —

738-421: A good choice of efficient algorithms and data structures , and efficient implementation of these algorithms and data structures comes next. After design, the choice of algorithms and data structures affects efficiency more than any other aspect of the program. Generally data structures are more difficult to change than algorithms, as a data structure assumption and its performance assumptions are used throughout

820-425: A mathematical formula like: The optimization, sometimes performed automatically by an optimizing compiler, is to select a method ( algorithm ) that is more computationally efficient, while retaining the same functionality. See algorithmic efficiency for a discussion of some of these techniques. However, a significant improvement in performance can often be achieved by removing extraneous functionality. Optimization

902-407: A modular system may allow rewrite of only some component – for example, a Python program may rewrite performance-critical sections in C. In a distributed system, choice of architecture ( client-server , peer-to-peer , etc.) occurs at the design level, and may be difficult to change, particularly if all components cannot be replaced in sync (e.g., old clients). Given an overall design,

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984-466: A practical implementation. It essentially does what the pseudocode section does. Using the STX/ETX control codes to mark the start and end of the text, and using s[i:] + s[:i] to construct the i th rotation of s , the forward transform takes the last character of each of the sorted rows: The inverse transform repeatedly inserts r as the left column of the table and sorts the table. After

1066-448: A pre-BWIC scan of the image in a vertical snake order fashion. More recently, additional works like that of have shown the implementation of the Burrows–Wheeler Transform in conjunction with the known move-to-front transform (MTF) achieve near lossless compression of images. Cox et al. presented a genomic compression scheme that uses BWT as the algorithm applied during the first stage of compression of several genomic datasets including

1148-498: A result, optimization or performance tuning is often performed at the end of the development stage . Donald Knuth made the following two statements on optimization: "We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil. Yet we should not pass up our opportunities in that critical 3%" (He also attributed the quote to Tony Hoare several years later, although this might have been an error as Hoare disclaims having coined

1230-494: A simple (though inefficient) way to calculate the BWT and its inverse. It assumes that the input string s contains a special character 'EOF' which is the last character and occurs nowhere else in the text. To understand why this creates more-easily-compressible data, consider transforming a long English text frequently containing the word "the". Sorting the rotations of this text will group rotations starting with "he " together, and

1312-427: A system, which can cause problems from memory use, and correctness issues from stale caches. Beyond general algorithms and their implementation on an abstract machine, concrete source code level choices can make a significant difference. For example, on early C compilers, while(1) was slower than for(;;) for an unconditional loop, because while(1) evaluated 1 and then had a conditional jump which tested if it

1394-403: A trade-off – where one factor is optimized at the expense of others. For example, increasing the size of cache improves run time performance, but also increases the memory consumption. Other common trade-offs include code clarity and conciseness. There are instances where the programmer performing the optimization must decide to make the software better for some operations but at

1476-444: Is a cycle of ANAN....) At this point, these words are sorted into reverse order: ( ^ ), (B), (AN), (AN), (A). These are then concatenated to get The Burrows–Wheeler transform can indeed be viewed as a special case of this bijective transform; instead of the traditional introduction of a new letter from outside our alphabet to denote the end of the string, we can introduce a new letter that compares as preceding all existing letters that

1558-443: Is also true that advances in hardware will more often than not obviate any potential improvements, yet the obscuring code will persist into the future long after its purpose has been negated. Optimization during code development using macros takes on different forms in different languages. In some procedural languages, such as C and C++ , macros are implemented using token substitution. Nowadays, inline functions can be used as

1640-401: Is different from Wikidata All article disambiguation pages All disambiguation pages Burrows%E2%80%93Wheeler transform When a character string is transformed by the BWT, the transformation permutes the order of the characters. If the original string had several substrings that occurred often, then the transformed string will have several places where a single character

1722-441: Is given to efficiency throughout a project – though this varies significantly – but major optimization is often considered a refinement to be done late, if ever. On longer-running projects there are typically cycles of optimization, where improving one area reveals limitations in another, and these are typically curtailed when performance is acceptable or gains become too small or costly. As performance

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1804-440: Is incorrect, because the code is complicated by the optimization and the programmer is distracted by optimizing. When deciding whether to optimize a specific part of the program, Amdahl's Law should always be considered: the impact on the overall program depends very much on how much time is actually spent in that specific part, which is not always clear from looking at the code without a performance analysis . A better approach

1886-423: Is known as Burrows–Wheeler transform with an inversion encoder (BWIC). The results shown by BWIC are shown to outperform the compression performance of well-known and widely used algorithms like Lossless JPEG and JPEG 2000 . BWIC is shown to outperform those in terms of final compression size of radiography medical images on the order of 5.1% and 4.1% respectively. The improvements are achieved by combining BWIC and

1968-422: Is no need to have an actual 'EOF' character. Instead, a pointer can be used that remembers where in a string the 'EOF' would be if it existed. In this approach, the output of the BWT must include both the transformed string, and the final value of the pointer. The inverse transform then shrinks it back down to the original size: it is given a string and a pointer, and returns just a string. A complete description of

2050-916: Is not always an obvious or intuitive process. In the example above, the "optimized" version might actually be slower than the original version if N were sufficiently small and the particular hardware happens to be much faster at performing addition and looping operations than multiplication and division. In some cases, however, optimization relies on using more elaborate algorithms, making use of "special cases" and special "tricks" and performing complex trade-offs. A "fully optimized" program might be more difficult to comprehend and hence may contain more faults than unoptimized versions. Beyond eliminating obvious antipatterns, some code level optimizations decrease maintainability. Optimization will generally focus on improving just one or two aspects of performance: execution time, memory usage, disk space, bandwidth, power consumption or some other resource. This will usually require

2132-457: Is part of the specification of a program – a program that is unusably slow is not fit for purpose: a video game with 60 Hz (frames-per-second) is acceptable, but 6 frames-per-second is unacceptably choppy – performance is a consideration from the start, to ensure that the system is able to deliver sufficient performance, and early prototypes need to have roughly acceptable performance for there to be confidence that

2214-484: Is put at the beginning of the string. The whole string is now a Lyndon word, and running it through the bijective process will therefore result in a transformed result that, when inverted, gives back the Lyndon word, with no need for reassembling at the end. Relatedly, the transformed text will only differ from the result of BWT by one character per Lyndon word; for example, if the input is decomposed into six Lyndon words,

2296-421: Is repeated multiple times in a row. For example: The output is easier to compress because it has many repeated characters. In this example the transformed string contains six runs of identical characters: XX , SS , PP , .. , II , and III , which together make 13 out of the 44 characters. The transform is done by sorting all the circular shifts of a text in lexicographic order and by extracting

2378-457: Is similar to a static "average case" analog of the dynamic technique of adaptive optimization. Self-modifying code can alter itself in response to run time conditions in order to optimize code; this was more common in assembly language programs. Some CPU designs can perform some optimizations at run time. Some examples include out-of-order execution , speculative execution , instruction pipelines , and branch predictors . Compilers can help

2460-436: Is the use of a fast path for common cases, improving performance by avoiding unnecessary work. For example, using a simple text layout algorithm for Latin text, only switching to a complex layout algorithm for complex scripts, such as Devanagari . Another important technique is caching, particularly memoization , which avoids redundant computations. Because of the importance of caching, there are often many levels of caching in

2542-463: Is then obtained by picking the final character of each string in this sorted list. The one important caveat here is that strings of different lengths are not ordered in the usual way; the two strings are repeated forever, and the infinite repeats are sorted. For example, "ORO" precedes "OR" because "OROORO..." precedes "OROROR...". For example, the text " ^ BANANA $ " is transformed into "ANNBAA ^ $ " through these steps (the red $ character indicates

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2624-436: Is therefore to design first, code from the design and then profile / benchmark the resulting code to see which parts should be optimized. A simple and elegant design is often easier to optimize at this stage, and profiling may reveal unexpected performance problems that would not have been addressed by premature optimization. In practice, it is often necessary to keep performance goals in mind when first designing software, but

2706-495: Is used, that is one way to ensure that such computations are only performed at parse-time, and sometimes the only way. Lisp originated this style of macro, and such macros are often called "Lisp-like macros". A similar effect can be achieved by using template metaprogramming in C++ . In both cases, work is moved to compile-time. The difference between C macros on one side, and Lisp-like macros and C++ template metaprogramming on

2788-473: The EOF pointer) in the original string. The EOF character is unneeded in the bijective transform, so it is dropped during the transform and re-added to its proper place in the file. The string is broken into Lyndon words so the words in the sequence are decreasing using the comparison method above. (Note that we're sorting ' ^ ' as succeeding other characters.) " ^ BANANA" becomes ( ^ ) (B) (AN) (AN) (A). Up until

2870-518: The FM-index and then performing a series of operations called backwardSearch, forwardSearch, neighbourExpansion, and getConsequents in order to search for predictions given a suffix . The predictions are then classified based on a weight and put into an array from which the element with the highest weight is given as the prediction from the SuBSeq algorithm. SuBSeq has been shown to outperform state of

2952-474: The Intel 432 (1981); or ones that take years of work to achieve acceptable performance, such as Java (1995), which only achieved acceptable performance with HotSpot (1999). The degree to which performance changes between prototype and production system, and how amenable it is to optimization, can be a significant source of uncertainty and risk. At the highest level, the design may be optimized to make best use of

3034-545: The executable program is optimized at least as much as the compiler can predict. At the lowest level, writing code using an assembly language , designed for a particular hardware platform can produce the most efficient and compact code if the programmer takes advantage of the full repertoire of machine instructions . Many operating systems used on embedded systems have been traditionally written in assembler code for this reason. Programs (other than very small programs) are seldom written from start to finish in assembly due to

3116-429: The BWT is not that it generates a more easily encoded output—an ordinary sort would do that—but that it does this reversibly , allowing the original document to be re-generated from the last column data. The inverse can be understood this way. Take the final table in the BWT algorithm, and erase all but the last column. Given only this information, you can easily reconstruct the first column. The last column tells you all

3198-410: The Burrows–Wheeler transform of an edited text from that of the original text, doing a limited number of local reorderings in the original Burrows–Wheeler transform, which can be faster than constructing the Burrows–Wheeler transform of the edited text directly. This Python implementation sacrifices speed for simplicity: the program is short, but takes more than the linear time that would be desired in

3280-461: The ERA015743 dataset by around 94%, to 8.2 GB. BWT has also been proved to be useful on sequence prediction which is a common area of study in machine learning and natural-language processing . In particular, Ktistakis et al. proposed a sequence prediction scheme called SuBSeq that exploits the lossless compression of data of the Burrows–Wheeler transform. SuBSeq exploits BWT by extracting

3362-462: The algorithms can be found in Burrows and Wheeler's paper, or in a number of online sources. The algorithms vary somewhat by whether EOF is used, and in which direction the sorting was done. In fact, the original formulation did not use an EOF marker. Since any rotation of the input string will lead to the same transformed string, the BWT cannot be inverted without adding an EOF marker to the end of

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3444-413: The amount of time that a program takes to perform some task at the price of making it consume more memory. In an application where memory space is at a premium, one might deliberately choose a slower algorithm in order to use less memory. Often there is no "one size fits all" design which works well in all cases, so engineers make trade-offs to optimize the attributes of greatest interest. Additionally,

3526-544: The art algorithms for sequence prediction both in terms of training time and accuracy. Optimization (computer science) In computer science , program optimization , code optimization , or software optimization is the process of modifying a software system to make some aspect of it work more efficiently or use fewer resources. In general, a computer program may be optimized so that it executes more rapidly, or to make it capable of operating with less memory storage or other resources, or draw less power. Although

3608-453: The available resources, given goals, constraints, and expected use/load. The architectural design of a system overwhelmingly affects its performance. For example, a system that is network latency-bound (where network latency is the main constraint on overall performance) would be optimized to minimize network trips, ideally making a single request (or no requests, as in a push protocol ) rather than multiple roundtrips. Choice of design depends on

3690-410: The characters in the text, so just sort these characters alphabetically to get the first column. Then, the last and first columns (of each row) together give you all pairs of successive characters in the document, where pairs are taken cyclically so that the last and first character form a pair. Sorting the list of pairs gives the first and second columns. Continuing in this manner, you can reconstruct

3772-408: The code written today is intended to run on as many machines as possible. As a consequence, programmers and compilers don't always take advantage of the more efficient instructions provided by newer CPUs or quirks of older models. Additionally, assembly code tuned for a particular processor without using such instructions might still be suboptimal on a different processor, expecting a different tuning of

3854-411: The code. Typically today rather than writing in assembly language, programmers will use a disassembler to analyze the output of a compiler and change the high-level source code so that it can be compiled more efficiently, or understand why it is inefficient. Just-in-time compilers can produce customized machine code based on run-time data, at the cost of compilation overhead. This technique dates to

3936-416: The constant factors matter: an asymptotically slower algorithm may be faster or smaller (because simpler) than an asymptotically faster algorithm when they are both faced with small input, which may be the case that occurs in reality. Often a hybrid algorithm will provide the best performance, due to this tradeoff changing with size. A general technique to improve performance is to avoid work. A good example

4018-442: The cost of making other operations less efficient. These trade-offs may sometimes be of a non-technical nature – such as when a competitor has published a benchmark result that must be beaten in order to improve commercial success but comes perhaps with the burden of making normal usage of the software less efficient. Such changes are sometimes jokingly referred to as pessimizations . Optimization may include finding

4100-448: The earliest regular expression engines, and has become widespread with Java HotSpot and V8 for JavaScript. In some cases adaptive optimization may be able to perform run time optimization exceeding the capability of static compilers by dynamically adjusting parameters according to the actual input or other factors. Profile-guided optimization is an ahead-of-time (AOT) compilation optimization technique based on run time profiles, and

4182-399: The effort required to make a piece of software completely optimal – incapable of any further improvement – is almost always more than is reasonable for the benefits that would be accrued; so the process of optimization may be halted before a completely optimal solution has been reached. Fortunately, it is often the case that the greatest improvements come early in

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4264-619: The encoded string can be computed as a simple modification of the suffix array , and suffix arrays can be computed with linear time and memory. The BWT can be defined with regards to the suffix array SA of text T as (1-based indexing): B W T [ i ] = { T [ S A [ i ] − 1 ] , if  S A [ i ] > 0 $ , otherwise {\displaystyle BWT[i]={\begin{cases}T[SA[i]-1],&{\text{if }}SA[i]>0\\\$ ,&{\text{otherwise}}\end{cases}}} There

4346-416: The encoding phase is the last column L = BNN ^ AA $ A after step 3, and the index (0-based) I of the row containing the original string S , in this case I = 6 . It is not necessary to use both $ and ^ , but at least one must be used, else we cannot invert the transform, since all circular permutations of a string have the same Burrows–Wheeler transform. The following pseudocode gives

4428-405: The entire list. Then, the row with the "end of file" character at the end is the original text. Reversing the example above is done like this: A number of optimizations can make these algorithms run more efficiently without changing the output. There is no need to represent the table in either the encoder or decoder. In the encoder, each row of the table can be represented by a single pointer into

4510-405: The final system will (with optimization) achieve acceptable performance. This is sometimes omitted in the belief that optimization can always be done later, resulting in prototype systems that are far too slow – often by an order of magnitude or more – and systems that ultimately are failures because they architecturally cannot achieve their performance goals, such as

4592-582: The first few bases are sequenced , yielding several millions of "reads", each 30 to 500 base pairs ("DNA characters") long. In many experiments, e.g., in ChIP-Seq , the task is now to align these reads to a reference genome , i.e., to the known, nearly complete sequence of the organism in question (which may be up to several billion base pairs long). A number of alignment programs, specialized for this task, were published, which initially relied on hashing (e.g., Eland , SOAP, or Maq ). In an effort to reduce

4674-425: The goals: when designing a compiler , if fast compilation is the key priority, a one-pass compiler is faster than a multi-pass compiler (assuming same work), but if speed of output code is the goal, a slower multi-pass compiler fulfills the goal better, even though it takes longer itself. Choice of platform and programming language occur at this level, and changing them frequently requires a complete rewrite, though

4756-432: The human genomic information. Their work proposed that BWT compression could be enhanced by including a second stage compression mechanism called same-as-previous encoding ("SAP"), which makes use of the fact that suffixes of two or more prefix letters could be equal. With the compression mechanism BWT-SAP, Cox et al. showed that in the genomic database ERA015743, 135.5 GB in size, the compression scheme BWT-SAP compresses

4838-472: The input or doing something equivalent, making it possible to distinguish the input string from all its rotations. Increasing the size of the alphabet (by appending the EOF character) makes later compression steps awkward. There is a bijective version of the transform, by which the transformed string uniquely identifies the original, and the two have the same length and contain exactly the same characters, just in

4920-538: The last character of that rotation (which is also the character before the "he ") will usually be "t", so the result of the transform would contain a number of "t" characters along with the perhaps less-common exceptions (such as if it contains "ache ") mixed in. So it can be seen that the success of this transform depends upon one value having a high probability of occurring before a sequence, so that in general it needs fairly long samples (a few kilobytes at least) of appropriate data (such as text). The remarkable thing about

5002-422: The last character; the two codes are actually the first . The rotation holds nevertheless.) As a lossless compression algorithm the Burrows–Wheeler transform offers the important quality that its encoding is reversible and hence the original data may be recovered from the resulting compression. The lossless quality of Burrows algorithm has provided for different algorithms with different purposes in mind. To name

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5084-487: The last column and the index of the original string in the set of sorted permutations of S . Given an input string S = ^ BANANA $ (step 1 in the table below), rotate it N times (step 2), where N = 8 is the length of the S string considering also the red ^ character representing the start of the string and the red $ character representing the ' EOF ' pointer; these rotations, or circular shifts, are then sorted lexicographically (step 3). The output of

5166-399: The last step, the process is identical to the inverse Burrows–Wheeler process, but here it will not necessarily give rotations of a single sequence; it instead gives rotations of Lyndon words (which will start to repeat as the process is continued). Here, we can see (repetitions of) four distinct Lyndon words: (A), (AN) (twice), (B), and ( ^ ). (NANA... doesn't represent a distinct word, as it

5248-465: The memory requirement for sequence alignment, several alignment programs were developed ( Bowtie , BWA, and SOAP2 ) that use the Burrows–Wheeler transform. The Burrows–Wheeler transformation has proved to be fundamental for image compression applications. For example, Showed a compression pipeline based on the application of the Burrows–Wheeler transformation followed by inversion, run-length, and arithmetic encoders. The pipeline developed in this case

5330-650: The need for auxiliary variables and can even result in faster performance by avoiding round-about optimizations. Between the source and compile level, directives and build flags can be used to tune performance options in the source code and compiler respectively, such as using preprocessor defines to disable unneeded software features, optimizing for specific processor models or hardware capabilities, or predicting branching , for instance. Source-based software distribution systems such as BSD 's Ports and Gentoo 's Portage can take advantage of this form of optimization. Use of an optimizing compiler tends to ensure that

5412-483: The optimal instruction scheduling might be different even on different processors of the same architecture. Computational tasks can be performed in several different ways with varying efficiency. A more efficient version with equivalent functionality is known as a strength reduction . For example, consider the following C code snippet whose intention is to obtain the sum of all integers from 1 to N : This code can (assuming no arithmetic overflow ) be rewritten using

5494-427: The other side, is that the latter tools allow performing arbitrary computations at compile-time/parse-time, while expansion of C macros does not perform any computation, and relies on the optimizer ability to perform it. Additionally, C macros do not directly support recursion or iteration , so are not Turing complete . As with any optimization, however, it is often difficult to predict where such tools will have

5576-428: The output will only differ in six characters. For example, applying the bijective transform gives: The bijective transform includes eight runs of identical characters. These runs are, in order: XX , II , XX , PP , .. , EE , .. , and IIII . In total, 18 characters are used in these runs. When a text is edited, its Burrows–Wheeler transform will change. Salson et al. propose an algorithm that deduces

5658-435: The phrase. ) "In established engineering disciplines a 12% improvement, easily obtained, is never considered marginal and I believe the same viewpoint should prevail in software engineering" "Premature optimization" is a phrase used to describe a situation where a programmer lets performance considerations affect the design of a piece of code. This can result in a design that is not as clean as it could have been or code that

5740-424: The process. Even for a given quality metric (such as execution speed), most methods of optimization only improve the result; they have no pretense of producing optimal output. Superoptimization is the process of finding truly optimal output. Optimization can occur at a number of levels. Typically the higher levels have greater impact, and are harder to change later on in a project, requiring significant changes or

5822-407: The program take advantage of these CPU features, for example through instruction scheduling . Code optimization can be also broadly categorized as platform -dependent and platform-independent techniques. While the latter ones are effective on most or all platforms, platform-dependent techniques use specific properties of one platform, or rely on parameters depending on the single platform or even on

5904-622: The program, though this can be minimized by the use of abstract data types in function definitions, and keeping the concrete data structure definitions restricted to a few places. For algorithms, this primarily consists of ensuring that algorithms are constant O(1), logarithmic O(log n ), linear O( n ), or in some cases log-linear O( n log n ) in the input (both in space and time). Algorithms with quadratic complexity O( n ) fail to scale, and even linear algorithms cause problems if repeatedly called, and are typically replaced with constant or logarithmic if possible. Beyond asymptotic order of growth,

5986-440: The programmer balances the goals of design and optimization. Modern compilers and operating systems are so efficient that the intended performance increases often fail to materialize. As an example, caching data at the application level that is again cached at the operating system level does not yield improvements in execution. Even so, it is a rare case when the programmer will remove failed optimizations from production code. It

6068-403: The same term [REDACTED] This disambiguation page lists articles associated with the title BWT . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=BWT&oldid=1078733539 " Category : Disambiguation pages Hidden categories: Short description

6150-404: The setup, initialization time, and constant factors of the more complex algorithm can outweigh the benefit, and thus a hybrid algorithm or adaptive algorithm may be faster than any single algorithm. A performance profiler can be used to narrow down decisions about which functionality fits which conditions. In some cases, adding more memory can help to make a program run faster. For example,

6232-508: The single processor. Writing or producing different versions of the same code for different processors might therefore be needed. For instance, in the case of compile-level optimization, platform-independent techniques are generic techniques (such as loop unrolling , reduction in function calls, memory efficient routines, reduction in conditions, etc.), that impact most CPU architectures in a similar way. A great example of platform-independent optimization has been shown with inner for loop, where it

6314-434: The strings, and the sort performed using the indices. In the decoder, there is also no need to store the table, and in fact no sort is needed at all. In time proportional to the alphabet size and string length, the decoded string may be generated one character at a time from right to left. A "character" in the algorithm can be a byte, or a bit, or any other convenient size. One may also make the observation that mathematically,

6396-447: The time and cost involved. Most are compiled down from a high level language to assembly and hand optimized from there. When efficiency and size are less important large parts may be written in a high-level language. With more modern optimizing compilers and the greater complexity of recent CPUs , it is harder to write more efficient code than what the compiler generates, and few projects need this "ultimate" optimization step. Much of

6478-528: The whole table is built, it returns the row that ends with ETX, minus the STX and ETX. Following implementation notes from Manzini, it is equivalent to use a simple null character suffix instead. The sorting should be done in colexicographic order (string read right-to-left), i.e. sorted ( ... , key = lambda s : s [:: - 1 ]) in Python. (The above control codes actually fail to satisfy EOF being

6560-423: The word "optimization" shares the same root as "optimal", it is rare for the process of optimization to produce a truly optimal system. A system can generally be made optimal not in absolute terms, but only with respect to a given quality metric, which may be in contrast with other possible metrics. As a result, the optimized system will typically only be optimal in one application or for one audience. One might reduce

6642-527: Was observed that a loop with an inner for loop performs more computations per unit time than a loop without it or one with an inner while loop. Generally, these serve to reduce the total instruction path length required to complete the program and/or reduce total memory usage during the process. On the other hand, platform-dependent techniques involve instruction scheduling, instruction-level parallelism , data-level parallelism, cache optimization techniques (i.e., parameters that differ among various platforms) and

6724-503: Was true, while for (;;) had an unconditional jump . Some optimizations (such as this one) can nowadays be performed by optimizing compilers . This depends on the source language, the target machine language, and the compiler, and can be both difficult to understand or predict and changes over time; this is a key place where understanding of compilers and machine code can improve performance. Loop-invariant code motion and return value optimization are examples of optimizations that reduce

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