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本帖最后由 wwqqer 于
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文中提到了李彦宏和他的算法。。。想要随时跟踪最新好书，请点击头像下方“加关注”。关注成功后，查看这里即可：。
The Real 10 Algorithms that Dominate Our World
什么是算法？What is an algorithm?
& & Informally, an algorithm is any well-defined computational procedure that takes some value, or set of values, as input and produces some value, or set of values, as output. An algorithm is thus a sequence of computational steps that transform the input into the output. Source: Thomas H. Cormen, Chales E. Leiserson (2009), Introduction to Algorithms 3rd edition. （论坛里有此书）
In simple terms, it is possible to say that an algorithm is a sequence of steps which allow to solve a certain task ( Yes, not just computers use algorithms, humans also use them). Now, an algorithm should have three important characteristics to be considered valid:
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& & It should be finite: If your algorithm never ends trying to solve the problem it was designed to solve then it is useless& & It should have well defined instructions: Each step of the algorithm has to
the instructions should be unambiguously specified for each case.& & It should be effective: The algorithm should solve the problem it was designed to solve. And it should be possible to demonstrate that the algorithm converges with just a paper and pencil.
Also it is important to point out that algorithms are not just used in Computing Sciences but are a mathematical entity. In fact the first recorded mathematical algorithms that we have date from 1600 BC — Babylonians develop earliest known algorithms for factorization and finding square roots. So here we have the first problem with the post mentioned before, it treats algorithms as computing entities, but if you take the formal meaning of the word the real top 10 algorithms that rule the world can be found in a book of arithmetic (addition, subtraction, product, etc).
But lets take computing algorithms as our definition of algorithm in this post, so the question remains: Which are the 10 algorithms that rule the world? Here I’ve put together a little list, in no particular order.
1. Merge Sort, Quick Sort and Heap Sort
23:23:50 上传
What is the best algorithm to sort elements? It depends on what you need, and that’s why I put the three more frequently used sort algorith maybe you have a preference for one, but all of them are equally important.
The Merge Sort algorithm is by far one of the most important algorithms that we have today. It is a comparison-based sorting algorithm that uses the divide-and-conquer approach to solve a problem that once was a O(n^2). It was invented by the mathematician John von Neumann in 1945.
Quick Sort is a different approach to the sorting problem, it can use in-place partition algorithms and is a divide and conquer algorithm as well. The problem with this algorithm is that is not a stable sort but is really efficient for sorting RAM-based arrays.
Finally, Heap Sort algorithm uses a priority queue that reduces the search time in the data. This algorithm is also an in-place algorithm and is not stable sort.
These algorithms are a big improvement over other approaches previously used like bubble sort, in fact, it is thanks to them that today we have Data mining, artificial intelligence, link analysis and most of the computing tools in the world including the web.
2. Fourier Transform and Fast Fourier Transform
Our entire digital world uses these simple but really powerful algorithms, which transform signals from their time domain into their frequency domain and vice versa. In fact, you are seeing this post thanks to these algorithms.
The internet, your WiFi, smartphone, phone, computer, router, satellites, almost everything that has a computer inside uses these algorithms in one way or another to function. You can’t get a degree in electronics, computing or telecommunications without studying these important algorithms.
3. Dijkstra’s algorithm
23:23:53 上传
It is not crazy to say that the internet wouldn't work as efficiently as it does if it wasn't because of this algorithm. This graph search algorithm is used in different applications where the problem can be modeled as a graph and you have to find the shortest path between two nodes.
Today, even when we have better solutions to the problem of finding the shortest path, Dijkstra’s algorithm is still used in systems that require stability.
4. RSA algorithm
The internet wouldn't be as important as it is today if it wasn't for cryptography and cyber security. You can think “Sure, security in the era of NSA and other intelligence agencies” or “You have to be really naive to think you are safe in the Internet”; but, people need to feel that they are secure in order to spend their money. After all, you wouldn't input your credit card number on a web service if you know it is not secure.
And from the field of cryptography there is an algorithm that remains one of the most important in the world: the RSA algorithm. Developed by the founders of the company RSA, this algorithm made cryptography available to everybody in the world and helped to shape how cryptography works today. The RSA algorithm is a solution to a simple but complex problem: how to share public keys between independent platforms and final users, in order to allow cryptography (I would argue that it hasn’t been completely solved, I think we need more work in this direction) .
5. Secure Hash Algorithm
This isn't exactly an algorithm but a family of cryptographic hash functions developed by the NIST in the USA. But this family of algorithms is fundamental for the functioning of the World. From your app store, your email, your antivirus, to your browser, etc , all of them use these algorithms (in reality the hash that results from them) to determine if you have downloaded what you wanted or if you have been the victim of a man in the middle attack or maybe a phishing attack.
6. Integer factorization
This is a mathematical algorithm that is heavily used in computing field. Without this algorithm, cryptography would be much more unsafe. The algorithm is a series of steps used to get the prime factorization of a composite number into smaller non-trivial divisors. This is considered an FNP problem, which is an extension of the class NP making the problem really hard to solve.
Many cryptographic protocols are based on the difficulty of factoring large composite integers or a related problem—for example, the RSA problem. An algorithm that efficiently factors an arbitrary integer would render RSA-based public-key cryptography insecure.
The birth of quantum computing is making it easier to solve this problem, opening a completely new field that uses properties of the quantum world to make systems safe.
7. Link Analysis
23:23:56 上传
In the era of internet, the analysis of relationships between different entities is crucial. From search engines and social networks to marketing analysis tools, everybody is trying to find the real structure of the Internet through time.
Link analysis is arguably one of the algorithms with the most myths and confusion in the general public. The problem is that there are different ways to make link analysis and there are also characteristics that make each algorithm a little different (which allows to patent the algorithms) but in their bases they are similar.
The idea behind link analysis is simple, you can represent a graph in a Matrix form making it a eigenvalue problem. This eigenvalues can give you a really good approach of the structure of the graph and the relative importance of each node. The algorithm was developed in 1976 by Gabriel Pinski and Francis Narin.
Who uses this algorithm? Google in its Page Rank, Facebook when it shows you your news feed (this is the reason why Facebook news feed is not an algorithm but the result of one), Google+ and Facebook friend suggestion, LinkedIn suggestions for jobs and contacts, Netflix and Hulu for movies, YouTube for videos, etc. Each one has a different objective and different parameters, but the math behind each remains the same.
Finally, I’d like to say that even thought it seems like Google was the first company to work with this type of algorithms, in 1996 (two years before Google) a little search engine called “RankDex” , founded by Robin Li, was already using this idea for page ranking. Finally Massimo Marchiori, the founder of “HyperSearch”, used an algorithm of page rank based on the relations between single pages. (The two founders are mentioned in the patents of Google).
8. Proportional Integral Derivative Algorithm
23:23:58 上传
Have you ever used an airplane, an automobile, a satellite service or a cellphone network? Have you ever been in a factory or seen a robot? If so, then you have seen this algorithm in action.
Basically, this algorithm uses a control loop feedback mechanism to minimize the error between the desired output signal and the real output signal. It is used wherever you need signal processing or you need an electronic system controlling a mechanical, hydraulic or thermal system using automation.
You could say that without this algorithm our modern civilization wouldn't exist.
9. Data compression algorithms
It is difficult to decide which is the most important compression algorithm because, depending on the application, the algorithm used can vary from zip to mp3 and from JPEG to MPEG-2. But there is something that everybody knows that these algorithms are really important in almost all the structures.
Where could you find them, besides the obvious zipped document? This web page used data compression to be downloaded into your computer, in video games, videos, music, data storage, cloud computing, databases, etc. You could say that everything uses data co they help make systems cheaper and more efficient.
10. Random Number Generation
23:23:59 上传
Today we don’t have a “true” random number generator, but we have some pseudo random number generators that are sufficient. These are used in a large number of applications, from interlink connection, cryptography, secure hash algorithm, video games, artificial intelligence, optimization, to initial conditions for problems, finances, etc.
Finally I just want to add that this list should be taken as an opinion, not a comprehensive list, because there are some algorithms in fields like Machine Learning, Matrix multiplication, categorization, etc, which are important in our world and are not mentioned here.
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Google的量子计算之梦：10年后机器学习全部量子化
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评论: |来自: 机器之心
摘要: 上周，谷歌宣布他们的量子计算机比传统计算机快上1亿倍，有人欢呼雀跃，有人提出质疑。让我们来看看背后的故事吧，看看物理学家John Martinis如何帮谷歌实现炙手可热的量子计算之梦。他或许正手握着量子计算的圣杯。 ...
上周，谷歌宣布他们的量子计算机比传统计算机快上1亿倍，有人欢呼雀跃，有人提出质疑。让我们来看看背后的故事吧，看看物理学家John Martinis如何帮谷歌实现炙手可热的量子计算之梦。他或许正手握着量子计算的圣杯。本文选自麻省理工科技评论。John Martinis用老花镜腿指向几年后即将造出新型计算机的地方，这种新型计算机将拥有超乎想象的计算能力。那是一个圆柱形的槽，约1.5英寸宽，位于一个半身雕塑大小的结构底部，这个结构由各种圆盘、块状物、电线、铜和金堆叠而成。今年秋天，在我拜访他的前一天，他在这个圆槽中装载了一个实验性的超导芯片，上面蚀刻着一个微缩的Google logo，并把这个装置降温到绝对零度以上1/100℃。为了庆祝测试机器的第一天，Martinis和同事们在一家自酿啤酒馆举办了一个他所谓的「小聚会」，这些同事都来自于Google在加州圣塔芭芭拉新购置的实验室。如果Martinis的团队真的造出他们追寻的神奇计算机，必将引发一场盛大的庆祝。与之相比，这场小聚会实在太寒碜。因为，这台计算机将能驾驭量子力学在极端环境（例如超冷芯片）中涌现的奇妙性质。它能让Google的程序员在一杯咖啡的休息时间内解决一个现有超级计算机需要几百万年才能解决的问题。Google在普通计算机上开发来驾驶汽车或回答问题的软件也将变得更加智能。而Google及其母公司（Alphabet）内部冒出的那些更加前沿的想法（例如救灾机器人或以人类水平对话的软件）可能将变成现实。John Martinis已经专注研究量子计算机30年，现在，他可能即将造出一台真正可用的量子计算机。前人已经奠定了量子计算的理论基础。物理学家们已经能够造出未来的量子计算机赖以存在的基本计算单元，也就是量子比特（qubit）。他们甚至能操控量子比特，使它们聚集成小型的组群。但是，他们还不能造出一台完全运转、实际有用的量子计算机。Martinis是该领域内的顶尖专家——他在加州大学圣塔芭芭拉分校的研究团队已经验证了某些最可靠的量子比特，并能让它们运行一些量子计算机运转所需的代码。2014年7月，他对Google说，只要有足够的支持，他团队的技术就能迅速达到成熟。Google被说服了，并聘用了他。他的新Google实验室建立并运作起来，Martinis认为，他能够在两三年内造出一台小而可用的量子计算机。他说，「我们常对彼此说，我们正处在孕育量子计算机产业的过程中。」Google和量子计算就像算法天堂中的一场角逐。常有人说，Google对数据有着贪得无厌的饥渴。但Google对量子计算的战略却比饥渴更加热切和上瘾——他们想从数据中汲取信息，甚至从中创造出智能。Google这家公司成立的初衷是商业化一款排名网页的算法，它赖以生存的经济基础是售卖和定位广告。而最近，Google投入大笔资金来研发人工智能（AI）软件，这些软件能够学习和理解语言或图像、进行基本的推理以及在拥堵路段驾驶汽车——这些任务对传统计算机十分困难，但对量子计算机来说却是小菜一碟。Google的CEO桑达尔·皮查伊（Sundar Pichai）最近对投资人说：「机器学习这一具有变革意义的核心技术将促使我们重新思考我们做所有事情的方式。」Martinis的新量子产业的首要任务就是证明这一点。筑梦者上周之前，几年内造出有用的量子计算机的前景似乎还很遥远。政府、学术机构和企业实验室的研究员还远不能聚集起足够的量子比特来建造一台简单的原理验证机。资金雄厚的加拿大初创公司D-Wave Systems出售了几台所谓的「全世界最早的商用量子计算机」，但是多年来都未能让业内专家信服这些机器能完成量子计算机理应完成的任务。接着，就在上周，NASA（美国宇航局）在加州山景城艾姆斯研究中心的N-258号楼召开了新闻发布会（N-258号楼是NASA的先进超级计算中心所在地。——译者注）。那里从2013年开始就放置着Google从D-Wave购买的一台计算机。在那里，Google建来用D-Wave计算机做实验的量子人工智能实验室主任Hartmut Neven公布了一个真实的证据，证明它能提供量子计算机允诺的计算能力。在一个设计严格的测试中，D-Wave计算机中被称为量子退火机（quantum annealer）的超导芯片比传统处理器快了1亿倍。然而，这种优势需要在实际的计算任务中实现，而不仅仅是有目的的测试。Neven是一个健谈的机器学习专家，他说：「我们需要让它把工程师办公桌上的实际问题变得更简单，并把它放入计算机。」这就是Martinis进入的领域。Neven认为D-Wave的量子退火机不会很快准备好为Google工程师服务，因此他雇佣了Martinis来干这活。Neven说：「很明显，我们不能只是一味的等待。为了达到一个真正的技术，我们需要克服一大串的问题。」他说D-Wave芯片上的量子比特太不靠谱，连接起来的厚度也不够。（D-Wave的CEO Vern Brownell回应说他不担心来自Google的竞争。）Google面临的竞争对手不仅有来自D-Wave的进展，还有微软与IBM，因为他们也拥有许多量子计算的项目。但是这些公司都更加关注设计，而不是让它们变得更实用。实际上，一个关于Google项目的大致时间线估计，最快到2017年，Martinis的团队就能用100个量子比特制造一个量子退火机。D-Wave最新的芯片已经有1097个量子比特，但是Neven说一个高质量芯片或许可用更少的量子比特就能完成一些任务。一个量子退火机只能运行一个特定的算法，但是，它碰巧非常适合Google最关心的领域。麻省理工学院（MIT）林肯实验室的高级职员William Oliver研究了量子计算的潜力，他说这种应用可能非常有利于模式识别和机器学习。John Martinis今年57岁，对解开量子物理研究复杂的链条、使其成为一个崭新的工程学科来说是一个完美的人选。他不仅能够潜心研究难懂的数学，还特别喜欢建造东西。操纵哪怕仅一个量子比特都是一个难题，因为这要涉及到量子理论、固态物理学、材料科学、精密加工、机械设计和传统电子业的组合。Martinis个子高高的，有着亲善的嗓音，大家公认他个人已经掌握了上述每块理论和技术实施。在带我们参观他的新Google实验室时，不管是面对传统车间区域的新烙铁和机械工具，还是面对冷却和运算芯片的复杂设备，他都兴奋不已。他说：「我认为这很有趣。我能完成别人无法做到的实验，是因为我能建造我自己的电子设备。」这种刻有Google logo的实验芯片被冷却到绝对零度以上一点点，目的是为了产生量子效应。Martinis和他的团队必须掌握许多技术，因为量子比特是如此变化多端。它们可以用多种不同的方法实现——Martinis的方法是用微电流来冷却铝环直至它们变成超导体。但不管采用什么方法，它们表示数据的方法都是微妙的量子状态，这种状态极易被热量和电磁噪声扭曲或破坏，并将计算破坏殆尽。量子比特用它们脆弱的物理性质所做的事，正相当于传统芯片上的晶体管用电流完成的事——也就是用0和1的二进制来表示信息。但是，量子比特还有一种称为叠加态的状态，能同时表示0和1。处于叠加态的量子比特还能以一种叫做量子纠缠的现象相互联系，也就是说一个量子比特的行为能瞬间影响到另一个量子比特。有了这些效应，量子计算机中的单个运算就完成传统计算机中很多很多运算才能完成的任务。在某些情况下，随着处理数据量的增加，量子计算机比传统计算机的优势会实现指数级的增长。下面视频为量子计算机的原理。字幕听译&时间轴：汪汪。无法保持量子比特的稳定状态正是我们尚未造出量子计算机的原因。但是，Martinis已经在此问题上研究了11年，他认为他已经接近答案了。他的量子比特的退相干时间（也就是量子比特保持叠加态的时长）是几十微秒——比D-Wave芯片的数据高1万倍。Martinis对他们团队的硬件很有信心。这种信心甚至让他认为除了量子退火机以外，他还能为Google建造出其他形式的量子计算机，甚至比量子退火机还更强大。它将被称为通用量子计算机（universal quantum computer），可被编程来处理任何问题，而不仅仅是一种数学问题。实际上，人们对这种方法背后的理论比量子退火机了解得更多，一部分是因为花费在量子计算研究上的大多数时间和金钱都用在了通用量子计算上。但是量子比特的可靠性还不够高，不足以将该理论转化成切实可行的通用量子计算机。金属板的这种结构对冷却和保护量子芯片非常必要。直到三月，Martinis和他的团队首次论证了位于通用量子计算机所需的可靠阈值之上的量子比特。他们让一个有9个量子比特的芯片运行了一个称为 surface code的错误检验程序，该程序对量子计算机的运行十分必要（IBM已经能让部分 surface code在4个量子比特上运行）。Martinis说：「我认为，我们对这种技术的验证已经到达了能够按比例放大的程度。这次是来真的。」Martinis的目标是大约2年内，在他推出Google新量子退火机的同时，也完成一台完全的通用量子计算机。那将会成为计算机科学领域的里程碑，但它不可能立即帮到Google的程序员。在威斯康辛州大学领导量子计算研究团队的Robert McDermott说，由于surface code的复杂性，即使一个有着100个量子比特的芯片能运行错误检验程序，但它不能完成任何额外的工作。然而Martinis认为，一旦他能提高量子比特的可靠性，在通用量子芯片上实现100个量子比特，就能打开通往更多量子比特的大门。他说：「这是我们擅长的事。尽管保持相干很困难，但是按比例扩大却很容易。」机器学习是「愚蠢的算法」当Martinis解释为什么Google需要他的技术时，他对于人工智能领域的工作者们毫不留情：「机器学习算法真的是一种愚蠢的做法，」他的话语中带有一丝怀疑，「（机器学习算法的实现）需要学习太多的范例。」事实上，Google和其他计算机公司所使用的机器学习技术与人类或动物学习新技能或知识的方式相比是可悲的。教会一个软件某种新的技能，比如，如何在照片中识别出汽车和猫，通常需要成千上万张精心挑选并注有标签的范例图片。尽管一种称为深度学习的技术最近在软件通过学习来诠释图像和语句的准确度方面有了显著的进步，但若是要学习更复杂的才能，比如理解语言中的细微差别等，仍然超出了机器的能力范围。Martinis的芯片如何才能使Google的软件变得不那么愚蠢？弄清这件事的任务落到了Neven身上。他认为量子比特的惊人力量将缩小机器学习和真实生物学习之间的差距——并且重塑人工智能这个领域。他说，「机器学习将转变为量子学习。」这可能意味着软件可以从混乱的数据，或是较少的数据，甚至是在没有明确指示的情况下进行学习。例如，Google的研究人员已经设计了一种算法，通过应用该种算法，他们认为即使在多达一半的范例数据被错误标记的情况下仍然可以让机器学习软件习得某种新的技能。Neven若有所思地说，这种计算能力可能是突破当今人类所能赋予计算机的能力上限的关键。 「人们都在谈论我们能否实现富有创造力的机器——我们能够建立的最富有创造力的系统将会是量子人工智能系统」他说。更现实地来看，在目前仅仅只有D-Wave的机器可供操作的情况下，Google的研究人员能做的只是推测他们应用Martinis制作的芯片之后，能真正实现或者应该去实现的究竟是些什么。即便他们开始着手实践，也需要时间来创造和构建操作大量外设所需的基础设施，之后才能真正对Google的商业业务有实质性的贡献。Neven坚信，Google的量子工匠以及他的团队可以顺利地通过这些考验。他设想在不远的将来，成排的超导芯片在为Google工程师们接入互联网所建立的数据中心里一字排开。他说，「我预测，在10年内最后只会剩下量子机器学习——你再也不用传统的方式来工作了。」面带笑容的Martinis谨慎地接受这一愿景。「我喜欢这一点，但实现它挺难的，」他说， 「他（Neven）可以用嘴说，但我必须建立并实现这一想法。」
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