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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/advanced-algorithms-and-complexity
课程评论：没有评论
课程名称：高级算法与复杂性 课程概述：在之前的在线专业课程中，您已学习了基础算法，现已准备好进入更复杂的算法与问题领域。高级算法是在基础算法基础上发展而来，融入了新的思路。本课程首先讨论网络流，这在应用中用于优化匹配、寻找不相交路径和航班调度，并且在计算机视觉中的图像分割等意想不到的问题中也会用到。接下来，我们将探讨线性规划及其在预算分配、投资组合优化、满足所有要求的便宜饮食的寻找等多方面的应用。我们还将讨论一些本质上难以解决的问题，这些问题没有已知的良好精确解法（而且不太可能找到）。最后，我们将对流式算法进行简单介绍，这些算法在大数据处理中的应用非常广泛，旨在处理巨大数据集而无需存储整个数据。 课程大纲： 1. 网络流 - 描述：网络流在许多现实情况中都会出现，例如需要在有限容量的网络中运输货物。我们将讨论网络流的数学基础及一些重要的流算法，并给出一些意想不到的例子，展示如何利用网络流来解决看似无关的问题。 2. 线性规划 - 描述：线性规划是一种强大的算法工具，其基本问题是要求在一组线性不等式约束下优化一个关于实变量的线性函数。该框架可广泛用于讨论协议优化、生产流程优化以及寻找最便宜的健康饮食方案等各种问题。本单元将强调线性规划问题的重要性及其解决工具。 3. NP完全问题 - 描述：虽然您所学的许多算法在实践中应用广泛，但许多实际问题并没有已知的有效算法。这些问题通常可以归约为经典的NP完全问题，这些问题无法通过多项式算法解决。我们将在本模块中学习经典的NP完全问题及它们之间的归约，并探讨如何使用专门的软件高效求解一些大规模实例。 4. 应对NP完全性 - 描述：在学习完前一个模块后，您可能会感到沮丧：您才刚学习完五门算法课程，却发现它们并不适用于大多数实际问题。然而，人们总能找到解决NP完全问题的创新方法。本单元中，我们将展示某些特殊情况下的NP完全问题实际上可以在多项式时间内解决，并探讨比暴力算法更快的精确算法以及接近最优解的近似算法。 5. 流式算法（可选） - 描述：在大多数之前的课程中，我们关注的是设计运行时间快的算法，并假设算法可以随机访问输入数据。然而，在大数据分析的现代应用中，输入数据通常过大以至于无法存储在内存中。这一单元研究了流式计算模型，并介绍了基于这一模型的小空间算法，其中一些强大的算法在实际大数据分析中具有影响力。我们将学习一种流式算法（CountSketch），用于在数据流中找到前k个最频繁的项。
Name:Flows in Networks
Description:Network flows show up in many real world situations in which a good needs to be transported across a network with limited capacity. You can see it when shipping goods across highways and routing packets across the internet. In this unit, we will discuss the mathematical underpinnings of network flows and some important flow algorithms. We will also give some surprising examples on seemingly unrelated problems that can be solved with our knowledge of network flows.
Name:Linear Programming
Description:Linear programming is a very powerful algorithmic tool. Essentially, a linear programming problem asks you to optimize a linear function of real variables constrained by some system of linear inequalities. This is an extremely versatile framework that immediately generalizes flow problems, but can also be used to discuss a wide variety of other problems from optimizing production procedures to finding the cheapest way to attain a healthy diet. Surprisingly, this very general framework admits efficient algorithms. In this unit, we will discuss some of the importance of linear programming problems along with some of the tools used to solve them.
Name:NP-complete Problems
Description:Although many of the algorithms you've learned so far are applied in practice a lot, it turns out that the world is dominated by real-world problems without a known provably efficient algorithm. Many of these problems can be reduced to one of the classical problems called NP-complete problems which either cannot be solved by a polynomial algorithm or solving any one of them would win you a million dollars (see Millenium Prize Problems) and eternal worldwide fame for solving the main problem of computer science called P vs NP. It's good to know this before trying to solve a problem before the tomorrow's deadline :) Although these problems are very unlikely to be solvable efficiently in the nearest future, people always come up with various workarounds. In this module you will study the classical NP-complete problems and the reductions between them. You will also practice solving large instances of some of these problems despite their hardness using very efficient specialized software based on tons of research in the area of NP-complete problems.
Name:Coping with NP-completeness
Description:After the previous module you might be sad: you've just went through 5 courses in Algorithms only to learn that they are not suitable for most real-world problems. However, don't give up yet! People are creative, and they need to solve these problems anyway, so in practice there are often ways to cope with an NP-complete problem at hand. We first show that some special cases on NP-complete problems can, in fact, be solved in polynomial time. We then consider exact algorithms that find a solution much faster than the brute force algorithm. We conclude with approximation algorithms that work in polynomial time and find a solution that is close to being optimal.
Name:Streaming Algorithms (Optional)
Description:In most previous lectures we were interested in designing algorithms with fast (e.g. small polynomial) runtime, and assumed that the algorithm has random access to its input, which is loaded into memory. In many modern applications in big data analysis, however, the input is so large that it cannot be stored in memory. Instead, the input is presented as a stream of updates, which the algorithm scans while maintaining a small summary of the stream seen so far. This is precisely the setting of the streaming model of computation, which we study in this lecture. The streaming model is well-suited for designing and reasoning about small space algorithms. It has received a lot of attention in the literature, and several powerful algorithmic primitives for computing basic stream statistics in this model have been designed, several of them impacting the practice of big data analysis. In this lecture we will see one such algorithm (CountSketch), a small space algorithm for finding the top k most frequent items in a data stream.
In previous courses of our online specialization you've learned the basic algorithms, and now you are ready to step into the area of more complex problems and algorithms to solve them. Advanced algorithms build upon basic ones and use new ideas. We will start with networks flows which are used in more typical applications such as optimal matchings, finding disjoint paths and flight scheduling as well as more surprising ones like image segmentation in computer vision. We then proceed to linear programming with applications in optimizing budget allocation, portfolio optimization, finding the cheapest diet satisfying all requirements and many others. Next we discuss inherently hard problems for which no exact good solutions are known (and not likely to be found) and how to solve them in practice. We finish with a soft introduction to streaming algorithms that are heavily used in Big Data processing. Such algorithms are usually designed to be able to process huge datasets without being able even to store a dataset.
