Computational complexity

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  1. computational complexity presents outstanding research in computational complexity.[1]
  2. In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it.[2]
  3. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.[2]
  4. The usual units of time (seconds, minutes etc.) are not used in complexity theory because they are too dependent on the choice of a specific computer and on the evolution of technology.[2]
  5. Complexity theory seeks to quantify the intrinsic time requirements of algorithms, that is, the basic time constraints an algorithm would place on any computer.[2]
  6. This is where computational complexity comes into picture.[3]
  7. The amount of resources required for executing a particular (computation or) algorithm is the computational complexity of that algorithm.[3]
  8. In general, when we talk about complexity we are talking about time complexity and space complexity.[3]
  9. With this in mind, we will be able to determine which algorithm is best for solving a problem, since we can estimate the complexity associated which each and every solution.[3]
  10. The other goal is to use complexity theory as an "excuse" to learn about several tools of broad applicability in computer science.[4]
  11. Computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other.[5]
  12. One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do.[5]
  13. More precisely, computational complexity theory tries to classify problems that can or cannot be solved with appropriately restricted resources.[5]
  14. In computational complexity theory, a problem refers to the abstract question to be solved.[5]
  15. The term “computational complexity” has two usages which must be distinguished.[6]
  16. Contents Algorithms and Complexity To understand what is meant by the complexity of an algorithm, we must define algorithms, problems, and problem instances.[6]
  17. Such a function is called the complexity or running time of the algorithm.[6]
  18. As we have seen, the complexity of an algorithm is only a rough estimate of the number of steps that will be required on an instance.[6]
  19. An historical overview of computational complexity is presented.[7]
  20. Emphasis is on the fundamental issues of defining the intrinsic computational complexity of a problem and proving upper and lower bounds on the complexity of problems.[7]
  21. This book is rooted in the thesis that complexity theory is extremely rich in conceptual content, and that this contents should be explicitly communicated in expositions and courses on the subject.[8]
  22. It focuses on several sub-areas of complexity theory, starting from the intuitive questions addresses by the sub-area.[8]
  23. It is concerned with the study of the intrinsic complexity of computational tasks.[8]
  24. The (half-century) history of Complexity Theory has witnessed two main research efforts (or directions).[8]
  25. The goal of computational complexity is to classify computational problems according to their intrinsic difficulty or “complexity”.[9]
  26. The theory of evolution in structured population has provided an impressive range of results, but an understanding of the computational complexity of even simple questions was missing.[10]
  27. We prove that some fundamental problems in ecology and evolution can be precisely characterized by well-established computational complexity classes.[10]
  28. Central results in computer science describe the complexity of algorithms that solve certain classes of problems.[10]
  29. The complexity hierarchy that is generated in this way is the foundation of theoretical computer science.[10]
  30. The theory of computational complexity provides tools for analysing the minimal amount of computational resources that are needed for algorithmically solving a problem.[11]
  31. Here, we use concepts from computational complexity theory to expose two major weaknesses of the framework.[12]
  32. Instead, we want to shed light on behaviour of biological organisms under complexity.[12]
  33. Then, in §4, we introduce some concepts from computational complexity theory, which we use to assess the computational tractability of the Savage framework.[12]
  34. In §4, we will use computational complexity theory to quantify the computational resource requirements that implementation of the completeness axiom would require.[12]
  35. Demonstrating the non-coincidence of these and other complexity classes remain important open problems in complexity theory.[13]
  36. These problems are typical of those studied in complexity theory in two fundamental respects.[13]
  37. A machine \(M_1\) is said to have lower time complexity (or to run faster than) another machine \(M_2\) if \(t_{M_1}(n) \in O(t_{M_2}(n))\), but not conversely.[13]
  38. The time and space complexity of a problem \(X\) are measured in terms of the worst case time and space complexity of the asymptotically most efficient algorithm for deciding \(X\).[13]
  39. In this article I’ll try to introduce you to the area of computation complexity.[14]
  40. Thus, we will use the O-notation to describe the time (and sometimes also memory) complexity of algorithms.[14]
  41. When speaking about the time/memory complexity of an algorithm, instead of using the formal (f (n))-notation we may simply state the class of functions f belongs to.[14]
  42. The size of alphabet is fixed (e.g. at most 255 in C), thus the algorithm is linear in N. Still, it is better to write that its time complexity is (| S|.N), where S is the alphabet used.[14]
  43. the Second Edition of Theory of Computational Complexity presents updates to the principles and applications essential to understanding modern computational complexity theory.[15]
  44. Each problem has an inherent computational complexity that determines if it is solvable and, if so, how efficiently it can be solved.[16]
  45. This leads to a categorization of problems in different classes with regard to their inherent complexity.[16]

소스

  1. ↑ computational complexity
  2. ↑ 2.0 2.1 2.2 2.3 Computational complexity
  3. ↑ 3.0 3.1 3.2 3.3 What is computational complexity?
  4. ↑ Computational Complexity
  5. ↑ 5.0 5.1 5.2 5.3 Computational complexity theory
  6. ↑ 6.0 6.1 6.2 6.3 Computational Complexity
  7. ↑ 7.0 7.1 An overview of computational complexity
  8. ↑ 8.0 8.1 8.2 8.3 Computational Complexity: A Conceptual Perspective [Goldreich]
  9. ↑ Computational Complexity (INFR11102)
  10. ↑ 10.0 10.1 10.2 10.3 Computational complexity of ecological and evolutionary spatial dynamics
  11. ↑ FIB - Barcelona School of Informatics
  12. ↑ 12.0 12.1 12.2 12.3 Uncertainty and computational complexity
  13. ↑ 13.0 13.1 13.2 13.3 Computational Complexity Theory (Stanford Encyclopedia of Philosophy)
  14. ↑ 14.0 14.1 14.2 14.3 Competitive Programming Tutorials
  15. ↑ Theory of Computational Complexity, 2nd Edition
  16. ↑ 16.0 16.1 Computational Complexity

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  • [{'LOWER': 'computational'}, {'LEMMA': 'complexity'}]
  • [{'LEMMA': 'complexity'}]
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