Average-case complexity

About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.

A Simple Modification of Xunrang and Yuzhang'S HEAPSORT Variant Improving its Complexity Significantly

Abstract: Xunrang and Yuzhang have presented the HEAPSORT variant NEWheapsort whose worst case complexity is (4/3)n log 2 n+O(n). By a simple modification this algorithm can he improved to have a better average case complexity and a worst case complexity of only (7/6)n log 2 n+O(n)

Complexity of parallel algorithms

Abstract: In this chapter we discuss the analysis of parallel algorithms, especially their complexity. The complexity of serial algorithms is usually measured by the number of arithmetic operations. But the complexity of parallel algorithms is measured by the time, in which they can be implemented on a k-processor computer.

Computational complexity theory

Abstract: Computational complexity is the study of the resources, such as time and space (memory), required to solve computational problems. By quantifying these resources, complexity theory has profoundly affected our thinking about computation. Computability theory establishes the existence of undecidable problems that cannot be solved in principle, regardless of the amount of time invested. In contrast, complexity theory establishes the existence of decidable problems that, although solvable in principle, cannot be solved in practice, because the time and space required would be larger than the age and size of the known universe [Stockmeyer and Chandra 1979]. The quest for the boundaries of the set of feasible problems, those solvable in practice, has led to one of the most important unresolved questions in computer science: Is P different from NP? Here P comprises the problems that can be solved feasibly in polynomial time and NP comprises the problems whose solutions can be verified in polynomial time. Hundreds of fundamental problems, including many ubiquitous optimization problems of operations research, are NP-complete—they are the hardest problems in NP. If there is a polynomial-time algorithm for any one NP-complete problem, then there would be polynomial-time algorithms for all of them. Despite the efforts of many scientists over several decades, no polynomialtime algorithm has been found for any NP-complete problem. Although no one knows whether P is different from NP, showing that a problem is NP-complete provides strong evidence that the problem is computationally infeasible and justifies the use of heuristics for solving the problem.

Algorithms and Their Complexity

Abstract: In this book we often describe and analyze algorithms on digraphs. We concentrate more on graph-theoretical aspects of these algorithms than on their actual implementation on a computer. Thus, in many cases only the most basic knowledge on algorithms and complexity is required and many readers are familiar with it. However, sometimes we use less familiar terminology and notation. In particular, we sometimes say that some problem is fixed-parameter tractable or W[1]-hard.

Linear complexity for sequences with characteristic polynomial ƒ v

Abstract: We present several generalisations of the Games-Chan algorithm. For a fixed monic irreducible polynomial ƒ we consider the sequences s that have as characteristic polynomial a power of ƒ. We propose an algorithm for computing the linear complexity of s given a full (not necessarily minimal) period of s. We give versions of the algorithm for fields of characteristic 2 and for arbitrary finite characteristic p, the latter generalising an algorithm of Kaida et al. We also propose an algorithm which computes the linear complexity given only a finite portion of s (of length greater than or equal to the linear complexity), generalising an algorithm of Meidl. All our algorithms have linear computational complexity. The algorithms for computing the linear complexity when a full period is known can be further generalised to sequences for which it is known a priori that the irreducible factors of the minimal polynomial belong to a given small set of polynomials.