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.

An Dynamic Lot-Sizing Model with Multi-Mode Shipments ∗

Abstract: In this paper, we consider a two-echelon dynamic lot-sizing problem with multiple ship- ment modes between the warehouse and the distribution center. We present an optimal polynomial algorithm for this problem. The computational complexity of the algorithm is O(T 5 ), where T is the length of the finite planning horizon.

On the average-case complexity of Shellsort

Abstract: We prove a lower bound expressed in the increment se- quence on the average-case complexity of the number of inversions of Shellsort. This lower bound is sharp in every case where it could be checked. A special case of this lower bound yields the general Jiang-Li-Vitanyi lower bound. We obtain new results, for example, determining the average- case complexity precisely in the Yao-Janson-Knuth 3-pass case.

Average-Case Complexity of Learning Polynomials

Abstract: The present paper deals with the averagecase complexity of various algorithms for learning univariate polynomials For this purpose an appropriate framework is introduced Based on it, the learnability of univariate polynomials evaluated over the natural numbers and of univariate polynomials defined over finite fields is analyzed Our results are manifold In the first case, convergence is measured not relative to the degree of a polynomial but with respect to a measure that takes the degree and the size of the coefficients into account Then standard interpolation is proved not to be the best possible algorithm with respect to the average number of examples needed In general, polynomials over finite fields are not uniquely specified by their input-outputbehavior Thus, as a new form of data representation the remainders modulo other polynomials is proposed and the expected example complexity is analyzed for a rather rich class of probability distributions

An average-case analysis for a continuous random search algorithm

Abstract: We give an upper bound for the average complexity (i.e. the expected number of steps until termination) for a continuous random search algorithm using results from renewal theory. It is thus possible to show that for a predefined accuracy £, the average complexity of the algorithm is 0 (-log £) for £ ~ ° which is optimal up to a constant factor. AVERAGE COMPLEXITY; BINARY SEARCH; RENEWAL THEORY

First look at average-case complexity for planar maximum-likelihood detection

Abstract: In this paper, an efficient exact maximum-likelihood (ML) detection scheme is presented for a multiple-input single-output (MISO) system with real signal constellations. The proposed technique has a geometrical interpretation of exploring the points jointly "close" in all coordinate axes around the decoding hyperplane and is therefore dubbed planar detection. The fact that the lattice points which are close in all coordinate axes are much less, leads to dramatic reduction in detection complexity. Making a few approximations, this paper derives the average-case complexity exponent, ec, for planar detection analytically in a closed form. Numerical results show that for an (n, 1) system, although the expected complexity is still exponential, complexity reduction of 2 exponents, i.e., from ec to ec -2, is realized and such advantage is promised irrespective of the size of the signal constellations and the received signal-to-noise ratio (SNR)