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.

Complexity-Reduced Algorithms for LDPC Decoder for DVB-S2 Systems

Abstract: This paper proposes two kinds of complexity-reduced algorithms for a low density parity check (LDPC) decoder. First, sequential decoding using a partial group is proposed. It has the same hardware complexity and requires a fewer number of iterations with little performance loss. The amount of performance loss can be determined by the designer, based on a tradeoff with the desired reduction in complexity. Second, an early detection method for reducing the computational complexity is proposed. Using a confidence criterion, some bit nodes and check node edges are detected early on during decoding. Once the edges are detected, no further iteration is required; thus early detection reduces the computational complexity.

Straight-line program length as a parameter for complexity measures

Abstract: This paper represents a continuation of work in [LBI] and [LB2] directed toward the development of a unified, relative model for complexity theory. The earlier papers establish a simple, natural and fairly general model, and demonstrated its attractiveness by using it to state and prove a variety of technical results. The present paper uses the same model but deals more specifically with the problems involved in stating complexity bounds in a usable closed form for arbitrary operations on arbitrary data types. Work currently in progress is directed toward similar unified treatment of complexity of data structures.

Machine-Independent Complexity Theory.

Abstract: Publisher Summary This chapter discusses machine-independent complexity theory. The familiar measures of computational complexity are time and space. Time is considered as the number of discrete steps in a computation, and space as the number of distinct storage locations accessed by the instructions of the computation. The machines consist of a finite-state program with access to an input tape and a single storage tape. Recorded on the input tape is an input word, a nonnull, finite string of characters from some finite input alphabet. Recorded on the storage tape is a string of characters from the fixed, binary alphabet. The initial content of the storage tape is the trivial word 0 of length 1. A separate tape head is maintained in some position, initially the leftmost one, on each of the two tapes. The finite-state program consists of a finite set of states, one of which is designated as the initial one, and a finite function indicating how each next computational action depends on the visible display of the current total state of the entire machine.

Complexity Results for Enhanced Qualitative Probabilistic Networks.

Abstract: While quantitative probabilistic networks (QPNs) allow experts to state influences between nodes in the network as influence signs, rather than conditional probabilities, inference in these networks often leads to ambiguous results due to unresolved trade-offs in the network. Various enhancements have been proposed that incorporate a notion of strength of the influence, such as enhanced and rich enhanced operators. Although inference in standard (i.e. not enhanced) QPNs can be done in time polynomial to the length of the input, the computational complexity of inference in these enhanced networks has not been determined yet. In this paper, we introduce relaxation schemes to relate these enhancements to the more general case, where continuous influence intervals are used. We show that inference in networks with continuous influence intervals is NP-hard, and remains NP-hard when the intervals are discretised and the interval [-1,1] is divided into blocks with length of 14. We discuss membership of NP and show how these general complexity results may be used to determine the complexity of specific enhancements to QPNs. Furthermore, this might give more insight in the particular properties of feasible and infeasible approaches to enhance QPNs.

Relativized Worlds without Worst-Case to Average-Case Reductions for NP

Abstract: We prove that, relative to an oracle, there is no worst-case to average-case reduction for NP. We also handle classes that are somewhat larger than NP, as well as worst-case to errorless-average-case reductions. In fact, we prove that relative to an oracle, there is no worst-case to errorless-average-case reduction from NP to BPPpNP. We also handle reductions from NP to the polynomial-time hierarchy and beyond, under strong restrictions on the number of queries the reductions can make.