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 efficient approach for network traffic classification

Abstract: Classifiers fail to handle high network traffic and changing node behaviors in efficient manner. Such applications require incremental learning algorithms with low computational complexity and low misclassification rate. This paper presents a model which partitions the training set into equivalence classes on the values of each feature. During classification, algorithm picks up one partial solution set per feature from respective equivalence partition. It collates weak classifiers, thus obtained to classify the test instance in partially lazy manner. The algorithm scores over contemporary classifiers in terms of better complexity for classification, incremental learning complexity and low misclassification rate.

The average time complexity to compute preffix functions in processor networks

Abstract: We analyze the average time complexity of evaluating all prefixes of an input vector over a given algebraic structure 〈Σ,⊗〉. As a computational model networks of finite controls are used and a complexity measure for the average delay of such networks is introduced. Based on this notion, we then define the average case complexity of a computational problem for arbitrary strictly positive input distributions. We give a complete characterization of the average complexity of prefix functions with respect to the underlying algebraic structure 〈Σ,⊗〉 resp. the corresponding Moore-machine M. By considering a related reachability problem for finite automata it is shown that the complexity only depends on two properties of M, called confluence and diffluence. We prove optimal lower bounds for the average case complexity. Furthermore, a network design is presented that achieves the optimal delay for all prefix functions and all inputs of a given length while keeping the network size linear. It differs substantially from the known constructions for the worst case.

Counting Functions for the k-Error Linear Complexity of 2n-Periodic Binary Sequences

Abstract: Linear complexity is an important measure of the cryptographic strength of key streams used in stream ciphers. The linear complexity of a sequence can decrease drastically when a few symbols are changed. Hence there has been considerable interest in the k-error linear complexity of sequences which measures this instability in linear complexity. For 2 n -periodic sequences it is known that minimum number of changes needed per period to lower the linear complexity is the same for sequences with fixed linear complexity. In this paper we derive an expression to enumerate all possible values for the k-error linear complexity of 2 n -periodic binary sequences with fixed linear complexity L, when k equals the minimum number of changes needed to lower the linear complexity below L. For some of these values we derive the expression for the corresponding number of 2 n -periodic binary sequences with fixed linear complexity and k-error linear complexity when k equals the minimum number of changes needed to lower the linear complexity. These results are of importance to compute some statistical properties concerning the stability of linear complexity of 2 n -periodic binary sequences.