Maximum-Order Complexity and Correlation Measures

The Maximum Order Complexity of Sequence Ensembles

Two Useful Measures Of Word Order Complexity

This paper presents a class of dependency-based for-real grammars (FODG) which can be parametrized by two different but similar measures of non-projectivity. The measures allow to formulate constraints on the degree of word-order freedom in a language described by a FODG. We discuss the problem of the degree of word-order freedom which should be allowed ~, a FODG describing the (surface) syntax...

The Complexity of Maximum k-Order Bounded Component Set Proble

Given a graph G = (V, E) and a positive integer k, in MAXIMUM k-ORDER BOUNDED COMPONENT SET (MAX-k-OBCS), it is required to find a vertex set S ⊆ V of maximum size such that each component in the induced graph G[S] has at most k vertices. We prove that for constant k, MAX-k-OBCS is hard to approximate within a factor of n1−e, for any e > 0, unless P = NP. This is an improvement on the previous ...

An Approximate Distribution for the Maximum Order Complexity

In this paper we give an approximate probability distribution for the maximum order complexity of a random binary sequence This enables the development of statistical tests based on maximum order complexity for the testing of a binary sequence generator These tests are analogous to those based on linear complexity

On Two Measures of Problem Instance Complexity and their Correlation with the Performance of SeDuMi on Second-Order Cone Problems

We evaluate the practical relevance of two measures of conic convex problem complexity as applied to second-order cone problems solved using the homogeneous self-dual (HSD) embedding model in the software SeDuMi. The first measure we evaluate is Renegar’s data-based condition measure C(d), and the second measure is a combined measure of the optimal solution size and the initial infeasibility/op...