Several graph theoretic watermark methods have been proposed to encode numbers as graph structures in software watermarking environments. In this paper we propose an efficient and easily implementable codec system for encoding watermark numbers as reducible permutation flow-graphs and, thus, we extend the class of graphs used in such a watermarking environment. More precisely, we present an alg...

We present simple proofs of transience/recurrence for certain card shuffling models, that is, random walks on the infinite symmetric group. 1. Card shuffling models In this note, we consider several models of shuffling an infinite deck of cards. One of these models has been considered previously by Lawler [La]; our methods (using flows, shorting and comparison of Dirichlet forms) will – partial...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fait...

The scheduling of flow shops with multiple parallel machines per stage, usually referred to as the Hybrid Flow Shop (HFS), is a complex combinatorial problem encountered in many real world applications. Given its importance and complexity, the HFS problem has been intensively studied. This paper presents a literature review on exact, heuristic and metaheuristic methods that have been proposed f...

Predicting how changes to the urban environment will affect town centre vitality, mediated as pedestrian flows, is important for environmental, social and economic sustainability. This study is a longitudinal investigation of before and after urban environmental change in a town centre and its association with vitality. The case study baseline is Cardiff town centre in 2007, prior and after maj...