We study the half-integral k-Directed Disjoint Paths Problem ( 2kDDPP) in highly strongly connected digraphs. The integral kDDPP is NP-complete even when restricted to instances where k = 2, and the input graph is L-strongly connected, for any L ≥ 1. We show that when the integrality condition is relaxed to allow each vertex to be used in two paths, the problem becomes efficiently solvable in h...

In this paper, we propose a metric for measuring the complexity of a DTD. For the same purpose, different designers may create different DTDs. A complexity metric can assist us to evaluate and compare their different merits. Through the recognition of strongly connected components, the metric accommodates the recursive relationship of elements in a DTD. The metric presented here can be expresse...

Article history: Received 15 April 2014 Accepted 5 May 2014 Available online 29 May 2014 Submitted by R. Brualdi MSC: 05C20 05C50 15A18

We present an algorithm for computing nearly recurrent components, that represent areas of close to circulating or stagnant flow, for 3D piecewise constant (PC) vector fields defined on regular grids. Using a number of analytical and simulated data sets, we demonstrate that nearly recurrent components can provide interesting insight into the topological structure of 3D vector fields. Our approa...

In this paper we introduce cyclic level planar graphs, which are a planar version of the recurrent hierarchies from Sugiyama et al. [8] and the cyclic extension of level planar graphs, where the first level is the successor of the last level. We study the testing and embedding problem and solve it for strongly connected graphs in time O(|V | log |V |).

In the paper different roles of users in social media, taking into consideration their strength of influence and different degrees of cooperativeness, are introduced. Such identified roles are used for the analysis of characteristics of groups of strongly connected entities. The different classes of groups, considering the distribution of roles of users belonging to them, are presented and disc...

Almost all numerical methods for solving conservative problems cannot avoid a more or less perceptible drift phenomenon. Considering that the drift would be absent on a periodic or quasi-periodic solution, one way to eliminate such unpleasant phenomenon is to look for discrete periodic or quasi-periodic solutions. It is quite easy to show that only symmetric methods are able to provide solution...

A multipartite tournament is an orientation of a complete c-partite graph. In [L. Volkmann, A remark on cycles through an arc in strongly connected multipartite tournaments, Appl. Math. Lett. 20 (2007) 1148–1150], Volkmann proved that a strongly connected cpartite tournament with c > 3 contains an arc that belongs to a directed cycle of length m for every m ∈ {3, 4, . . . , c}. He also conjectu...

This paper presents an algorithm which solves exponentially fast the average consensus problem on strongly connected network of digital links. The algorithm is based on an efficient zooming-in/zooming-out quantization scheme.