A cyclic order in the vertex set of a digraph is said to be coherent if any arc is contained in a directed cycle whose winding number is one. This notion plays a key role in the proof by Bessy and Thomassé (2004) of a conjecture of Gallai (1964) on covering the vertex set by directed cycles. This paper presents an efficient algorithm for finding a coherent cyclic order in a strongly connected d...

A star is an arborescence in which the root dominates all the other vertices. A galaxy is a vertex-disjoint union of stars. The directed star arboricity of a digraph D, denoted by dst(D), is the minimum number of galaxies needed to cover A(D). In this paper, we show that dst(D) ≤ Δ(D) + 1 and that if D is acyclic then dst(D) ≤ Δ(D). These results are proved by considering the existence of spann...

We study the problem of gathering at the same location two mobile agents that are dispersed in an unknown and unlabeled environment. This problem called Rendezvous, is a fundamental task in distributed coordination among autonomous entities. Most previous studies on the subject model the environment as an undirected graph and the solution techniques rely heavily on the fact that an agent can ba...

6 The dicycle transversal number τ(D) of a digraph D is the mini7 mum size of a dicycle transversal of D, i. e. a set T ⊆ V (D) such that 8 D − T is acyclic. We study the following problem: Given a digraph D, 9 decide if there is a dicycle B in D and a cycle C in its underlying undi10 rected graph UG(D) such that V (B)∩V (C) = ∅. It is known that there is 11 a polynomial time algorithm for this...

We study the following problem: given a strongly connected digraph, find a minimal strongly connected spanning subgraph of it. Our main result is a parallel algorithm for this problem, which runs in polylog parallel time and uses O(n) processors on a PRAM. Our algorithm is simple and the major tool it uses is computing a minimum-weight branching with zero-one weights. We also present sequential...

The Gallai-Milgram theorem states that every directed graph D is spanned by α(D) disjoint directed paths, where α(D) is the size of a largest stable set of D. When α(D) > 1 and D is strongly connected, it has been conjectured by Las Vergnas (cited in [1] and [2]) that D is spanned by an arborescence with α(D)− 1 leaves. The case α = 2 follows from a result of Chen and Manalastas [5] (see also B...

In this paper, we study the structural state and input observability of continuous-time switched linear time-invariant systems unknown inputs. First, provide necessary sufficient conditions for their that can be efficiently verified in O ( m n + p ) 2 , where is number variables, inputs, modes. Moreover, address minimum sensor placement problem these by adopting a feed-forward analysis providin...

In this paper we propose a new decentralized algorithm to solve the consensus on the average problem on arbitrary strongly connected digraphs through a gossip algorithm based on broadcasts. We directly extend previous results by not requiring that the digraph is balanced. Our algorithm is an improvement respect to known gossip algorithms based on broadcasts in that the average of the initial st...

The statistical properties for bicoherence estimation are shown to be strongly connected to the properties of the powerand bispectral estimator used. Data tapering will reduce spectral leakage and frequency smoothing will reduce the variance. It is shown that correct normalization is essential to ensure unbiased results. The multitaper approach is shown to be superior to other non-parametric es...

A distributed algorithm is developed that can be used to compute the topology of a network, given that each site starts with information about sites it is adjacent to, the network is strongly connected, and communication channels are unidirectional. The program is derived using assertional reasoning.