We deene a notion of asynchronous sliding block map that can be realized by transducers labeled in A B. We show that, under some conditions, it is possible to synchronize this transducer by state splitting, in order to get a transducer which deenes the same sliding block map and which is labeled in A B k , where k is a constant integer. In the case of a transducer with a strongly connected grap...

The Connectivity Server is a special-purpose database whose schema models the Web as a graph graph where URLs are nodes and hyperlinks are directed edges. The Link Database provides fast access to the hyperlinks. To support a wide range of graph algorithms, we find it important to fit the Link Database into memory. In the first version of the Link Database, we achieved this fit by using machine...

We study a connection between synchronizing automata and its set M of minimal reset words, i.e., such that no proper factor is a reset word. We first show that any synchronizing automaton having the set of minimal reset words whose set of factors does not contain a word of length at most 1 4 min{|u| : u ∈ I} + 1 16 has a reset word of length at most (n − 1 2 ) 2. In the last part of the paper w...

We provide space-efficient linear time algorithms for computing bridges, topological sorting, and strongly connected components improving on several recent results of Elmasry et al. [STACS’15], Banerjee et al. [COCOON’16] and Chakraborty et al. [ISAAC’16]. En route, we also provide another DFS implementation with weaker input graph representation assumption without compromising on the time and ...

A complementation operation on a vertex of a digraph changes all outgoing arcs into non-arcs, and outgoing non-arcs into arcs. This defines an equivalence relation where two digraphs are equivalent if one can be obtained from the other by a sequence of such operations. We show that given an adjacency-list representation of a digraph G, many fundamental graph algorithms can be carried out on any...

In this paper we present a formal description of PROSA, a P2P resource management system heavily inspired by social networks. Social networks have been deeply studied in the last two decades in order to understand how communities of people arise and grow. It is a widely known result that networks of social relationships usually evolves to small–worlds, i.e. networks where nodes are strongly con...

A conjecture of Thomassen from 1982 states that, for every k, there is an f(k) so that every strongly f(k)-connected tournament contains k edge-disjoint Hamilton cycles. A classical theorem of Camion, that every strongly connected tournament contains a Hamilton cycle, implies that f(1) = 1. So far, even the existence of f(2) was open. In this paper, we prove Thomassen’s conjecture by showing th...

An out-tree T of a directed graph D is a rooted tree subgraph with all arcs directed outwards from the root. An out-branching is a spanning out-tree. By l(D) and ls(D) we denote the maximum number of leaves over all out-trees and out-branchings of D, respectively. We give fixed parameter tractable algorithms for deciding whether ls(D) ≥ k and whether l(D) ≥ k for a digraph D on n vertices, both...

In this paper we introduce an algorithm for the creation of polyhedral approximations for certain kinds of digital objects in a three-dimensional space. The objects are sets of voxels represented as strongly connected subsets of an abstract cell complex. The proposed algorithm generates the convex hull of a given object and modifies the hull afterwards by recursive repetitions of generating con...