Computing short regular expressions equivalent to a given finite automaton is a hard task. In this work we present a class of acyclic automata for which it is easy to find a regular expression that has linear size. We call those automata UDR. A UDR automaton is characterized by properties of its underlying digraph. We present a characterisation theorem and an efficient algorithm to determine if...

The competition hypergraph CH(D) of a digraph D is the hypergraph such that the vertex set is the same as D and e ⊆ V (D) is a hyperedge if and only if e contains at least 2 vertices and e coincides with the in-neighborhood of some vertex v in the digraph D. Any hypergraph H with sufficiently many isolated vertices is the competition hypergraph of an acyclic digraph. The hypercompetition number...

The main purpose of this paper is to exhibit non-algebraic problems that are computationally equivalent to computing the integer determinant. For this purpose, some graph-theoretic counting problems are shown to be equivalent to the integer determinant problem under suitable reducibilities. Those are the problems of counting the number of all paths between two nodes of a given acyclic digraph, ...

We prove a conjecture of Younger, that for every integer n ≥ 0 there exists an integer t ≥ 0 such that for every digraph G, either G has n vertex-disjoint directed circuits, or G can be made acyclic by deleting at most t vertices.

The acyclic directed Steiner tree problem (ADSP) requires a minimal outward tree within an acyclic digraph with edge costs G = (V; E; d) which connects a root r with a distinguished subset S V , #S = k. The best possible performance guarantee of any polynomial approximation algorithm for ADSP cannot be less than 1 4 log k unless ~ P NP. The presented series of heuristics A n has a performance g...

Let C and D be digraphs. A mapping f : V (D) → V (C) is a Ccolouring if for every arc uv of D, either f(u)f(v) is an arc of C or f(u) = f(v), and the preimage of every vertex of C induces an acyclic subdigraph in D. We say that D is C-colourable if it admits a C-colouring and that D is uniquely Ccolourable if it is surjectively C-colourable and any two C-colourings of D differ by an automorphis...

The research reported in this thesis has been partially carried out at CWI, the Dutch national research laboratory for mathematics and computer science, within the theme Data Mining and Knowledge Discovery, a subdivision of the research cluster Information Systems. To the memory of my mother A la memòria de ma mare

Graphical Markov models determined by acyclic digraphs (ADGs), also called directed acyclic graphs (DAOs), are widely studied in statistics, computer science (as Bayesian networks), operations research (as influence diagrams), and many related fields. Because different ADOs may determine the same Markov equivalence class, it long has been of interest to determine the efficiency gained in model ...

Given an undirected graph G = (V,E), and a vertex r ∈ V , an r-acyclic orientation of G is an orientation OE of the edges of G such that the digraph OG = (V,OE) is acyclic and r is the unique vertex with indegree equal to 0. For w ∈ RE+, k(G,w) is the w-maximum packing of r-arborescences for all r ∈ V and all racyclic orientations OE of G. In this case, the Broadcast Routing (in Computers Netwo...