Search results for "data structures"
showing 10 items of 258 documents
Grundy coloring for power graphs
2003
International audience
Partially Square Graphs, Hamiltonicity and Circumference II
2000
Abstract Given a graph G, its partially square graph G∗ is a graph obtained by adding an edge uv for each pair u, v of vertices of G at distance 2 whenever the vertices u and v have a common neighbor x satisfying the condition NG(x) ⊆ NG[u] ∪ NG[v], where NG[x]= NG(x) ∪ {x}. In case G is a claw-free graph, G∗ is equal to G2, We define σ ∗ t = min{ ∑ x∈ d ∗ G (x): S is an independent set in G ∗ and ∣S∣ = t} , where d ∗ G (x) = ∣{y ∈ V∣ xy ∈ E(G∗)}∣ . We give for hamiltonicity and circumference new sufficient conditions depending on and we improve some known results.
Forbidden words in symbolic dynamics
2000
AbstractWe introduce an equivalence relation≃between functions from N to N. By describing a symbolic dynamical system in terms of forbidden words, we prove that the≃-equivalence class of the function that counts the minimal forbidden words of a system is a topological invariant of the system. We show that the new invariant is independent from previous ones, but it is not characteristic. In the case of sofic systems, we prove that the≃-equivalence of the corresponding functions is a decidable question. As a more special application, we show, by using the new invariant, that two systems associated to Sturmian words having “different slope” are not conjugate.
Generation of Valid Labeled Binary Trees
2003
International audience; Generating binary trees is a well-known problem. In this paper, we add some constraints to leaves of these trees. Such trees are used in the morphing of polygons, where a polygon P is represented by a binary tree T and each angle of P is a weight on a leaf of T. In the following, we give two algorithms to generate all binary trees, without repetitions, having the same weight distribution to their leaves and representing all parallel polygons to P.
NP-completeness of the hamming salesman problem
1985
It is shown that the traveling salesman problem, where cities are bit strings with Hamming distances, is NP-complete.
Combinatorics of Finite Words and Suffix Automata
2009
The suffix automaton of a finite word is the minimal deterministic automaton accepting the language of its suffixes. The states of the suffix automaton are the classes of an equivalence relation defined on the set of factors. We explore the relationship between the combinatorial properties of a finite word and the structural properties of its suffix automaton. We give formulas for expressing the total number of states and the total number of edges of the suffix automaton in terms of special factors of the word.
Sturmian Graphs and a conjecture of Moser
2004
In this paper we define Sturmian graphs and we prove that all of them have a “counting” property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of CDAWGs of central Sturmian words. We show also that, analogously to the case of Sturmian words, these graphs converge to infinite ones.
The Alternating BWT: an algorithmic perspective
2020
Abstract The Burrows-Wheeler Transform (BWT) is a word transformation introduced in 1994 for Data Compression. It has become a fundamental tool for designing self-indexing data structures, with important applications in several areas in science and engineering. The Alternating Burrows-Wheeler Transform (ABWT) is another transformation recently introduced in Gessel et al. (2012) [21] and studied in the field of Combinatorics on Words. It is analogous to the BWT, except that it uses an alternating lexicographical order instead of the usual one. Building on results in Giancarlo et al. (2018) [23] , where we have shown that BWT and ABWT are part of a larger class of reversible transformations, …
Minimal forbidden words and symbolic dynamics
1996
We introduce a new complexity measure of a factorial formal language L: the growth rate of the set of minimal forbidden words. We prove some combinatorial properties of minimal forbidden words. As main result we prove that the growth rate of the set of minimal forbidden words for L is a topological invariant of the dynamical system defined by L.
A Graph Based Algorithm For Intersection Of Subdivision Surfaces
2003
Computing surface intersections is a fundamental problem in geometric modeling. Any boolean operation can be seen as an intersection calculation followed by a selection of the parts necessary for building the surface of the resulting object. A robust and efficient algorithm to compute intersection on subdivision surfaces (surfaces generated by the Loop scheme) is proposed here. This algorithm relies on the concept of a bipartite graph which allows the reduction of the number of faces intersection tests. Intersection computations are accelerated by the use of the bipartite graph and the neighborhood of intersecting faces at a given level of subdivision to deduce intersecting faces at the fol…