COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions
http://hdl.handle.net/2117/3178
2017-04-29T15:37:00ZGeneral properties of c-circulant digraphs
http://hdl.handle.net/2117/103764
General properties of c-circulant digraphs
Mora Giné, Mercè; Serra Albó, Oriol; Fiol Mora, Miquel Àngel
A digraph is said to be a c-circulant if its adjacency matrix is c-circulant. This paper deals with general properties of this family of digraphs, as isomorphisms, regularity, strong connectivity, diameter and the relation between c-circulant digraphs and the line digraph technique.
2017-04-26T17:41:13ZMora Giné, MercèSerra Albó, OriolFiol Mora, Miquel ÀngelA digraph is said to be a c-circulant if its adjacency matrix is c-circulant. This paper deals with general properties of this family of digraphs, as isomorphisms, regularity, strong connectivity, diameter and the relation between c-circulant digraphs and the line digraph technique.Online graph coloring with advice and randomized adversary
http://hdl.handle.net/2117/103686
Online graph coloring with advice and randomized adversary
Muñoz López, Francisco Javier
We generalize the model of online computation with three players (algorithm, adversary and an oracle called advisor) by strength- ening the power of the adversary by randomization. In our generalized model, the advisor knows everything about the adversary except the ran- dom bits the adversary may use.
We examine the expected competitive ratio of online algorithms within this model in order to measure the hardness of online problems in a new way. We start our investigation by proving upper and lower bounds on the competitive ratio for the online graph coloring problem.
2017-04-25T08:19:49ZMuñoz López, Francisco JavierWe generalize the model of online computation with three players (algorithm, adversary and an oracle called advisor) by strength- ening the power of the adversary by randomization. In our generalized model, the advisor knows everything about the adversary except the ran- dom bits the adversary may use.
We examine the expected competitive ratio of online algorithms within this model in order to measure the hardness of online problems in a new way. We start our investigation by proving upper and lower bounds on the competitive ratio for the online graph coloring problem.Rainbow eulerian multidigraphs and the product of cycles
http://hdl.handle.net/2117/103675
Rainbow eulerian multidigraphs and the product of cycles
López Masip, Susana Clara; Muntaner Batle, Francesc Antoni
An arc colored eulerian multidigraph with l colors is rainbow eulerian if there is an
eulerian circuit in which a sequence of l colors repeats. The digraph product that refers the title was introduced by Figueroa-Centeno et al. as follows: let D be a digraph and let G be a family of digraphs such that V (F) = V for every F ¿ G
2017-04-24T12:14:28ZLópez Masip, Susana ClaraMuntaner Batle, Francesc AntoniAn arc colored eulerian multidigraph with l colors is rainbow eulerian if there is an
eulerian circuit in which a sequence of l colors repeats. The digraph product that refers the title was introduced by Figueroa-Centeno et al. as follows: let D be a digraph and let G be a family of digraphs such that V (F) = V for every F ¿ GDistance labelings: a generalization of Langford sequences
http://hdl.handle.net/2117/103670
Distance labelings: a generalization of Langford sequences
López Masip, Susana Clara; Muntaner Batle, Francesc Antoni
A Langford sequence of order m and defect d can be identified with a labeling of the
vertices of a path of order 2m in which each labeled from d up to d + m - 1 appears twice and in which the vertices that have been label with k are at distance k. In this paper, we introduce two generalizations of this labeling that are related to distances.; Articles in this journal are published under Creative Commons Attribution 3.0 License
http://creativecommons.org/licenses/by/3.0/
2017-04-24T11:38:49ZLópez Masip, Susana ClaraMuntaner Batle, Francesc AntoniA Langford sequence of order m and defect d can be identified with a labeling of the
vertices of a path of order 2m in which each labeled from d up to d + m - 1 appears twice and in which the vertices that have been label with k are at distance k. In this paper, we introduce two generalizations of this labeling that are related to distances.
Articles in this journal are published under Creative Commons Attribution 3.0 License
http://creativecommons.org/licenses/by/3.0/Feedforwarding : Plan, desarrollo y evaluación de un caso mediante el uso de campus virtual
http://hdl.handle.net/2117/103659
Feedforwarding : Plan, desarrollo y evaluación de un caso mediante el uso de campus virtual
Fabregat Fillet, Jaume; Pelayo Melero, Ignacio Manuel
La población de estudiantes puede ver los espacios de evaluación más
como calificadores/clasificadores que como formativos; en numerosos
contextos no se trata exclusivamente de una perspectiva, de “su” perspectiva
personal, sino que muchas veces, de hecho, “por tradición” las
cosas han sido así.
2017-04-24T10:04:17ZFabregat Fillet, JaumePelayo Melero, Ignacio ManuelLa población de estudiantes puede ver los espacios de evaluación más
como calificadores/clasificadores que como formativos; en numerosos
contextos no se trata exclusivamente de una perspectiva, de “su” perspectiva
personal, sino que muchas veces, de hecho, “por tradición” las
cosas han sido así.Genera Esfera: Interacting with a trackball mapped onto a sphere to explore generative visual worlds
http://hdl.handle.net/2117/103657
Genera Esfera: Interacting with a trackball mapped onto a sphere to explore generative visual worlds
Barrière Figueroa, Eulalia; Carreras, Anna
Genera Esfera is an interactive installation that allows the audience to interact and easily become a VJ (visual
DJ) in a world of generative visuals. It is an animated and generative graphic environment with a music playlist,
a visual spherical world related with and suggested by the music, which reacts and evolves. The installation has
been presented at MIRA Live Visual Arts Festival 2015, in Barcelona. Genera Esfera was envisioned, developed
and programmed on the basis of two initial ideas: first, to generate our spherical planets we need to work with
spherical geometry and program 3D graphics; second, the interaction should be easy to understand, proposing a
direct mapping between the visuals and the interface. Our main goal is that participants can focus on exploring the
graphic worlds rather than concentrate on understanding the interface. For that purpose we use a trackball to map
its position onto sphere rotations. In this paper, we present the interactive installation Genera Esfera, the design
guidelines, the mathematics behind the generative visuals and its results.
2017-04-24T09:27:48ZBarrière Figueroa, EulaliaCarreras, AnnaGenera Esfera is an interactive installation that allows the audience to interact and easily become a VJ (visual
DJ) in a world of generative visuals. It is an animated and generative graphic environment with a music playlist,
a visual spherical world related with and suggested by the music, which reacts and evolves. The installation has
been presented at MIRA Live Visual Arts Festival 2015, in Barcelona. Genera Esfera was envisioned, developed
and programmed on the basis of two initial ideas: first, to generate our spherical planets we need to work with
spherical geometry and program 3D graphics; second, the interaction should be easy to understand, proposing a
direct mapping between the visuals and the interface. Our main goal is that participants can focus on exploring the
graphic worlds rather than concentrate on understanding the interface. For that purpose we use a trackball to map
its position onto sphere rotations. In this paper, we present the interactive installation Genera Esfera, the design
guidelines, the mathematics behind the generative visuals and its results.A geometric approach to dense Cayley digraphs of finite Abelian groups
http://hdl.handle.net/2117/103505
A geometric approach to dense Cayley digraphs of finite Abelian groups
Aguiló Gost, Francisco de Asis L.; Fiol Mora, Miquel Àngel; Pérez Mansilla, Sonia
We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related {\em minimum distance diagrams}. A {\em dilating} technique for these diagrams, which can be used for any degree of the digraph, is applied to generate the digraphs of the family. Moreover, two infinite families of digraphs with distinguished metric properties will be given using these methods. The first family contains digraphs with asymptotically large ratio between the order and the diameter as the degree increases (moreover it is the first known asymptotically dense family). The second family, for fixed degree $d=3$, contains digraphs with the current best known density.
2017-04-18T10:02:58ZAguiló Gost, Francisco de Asis L.Fiol Mora, Miquel ÀngelPérez Mansilla, SoniaWe give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related {\em minimum distance diagrams}. A {\em dilating} technique for these diagrams, which can be used for any degree of the digraph, is applied to generate the digraphs of the family. Moreover, two infinite families of digraphs with distinguished metric properties will be given using these methods. The first family contains digraphs with asymptotically large ratio between the order and the diameter as the degree increases (moreover it is the first known asymptotically dense family). The second family, for fixed degree $d=3$, contains digraphs with the current best known density.Commensurations and metric properties of Houghton's groups
http://hdl.handle.net/2117/103242
Commensurations and metric properties of Houghton's groups
Burillo Puig, José; Cleary, Sean; Martino, Armando; Röver, Claas E.
We describe the automorphism groups and the abstract commensurators of Houghton’s groups. Then we give sharp estimates for the word metric of these groups and deduce that the commensurators embed into the corresponding quasi-isometry groups. As a further consequence, we obtain that the Houghton group on two rays is at least quadratically distorted in those with three or more rays.
2017-04-04T07:32:32ZBurillo Puig, JoséCleary, SeanMartino, ArmandoRöver, Claas E.We describe the automorphism groups and the abstract commensurators of Houghton’s groups. Then we give sharp estimates for the word metric of these groups and deduce that the commensurators embed into the corresponding quasi-isometry groups. As a further consequence, we obtain that the Houghton group on two rays is at least quadratically distorted in those with three or more rays.Layer structure of De Bruijn and Kautz digraphs: an application to deflection routing
http://hdl.handle.net/2117/103040
Layer structure of De Bruijn and Kautz digraphs: an application to deflection routing
Fàbrega Canudas, José; Martí Farré, Jaume; Muñoz López, Francisco Javier
In the main part of this paper we present polynomial expressions for the cardinalities of some sets of interest of the nice distance-layer structure of the well-known De Bruijn and Kautz digraphs. More precisely, given a vertex $v$, let $S_{i}^\star(v)$ be the set of vertices at distance $i$ from $v$. We show that $|S_{i}^\star(v)|=d^i-a_{i-1}d^{i-1}-\cdots -a_{1} d-a_{0}$, where $d$ is the degree of the digraph and the coefficients $a_{k}\in\{0,1\}$ are explicitly calculated. Analogously, let $w$ be a vertex adjacent from $v$ such that $S_{i}^\star(v)\cap S_j^{\ast}(w)\neq \emptyset$ for some $j$. We prove that $\big |S_{i}^\star(v) \cap S_j^{\ast}(w) \big |=d^i-b_{i-1}d^{i-1}-\ldots -b_{1} d-b_{0},$ where the coefficients $b_{t}\in\{0,1\}$ are determined from the coefficients $a_k$ of the polynomial expression of $|S_{i}^\star(v)|$. An application to deflection routing in De Bruijn and Kautz networks serves as motivation for our study. It is worth-mentioning that our analysis can be extended to other families of digraphs on alphabet or to general iterated line digraphs.
2017-03-29T12:12:53ZFàbrega Canudas, JoséMartí Farré, JaumeMuñoz López, Francisco JavierIn the main part of this paper we present polynomial expressions for the cardinalities of some sets of interest of the nice distance-layer structure of the well-known De Bruijn and Kautz digraphs. More precisely, given a vertex $v$, let $S_{i}^\star(v)$ be the set of vertices at distance $i$ from $v$. We show that $|S_{i}^\star(v)|=d^i-a_{i-1}d^{i-1}-\cdots -a_{1} d-a_{0}$, where $d$ is the degree of the digraph and the coefficients $a_{k}\in\{0,1\}$ are explicitly calculated. Analogously, let $w$ be a vertex adjacent from $v$ such that $S_{i}^\star(v)\cap S_j^{\ast}(w)\neq \emptyset$ for some $j$. We prove that $\big |S_{i}^\star(v) \cap S_j^{\ast}(w) \big |=d^i-b_{i-1}d^{i-1}-\ldots -b_{1} d-b_{0},$ where the coefficients $b_{t}\in\{0,1\}$ are determined from the coefficients $a_k$ of the polynomial expression of $|S_{i}^\star(v)|$. An application to deflection routing in De Bruijn and Kautz networks serves as motivation for our study. It is worth-mentioning that our analysis can be extended to other families of digraphs on alphabet or to general iterated line digraphs.The conjugacy problem in extensions of Thompson's group F
http://hdl.handle.net/2117/102759
The conjugacy problem in extensions of Thompson's group F
Burillo Puig, José; Matucci, Francesco; Ventura Capell, Enric
We solve the twisted conjugacy problem on Thompson’s group F. We also exhibit orbit undecidable subgroups of Aut(F), and give a proof that Aut(F) and Aut+(F) are orbit decidable provided a certain conjecture on Thompson’s group T is true. By using general criteria introduced by Bogopolski, Martino and Ventura in [5], we construct a family of free extensions of F where the conjugacy problem is unsolvable. As a byproduct of our techniques, we give a new proof of a result of Bleak–Fel’shtyn–Gonçalves in [4] showing that F has property R8, and which can be extended to show that Thompson’s group T also has property R8.
The final publication is available at Springer via http://dx.doi.org/10.1007/s11856-016-1403-9
2017-03-21T17:43:46ZBurillo Puig, JoséMatucci, FrancescoVentura Capell, EnricWe solve the twisted conjugacy problem on Thompson’s group F. We also exhibit orbit undecidable subgroups of Aut(F), and give a proof that Aut(F) and Aut+(F) are orbit decidable provided a certain conjecture on Thompson’s group T is true. By using general criteria introduced by Bogopolski, Martino and Ventura in [5], we construct a family of free extensions of F where the conjugacy problem is unsolvable. As a byproduct of our techniques, we give a new proof of a result of Bleak–Fel’shtyn–Gonçalves in [4] showing that F has property R8, and which can be extended to show that Thompson’s group T also has property R8.