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1 to 50 of 93 results
  • On the Fiedler value of large planar graphs

     Barriere Figueroa, Eulalia; Huemer, Clemens; Mitsche, Dieter Wilhelm; Orden, David
    Linear algebra and its applications
    Date of publication: 2013
    Journal article

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  • Connected graph searching

     Barriere Figueroa, Eulalia; Flocchini, Paola; Fomin, Fedor V.; Fraigniaud, Pierre; Nisse, Nicolas; Santoro, Nicola; Thilikos, Dimitrios
    Information and computation
    Date of publication: 2012-10
    Journal article

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  • 4-labelings and grid embeddings of plane quadrangulations

     Barriere Figueroa, Eulalia; Huemer, Clemens
    Discrete mathematics
    Date of publication: 2012-05-28
    Journal article

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  • Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación

     Aguilo Gost, Francisco de Asis Luis; Abiad Monge, Aida; Andrés Yebra, José Luis; Barriere Figueroa, Eulalia; Cámara Vallejo, Marc; Ball, Simeon Michael; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Pérez Mansilla, Sonia; Rius Font, Miquel; Serra Albo, Oriol; Vena, Lluis; Vilaltella Castanyer, Joan; Zaragoza Monroig, Maria Luisa; Espona Dones, Margarida; Sau Valls, Ignasi; Montejano Cantoral, Amanda; Perarnau Llobet, Guillem; Moragas Vilarnau, Jordi; Vena Cros, Lluís; Andres Yebra, Jose Luis; Fiol Mora, Miquel Àngel
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  • On the Fiedler value of large planar graphs

     Barriere Figueroa, Eulalia; Huemer, Clemens; Mitsche, Dieter Wilhelm; Orden, David
    Electronic notes in discrete mathematics
    Date of publication: 2011-12-01
    Journal article

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  • Uniform scattering of autonomous mobile robots in a grid

     Barriere Figueroa, Eulalia; Flocchini, Paola; Mesa Barrameda, Eduardo; Santoro, Nicola
    International journal of foundations of computer science
    Date of publication: 2011
    Journal article

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  • On the Fiedler value of large planar graphs

     Barriere Figueroa, Eulalia; Huemer, Clemens; Mitsche, Dieter Wilhelm; Orden, David
    European Conference on Combinatorics, Graph Theory and Applications
    Presentation's date: 2011-08-29
    Presentation of work at congresses

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    The Fiedler value ¿2, also known as algebraic connectivity, is the second smallest Laplacian eigenvalue of a graph. We study upper bounds on the Fiedler value of planar graphs. Let ¿2max be the maximum Fiedler value among all planar graphs G with n vertices. We show here the bounds View the MathML source. Similar lower and upper bounds on the maximum Fiedler value are obtained for the classes of bipartite planar graphs, bipartite planar graphs with minimum vertex degree 3 and outerplanar graphs. We also derive almost tight bounds on ¿2max for the classes of graphs of bounded genus and Kh-minor-free graphs. The proofs rely on a result of Spielman and Teng stating that View the MathML source for any planar graph with n vertices and maximum vertex degree ¿, on a result of Kelner stating that View the MathML source for genus g graphs of bounded degree, and on the separator theorem.

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    Connected graph searching  Open access

     Barriere Figueroa, Eulalia; Flocchini, Paola; Fomin, Fedor V.; Fraigniaud, Pierre; Nisse, Nicolas; Santoro, Nicola; Thilikos, Dimitrios
    Date: 2010-09-26
    Report

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    In graph searching game the opponents are a set of searchers and a fugitive in a graph. The searchers try to capture the fugitive by applying some sequence moves that include placement, removal, or sliding of a searcher along an edge. The fugitive tries to avoid capture by moving along unguarded paths. The search number of a graph is the minimum number of searchers required to guarantee the capture of the fugitive. In this paper, we initiate the study of this game under the natural restriction of connectivity where we demand that in each step of the search the locations of the graph that are clean (i.e. non-accessible to the fugitive) remain connected. We give evidence that many of the standard mathematical tools used so far in the classic graph searching fail under the connectivity requirement. We also settle the question on “the price of connectivity” that is how many searchers more are required for searching a graph when the connectivity demand is imposed. We make estimations of the price of connectivity on general graphs and we provide tight bounds for the case of trees. In particular for an n-vertex graph the ratio between the connected searching number and the non-connected one is O(log n) while for trees this ratio is always at most 2. We also conjecture that this constant-ratio upper bound for trees holds also for all graphs. Our combinatorial results imply a complete characterization of connected graph searching on trees. It is based on a forbidden-graph characterization of the connected search number. We prove that the connected search game is monotone for trees, i.e. restricting search strategies to only those where the clean territories increase monotonically does not require more searchers. A consequence of our results is that the connected search number can be computed in polynomial time on trees, moreover, we show how to make this algorithm distributed. Finally, we reveal connections of this parameter to other invariants on trees such as the Horton-Stralher number.

  • The hierarchical product of graphs

     Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    Discrete applied mathematics
    Date of publication: 2009-01
    Journal article

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  • On the hierarchical product of graphs and the generalized binomial tree

     Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    Linear and multilinear algebra
    Date of publication: 2009
    Journal article

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  • The generalized hierarchical product of graphs

     Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Discrete mathematics
    Date of publication: 2009-06
    Journal article

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  • Fonaments matemàtics per a l'enginyeria de telecomunicació

     Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Gago Alvarez, Silvia; Heymann Pignolo, Marco; Tramuns Figueras, Eulalia
    Date of publication: 2009-07
    Book

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  • COMBINATÒRIA , TEORIA DE GRAFS I APLICACIONS

     Comellas Padro, Francesc de Paula; López Masip, Susana Clara; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Espona Dones, Margarida; Rius Font, Miquel; Aroca Farrerons, Josep Maria; Aguilo Gost, Francisco de Asis Luis; Dalfo Simo, Cristina; Moragas Vilarnau, Jordi; Cámara Vallejo, Marc; Gago Alvarez, Silvia; Ball, Simeon Michael; Andres Yebra, Jose Luis; Pérez Mansilla, Sonia; Mitjana Riera, Margarida; Llado Sanchez, Anna; Barriere Figueroa, Eulalia; Fàbrega Canudas, Josep; Muñoz Lopez, Francisco Javier; Zaragoza Monroig, Maria Luisa; Gomez Marti, Jose; Miralles De La Asuncion, Alicia; Pelayo Melero, Ignacio Manuel; Serra Albo, Oriol
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  • PROBLEMAS EXTREMALES Y DE OPTIMIZACIÓN EN TEORIA DE GRAFOS Y COMBINATORIA: APLICACIÓN AL ANALISIS Y ALGORITMOS DE REDES DE COMUNICAC

     Abiad Monge, Aida; Andres Yebra, Jose Luis; Aguilo Gost, Francisco de Asis Luis; Aroca Farrerons, Josep Maria; Ball, Simeon Michael; Barajas Tomas, Javier; Barguilla Navarrete, Jorge; Barriere Figueroa, Eulalia; Cámara Vallejo, Marc; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Espona Dones, Margarida; Fàbrega Canudas, Josep; Gago Alvarez, Silvia; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Montejano Cantoral, Amanda; Moragas Vilarnau, Jordi; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Perarnau Llobet, Guillem; Pérez Mansilla, Sonia; Rius Font, Miquel; Sau Valls, Ignasi; Serra Albo, Oriol; Vena, Lluis; Vilaltella Castanyer, Joan; Zaragoza Monroig, Maria Luisa; Vena Cros, Lluís; Fiol Mora, Miquel Àngel
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  • 4-labelings and grid embeddings of plane quadrangulations

     Barriere Figueroa, Eulalia; Huemer, Clemens
    Symposium on Graph Drawing
    Presentation's date: 2009-09
    Presentation of work at congresses

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  • On the spectra of hypertrees

     Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    Linear algebra and its applications
    Date of publication: 2008-04
    Journal article

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  • On middle cube graphs

     Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida; Dalfo Simo, Cristina; Barriere Figueroa, Eulalia
    SIAM Conference on Discrete Mathematics
    Presentation's date: 2008
    Presentation of work at congresses

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  • Analizando el problema de Frobenius

     Miralles De La Asuncion, Alicia; Barriere Figueroa, Eulalia
    Jornadas de Matemática Discreta y Algorítmica
    Presentation of work at congresses

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  • New operations on graphs and digraphs. Algebraic properties

     Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    (SGT in Rio 08) Workshop on spectral graph theory with appl. on computer science, combinatorial optimization and chemistry
    Presentation's date: 2008-12
    Presentation of work at congresses

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  • Some properties of the generalized hierarchical product of graphs

     Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Jornadas de Matemática Discreta y Algorítmica
    Presentation's date: 2008-07
    Presentation of work at congresses

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  • Algebraic properties of the generalized hierarchical product of graphs

     Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Geometric and Algebraic Combinatorics 4
    Presentation's date: 2008-08
    Presentation of work at congresses

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  • Algebraic properties of the generalized hierarchical product of graphs

     Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Jornadas de Matemática Discreta y Algorítmica
    Presentation's date: 2008-07
    Presentation of work at congresses

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    The Frobenius problem: a geometric approach  Open access

     Barriere Figueroa, Eulalia; Miralles De La Asuncion, Alicia
    Date: 2007-07
    Report

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    For the well known Frobenius problem, we present a new geometric approach, based on the use of the $n$-dimensional lattice $\mathbb{Z}^n$, where $n$ is the number of generators. Within this approach we are able to study the cases of two and three generators. The main feature of our geometric representation is that we can nicely visualize the set of {\em gaps}, i.e., the non-representable positive integers. In the case of two generators, we give a description of the set of gaps. Moreover, for any positive integer, $m$, we derive a simple expression for the denumerant $d(m;a,b)$. We show that we can use the $2$-dimensional lattice associated to the set of generators $\{ a,b\}$ to study the Frobenius problem with generators $\{ a,b,c\}$. In particular, we give, as for two generators, a graphical representation of the set of gaps. For a large set of possible values of $c$, this representation allows us to simplify the computation of the Frobenius number and compute the number of gaps.

  • Rendezvous and election of mobile agents: Impact of sense of direction

     Barriere Figueroa, Eulalia; Flocchini, P; Fraigniaud, P; Santoro, N
    Theory of computing systems
    Date of publication: 2007-02
    Journal article

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  • On the spectra of hypertrees

     Barriere Figueroa, Eulalia
    European Conference on Combinatorics, Graph Theory, and Applications
    Presentation's date: 2007-09-13
    Presentation of work at congresses

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  • The multidimensional Manhattan Network

     Barriere Figueroa, Eulalia
    European Conference on Combinatorics, Graph Theory, and Applications
    Presentation's date: 2007-09-13
    Presentation of work at congresses

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  • The hierarchical product of graphs

     Barriere Figueroa, Eulalia
    European Conference on Combinatorics, Graph Theory, and Applications
    Presentation's date: 2007-09-13
    Presentation of work at congresses

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  • On the Spectra of Hypertrees

     Barriere Figueroa, Eulalia
    European Conference on Combinatorics, Graph Theory, and Applications
    Presentation's date: 2007-09-13
    Presentation of work at congresses

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  • A spectral study of the Manhattan Networks

     Barriere Figueroa, Eulalia
    European Conference on Combinatorics, Graph Theory, and Applications
    Presentation's date: 2007-09-13
    Presentation of work at congresses

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  • On the Spectra of Hypertrees

     Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    European Conference on Combinatorics, Graph Theory, and Applications
    Presentation of work at congresses

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  • The Hierarchical Product of Graphs

     Comellas Padro, Francesc de Paula; Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    European Conference on Combinatorics, Graph Theory, and Applications
    Presentation of work at congresses

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  • The Frobenius problem: a geometric approach

     Barriere Figueroa, Eulalia; Miralles De La Asuncion, Alicia
    British Combinatorial Conference
    Presentation of work at congresses

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  • The Frobenius problem: ageometric approach

     Barriere Figueroa, Eulalia
    British Combinatorial Conference
    Presentation's date: 2007-07-13
    Presentation of work at congresses

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  • Nombres complexos

     Barriere Figueroa, Eulalia
    Date of publication: 2007-09-30
    Book chapter

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  • Integració de funcions de dues variables

     Barriere Figueroa, Eulalia
    Date of publication: 2007-09-30
    Book chapter

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    The hierarchical product of graphs  Open access

     Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Fiol Mora, Miquel Àngel
    Date: 2007-03
    Report

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    A new operation on graphs is introduced and some of its properties are studied. We call it hierarchical product, because of the strong (connectedness) hierarchy of the vertices in the resulting graphs. In fact, the obtained graphs turn out to be subgraphs of the cartesian product of the corresponding factors. Some well-known properties of the cartesian product, such as a reduced mean distance and diameter, simple routing algorithms and some optimal communication protocols are inherited by the hierarchical product. We also address the study of some algebraic properties of the hierarchical product of two or more graphs. In particular, the spectrum of the binary hypertree $T_m$ (which is the hierarchical product of several copies of the complete graph on two vertices) is fully characterized; turning out to be an interesting example of graph with all its eigenvalues distinct. Finally, some natural generalizations of the hierarchic product are proposed.

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    On the spectra of hypertrees  Open access

     Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Fiol Mora, Miquel Àngel
    Date: 2007-05
    Report

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    In this paper we study the spectral properties of a family of trees characterized by two main features: they are spanning subgraphs of the hypercube, and their vertices bear a high degree of (connectedness) hierarchy. Such structures are here called binary hypertrees and they can be recursively defined as the so-called hierarchical product of several complete graphs on two vertices.

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    On the hierarchical product of graphs and the generalized binomial tree  Open access

     Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Fiol Mora, Miquel Àngel
    Date: 2007-09
    Report

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    In this paper we follow the study of the hierarchical product of graphs, an operation recently introduced in the context of networks. A well-known example of such a product is the binomial tree which is the (hierarchical) power of the complete graph on two vertices. An appealing property of this structure is that all the eigenvalues are distinct. Here we show how to obtain a graph with this property by applying the hierarchical product. In particular, we propose a generalization of the binomial tree and some of its main properties are studied.

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    Deterministic hierarchical networks  Open access

     Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel
    Date: 2007-11
    Report

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    Recently it has been shown that many networks associated with complex systems are small-world (they have both a large local clustering and a small diameter) and they are also scale-free (the degrees are distributed according to a power-law). Moreover, these networks are very often hierarchical, as they describe the modularity of the systems which are modeled. Most of the studies for complex networks are based on stochastic methods. However, a deterministic method, with an exact determination of the main relevant parameters of the networks, has proven useful. Indeed, this approach complements and enhances the probabilistic and simulation techniques and, therefore, it provides a better understanding of the systems modeled. In this paper we find the radius, diameter, clustering and degree distribution of a generic family of deterministic hierarchical small-world scale-free networks which has been considered for modeling real life complex systems. Moreover a routing algorithm is proposed.

  • Fractality and the small-world effect in Sierpinski graphs

     Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina
    Journal of physics A. Mathematical and general
    Date of publication: 2006-09
    Journal article

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  • Fractalidad y efecto small-world en grafos Sierpinski

     Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina
    Jornadas de Matemática Discreta y Algorítmica
    Presentation's date: 2006-07-14
    Presentation of work at congresses

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  • Introducció a la lògica

     Claverol Aguas, Merce; Barriere Figueroa, Eulalia
    Date of publication: 2006-10-31
    Book

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  • Review sobre s-regular cubic graphs as coverings of the complete bipartite graph k_3,3 by Feng, Y-Q and Kwak, J-H

     Barriere Figueroa, Eulalia
    Mathematical reviews
    Date of publication: 2005-06
    Journal article

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  • Rendezvous and Election of Mobile Agents: Impact of Sense of Direction

     Barriere Figueroa, Eulalia; Flocchini, Paola; Fraigniaud, Pierre And Nicola Santoro
    Theory of computing systems: an international journal
    Date of publication: 2005-08
    Journal article

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  • Combinatòria, Teoria de Grafs i Aplicacions

     Aguilo Gost, Francisco de Asis Luis; Serra Albo, Oriol; Andrés Yebra, José Luis; Balbuena Martinez, Maria Camino Teofila; Ball, Simeon Michael; Barajas Tomas, Javier; Barguilla Navarrete, Jorge; Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Marcote Ordax, Francisco Javier; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Moragas Vilarnau, Jordi; Montejano Cantoral, Amanda; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Pérez Mansilla, Sonia; Rius Font, Miquel; Zaragoza Monroig, Maria Luisa
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  • Grandes redes tolerantes a fallos: nuevos modelos, diseño, análisis y algoritmos

     Mitjana Riera, Margarida; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Gago Alvarez, Silvia; Muñoz Lopez, Francisco Javier; Barriere Figueroa, Eulalia; Zaragoza Monroig, Maria Luisa
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  • Robust position-based routing in wireless ad hoc networks with irregular transmission ranges

     Barriere Figueroa, Eulalia; Fraigniad, Pierre; Narayanan, Lata; Jaroslav, Opatrny
    Wireless communications and mobile computing
    Date of publication: 2003-03
    Journal article

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