Articles de revista
http://hdl.handle.net/2117/3197
Wed, 26 Apr 2017 19:50:47 GMT2017-04-26T19:50:47ZGeneral 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.
Wed, 26 Apr 2017 17:41:13 GMThttp://hdl.handle.net/2117/1037642017-04-26T17:41:13ZMora 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.Production matrices for geometric graphs
http://hdl.handle.net/2117/103649
Production matrices for geometric graphs
Huemer, Clemens; Pilz, Alexander; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio
We present production matrices for non-crossing geometric graphs on point sets in convex position, which allow us to derive formulas for the numbers of such graphs. Several known identities for Catalan numbers, Ballot numbers, and Fibonacci numbers arise in a natural way, and also new formulas are obtained, such as a formula for the number of non-crossing geometric graphs with root vertex of given degree. The characteristic polynomials of some of these production matrices are also presented. The proofs make use of generating trees and Riordan arrays.
Mon, 24 Apr 2017 08:25:14 GMThttp://hdl.handle.net/2117/1036492017-04-24T08:25:14ZHuemer, ClemensPilz, AlexanderSeara Ojea, CarlosSilveira, Rodrigo IgnacioWe present production matrices for non-crossing geometric graphs on point sets in convex position, which allow us to derive formulas for the numbers of such graphs. Several known identities for Catalan numbers, Ballot numbers, and Fibonacci numbers arise in a natural way, and also new formulas are obtained, such as a formula for the number of non-crossing geometric graphs with root vertex of given degree. The characteristic polynomials of some of these production matrices are also presented. The proofs make use of generating trees and Riordan arrays.New results on stabbing segments with a polygon
http://hdl.handle.net/2117/103547
New results on stabbing segments with a polygon
Díaz Bañez, José Miguel; Korman Cozzetti, Matías; Pérez Lantero, Pablo; Pilz, Alexander; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio
We consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed by P if P stabs every element of S. Given a segment set S, we study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or perimeter) is optimized. We show that if the elements of S are pairwise disjoint, the problem can be solved in polynomial time. In particular, this solves an open problem posed by Loftier and van Kreveld [Algorithmica 56(2), 236-269 (2010)] [16] about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments. Our algorithm can also be extended to work for a more general problem, in which instead of segments, the set S consists of a collection of point sets with pairwise disjoint convex hulls. We also prove that for general segments our stabbing problem is NP-hard. (C) 2014 Elsevier B.V. All rights reserved.
Wed, 19 Apr 2017 12:27:10 GMThttp://hdl.handle.net/2117/1035472017-04-19T12:27:10ZDíaz Bañez, José MiguelKorman Cozzetti, MatíasPérez Lantero, PabloPilz, AlexanderSeara Ojea, CarlosSilveira, Rodrigo IgnacioWe consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed by P if P stabs every element of S. Given a segment set S, we study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or perimeter) is optimized. We show that if the elements of S are pairwise disjoint, the problem can be solved in polynomial time. In particular, this solves an open problem posed by Loftier and van Kreveld [Algorithmica 56(2), 236-269 (2010)] [16] about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments. Our algorithm can also be extended to work for a more general problem, in which instead of segments, the set S consists of a collection of point sets with pairwise disjoint convex hulls. We also prove that for general segments our stabbing problem is NP-hard. (C) 2014 Elsevier B.V. All rights reserved.Adjacency-preserving spatial treemaps
http://hdl.handle.net/2117/101755
Adjacency-preserving spatial treemaps
Buchin, Kevin; Eppstein, David; Löffler, Maarten; Nöllenburg, Martin; Silveira, Rodrigo Ignacio
Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political regions. A spatial treemap is a rectangular layout with a hierarchical structure: the outer rectangle is subdivided into rectangles that are in turn subdivided into smaller rectangles. We describe algorithms for transforming a rectangular layout that does not have this hierarchical structure, together with a clustering of the rectangles of the layout, into a spatial treemap that respects the clustering and also respects to the extent possible the adjacencies of the input layout.
Wed, 01 Mar 2017 07:41:22 GMThttp://hdl.handle.net/2117/1017552017-03-01T07:41:22ZBuchin, KevinEppstein, DavidLöffler, MaartenNöllenburg, MartinSilveira, Rodrigo IgnacioRectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political regions. A spatial treemap is a rectangular layout with a hierarchical structure: the outer rectangle is subdivided into rectangles that are in turn subdivided into smaller rectangles. We describe algorithms for transforming a rectangular layout that does not have this hierarchical structure, together with a clustering of the rectangles of the layout, into a spatial treemap that respects the clustering and also respects to the extent possible the adjacencies of the input layout.Widening the analysis of Energy Return On Investment (EROI) in agroecosystems: A proposal to study socio-ecological transitions to industrialized farm systems (the Vallès County, Catalonia, c.1860 and 1999)
http://hdl.handle.net/2117/100439
Widening the analysis of Energy Return On Investment (EROI) in agroecosystems: A proposal to study socio-ecological transitions to industrialized farm systems (the Vallès County, Catalonia, c.1860 and 1999)
Galán, E.; Padró, R.; Marco, I.; Tello Aragay, Enric; Cunfer, G.; Guzmán, G. I.; González de Molina, M.; Krausmann, F.; Gingrich, S.; Sacristán Adinolfi, Vera; Moreno-Delgado, D.
Energy balances of farm systems have overlooked the role of energy flows that remain within agro-ecosystems. Yet, such internal flows fulfil important socio-ecological functions, including maintenance of farmers themselves and agro-ecosystem structures. Farming can either give rise to complex landscapes that favour associated biodiversity, or the opposite. This variability can be understood by assessing several types of Energy Returns on Investment (EROI). Applying these measures to a farm system in Catalonia, Spain in 1860 and in 1999, reveals the expected decrease in the ratio of final energy output to total and external inputs. The transition from solar-based to a fossil fuel based agro-ecosystem was further accompanied by an increase in the ratio of final energy output to biomass reused, as well as an absolute increase of Unharvested Phytomass grown in derelict forestland. The study reveals an apparent link between reuse of biomass and the decrease of landscape heterogeneity along with its associated biodiversity.
Wed, 01 Feb 2017 10:58:29 GMThttp://hdl.handle.net/2117/1004392017-02-01T10:58:29ZGalán, E.Padró, R.Marco, I.Tello Aragay, EnricCunfer, G.Guzmán, G. I.González de Molina, M.Krausmann, F.Gingrich, S.Sacristán Adinolfi, VeraMoreno-Delgado, D.Energy balances of farm systems have overlooked the role of energy flows that remain within agro-ecosystems. Yet, such internal flows fulfil important socio-ecological functions, including maintenance of farmers themselves and agro-ecosystem structures. Farming can either give rise to complex landscapes that favour associated biodiversity, or the opposite. This variability can be understood by assessing several types of Energy Returns on Investment (EROI). Applying these measures to a farm system in Catalonia, Spain in 1860 and in 1999, reveals the expected decrease in the ratio of final energy output to total and external inputs. The transition from solar-based to a fossil fuel based agro-ecosystem was further accompanied by an increase in the ratio of final energy output to biomass reused, as well as an absolute increase of Unharvested Phytomass grown in derelict forestland. The study reveals an apparent link between reuse of biomass and the decrease of landscape heterogeneity along with its associated biodiversity.Computing the canonical representation of constructible sets
http://hdl.handle.net/2117/100350
Computing the canonical representation of constructible sets
Brunat Blay, Josep Maria; Montes Lozano, Antonio
Constructible sets are needed in many algorithms of Computer Algebra, particularly in the GröbnerCover and other algorithms for parametric polynomial systems. In this paper we review the canonical form ofconstructible sets and give algorithms for computing it.
Tue, 31 Jan 2017 09:20:18 GMThttp://hdl.handle.net/2117/1003502017-01-31T09:20:18ZBrunat Blay, Josep MariaMontes Lozano, AntonioConstructible sets are needed in many algorithms of Computer Algebra, particularly in the GröbnerCover and other algorithms for parametric polynomial systems. In this paper we review the canonical form ofconstructible sets and give algorithms for computing it.The degree/diameter problem in maximal planar bipartite graphs
http://hdl.handle.net/2117/89907
The degree/diameter problem in maximal planar bipartite graphs
Dalfó Simó, Cristina; Huemer, Clemens; Salas Piñon, Julián
The (Δ,D)(Δ,D) (degree/diameter) problem consists of finding the largest possible number of vertices nn among all the graphs with maximum degree ΔΔ and diameter DD. We consider the (Δ,D)(Δ,D) problem for maximal planar bipartite graphs, that is, simple planar graphs in which every face is a quadrangle. We obtain that for the (Δ,2)(Δ,2) problem, the number of vertices is n=Δ+2n=Δ+2; and for the (Δ,3)(Δ,3) problem, n=3Δ−1n=3Δ−1 if ΔΔ is odd and n=3Δ−2n=3Δ−2 if ΔΔ is even. Then, we prove that, for the general case of the (Δ,D)(Δ,D) problem, an upper bound on nn is approximately 3(2D+1)(Δ−2)⌊D/2⌋3(2D+1)(Δ−2)⌊D/2⌋, and another one is C(Δ−2)⌊D/2⌋C(Δ−2)⌊D/2⌋ if Δ≥DΔ≥D and CC is a sufficiently large constant. Our upper bounds improve for our kind of graphs the one given by Fellows, Hell and Seyffarth for general planar graphs. We also give a lower bound on nn for maximal planar bipartite graphs, which is approximately (Δ−2)k(Δ−2)k if D=2kD=2k, and 3(Δ−3)k3(Δ−3)k if D=2k+1D=2k+1, for ΔΔ and DD sufficiently large in both cases.
Wed, 14 Sep 2016 10:33:44 GMThttp://hdl.handle.net/2117/899072016-09-14T10:33:44ZDalfó Simó, CristinaHuemer, ClemensSalas Piñon, JuliánThe (Δ,D)(Δ,D) (degree/diameter) problem consists of finding the largest possible number of vertices nn among all the graphs with maximum degree ΔΔ and diameter DD. We consider the (Δ,D)(Δ,D) problem for maximal planar bipartite graphs, that is, simple planar graphs in which every face is a quadrangle. We obtain that for the (Δ,2)(Δ,2) problem, the number of vertices is n=Δ+2n=Δ+2; and for the (Δ,3)(Δ,3) problem, n=3Δ−1n=3Δ−1 if ΔΔ is odd and n=3Δ−2n=3Δ−2 if ΔΔ is even. Then, we prove that, for the general case of the (Δ,D)(Δ,D) problem, an upper bound on nn is approximately 3(2D+1)(Δ−2)⌊D/2⌋3(2D+1)(Δ−2)⌊D/2⌋, and another one is C(Δ−2)⌊D/2⌋C(Δ−2)⌊D/2⌋ if Δ≥DΔ≥D and CC is a sufficiently large constant. Our upper bounds improve for our kind of graphs the one given by Fellows, Hell and Seyffarth for general planar graphs. We also give a lower bound on nn for maximal planar bipartite graphs, which is approximately (Δ−2)k(Δ−2)k if D=2kD=2k, and 3(Δ−3)k3(Δ−3)k if D=2k+1D=2k+1, for ΔΔ and DD sufficiently large in both cases.Perfect and quasiperfect domination in trees
http://hdl.handle.net/2117/86561
Perfect and quasiperfect domination in trees
Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, Maria Luz
A k quasip erfect dominating set of a connected graph G is a vertex subset S such that every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum k-quasip erfect dominating set in G is denoted by 1 k ( G ) . These graph parameters were rst intro duced by Chellali et al. (2013) as a generalization of b oth the p erfect domination numb er 11 ( G ) and the domination numb er ( G ) . The study of the so-called quasip erfect domination chain 11 ( G ) 12 ( G ) 1 ( G ) = ( G ) enable us to analyze how far minimum dominating sets are from b eing p erfect. In this pap er, we provide, for any tree T and any p ositive integer k , a tight upp er b ound of 1 k ( T ) . We also prove that there are trees satisfying all p ossible equalities and inequalities in this chain. Finally a linear algorithm for computing 1 k ( T ) in any tree T is presente
Wed, 04 May 2016 10:50:08 GMThttp://hdl.handle.net/2117/865612016-05-04T10:50:08ZCáceres, JoséHernando Martín, María del CarmenMora Giné, MercèPelayo Melero, Ignacio ManuelPuertas, Maria LuzA k quasip erfect dominating set of a connected graph G is a vertex subset S such that every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum k-quasip erfect dominating set in G is denoted by 1 k ( G ) . These graph parameters were rst intro duced by Chellali et al. (2013) as a generalization of b oth the p erfect domination numb er 11 ( G ) and the domination numb er ( G ) . The study of the so-called quasip erfect domination chain 11 ( G ) 12 ( G ) 1 ( G ) = ( G ) enable us to analyze how far minimum dominating sets are from b eing p erfect. In this pap er, we provide, for any tree T and any p ositive integer k , a tight upp er b ound of 1 k ( T ) . We also prove that there are trees satisfying all p ossible equalities and inequalities in this chain. Finally a linear algorithm for computing 1 k ( T ) in any tree T is presenteOpening the black box of energy throughputs in farm systems: a decomposition analysis between the energy returns to external inputs, internal biomass reuses and total inputs consumed (the Vallès County, Catalonia, c.1860 and 1999)
http://hdl.handle.net/2117/86061
Opening the black box of energy throughputs in farm systems: a decomposition analysis between the energy returns to external inputs, internal biomass reuses and total inputs consumed (the Vallès County, Catalonia, c.1860 and 1999)
Tello, E.; Galán, E.; Sacristán Adinolfi, Vera; Cunfer, G.; Guzmán, G. I.; González de Molina, M.; Krausmann, F.; Gringrich, S.; Padró, R.; Marco, I.; Moreno-Delgado, D.
We present an energy analysis of past and present farm systems aimed to contribute to their sustainability assessment. Looking at agroecosystems as a set of energy loops between nature and society, and adopting a farm-operator standpoint at landscape level to set the system boundaries, enthalpy values of energy carriers are accounted for net Final Produce going outside as well as for Biomass Reused cycling inside, and External Inputs are accounted using embodied values. Human Labour is accounted for the fraction of the energy intake of labouring people devoted to perform farm work, considering the local or external origin of their food basket. In this approach the proportion of internal Biomass Reused becomes a hallmark of organic farm systems that tend to save External Inputs, whereas industrial farming and livestock breeding in feedlots tend to get rid of reuses replacing them with inputs coming from outside. Hence, decomposing the internal or external energy throughputs may bring to light their contrasting sociometabolic profiles. A Catalan case study in 1860 and 1990 is used as a test bench to show how revealing this decomposing analysis may be to plot the energy profiles of farm systems and their possible improvement pathways.
Thu, 21 Apr 2016 12:18:30 GMThttp://hdl.handle.net/2117/860612016-04-21T12:18:30ZTello, E.Galán, E.Sacristán Adinolfi, VeraCunfer, G.Guzmán, G. I.González de Molina, M.Krausmann, F.Gringrich, S.Padró, R.Marco, I.Moreno-Delgado, D.We present an energy analysis of past and present farm systems aimed to contribute to their sustainability assessment. Looking at agroecosystems as a set of energy loops between nature and society, and adopting a farm-operator standpoint at landscape level to set the system boundaries, enthalpy values of energy carriers are accounted for net Final Produce going outside as well as for Biomass Reused cycling inside, and External Inputs are accounted using embodied values. Human Labour is accounted for the fraction of the energy intake of labouring people devoted to perform farm work, considering the local or external origin of their food basket. In this approach the proportion of internal Biomass Reused becomes a hallmark of organic farm systems that tend to save External Inputs, whereas industrial farming and livestock breeding in feedlots tend to get rid of reuses replacing them with inputs coming from outside. Hence, decomposing the internal or external energy throughputs may bring to light their contrasting sociometabolic profiles. A Catalan case study in 1860 and 1990 is used as a test bench to show how revealing this decomposing analysis may be to plot the energy profiles of farm systems and their possible improvement pathways.Lower bounds on the maximum number of non-crossing acyclic graphs
http://hdl.handle.net/2117/86044
Lower bounds on the maximum number of non-crossing acyclic graphs
Huemer, Clemens; Mier Vinué, Anna de
This paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain point configuration of N points has Omega (12.52(N)) non-crossing spanning trees and Omega (13.61(N)) non-crossing forests. This improves the previous lower bounds on the maximum number of non-crossing spanning trees and of non-crossing forests among all sets of N points in general position given by Dumitrescu, Schulz, Sheffer and Toth (2013). Our analysis relies on the tools of analytic combinatorics, which enable us to count certain families of forests on points in convex position, and to estimate their average number of components. A new upper bound of O(22.12(N)) for the number of non-crossing spanning trees of the double chain is also obtained. (C) 2015 Elsevier Ltd. All rights reserved.
Thu, 21 Apr 2016 10:27:51 GMThttp://hdl.handle.net/2117/860442016-04-21T10:27:51ZHuemer, ClemensMier Vinué, Anna deThis paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain point configuration of N points has Omega (12.52(N)) non-crossing spanning trees and Omega (13.61(N)) non-crossing forests. This improves the previous lower bounds on the maximum number of non-crossing spanning trees and of non-crossing forests among all sets of N points in general position given by Dumitrescu, Schulz, Sheffer and Toth (2013). Our analysis relies on the tools of analytic combinatorics, which enable us to count certain families of forests on points in convex position, and to estimate their average number of components. A new upper bound of O(22.12(N)) for the number of non-crossing spanning trees of the double chain is also obtained. (C) 2015 Elsevier Ltd. All rights reserved.