EXTREMAL PROBLEMS CONCERNING CYCLES IN GRAPHS AND THEIR COMPLEMENTS

Let Gt(n) be the class of connected graphs on n vertices having the longest cycle of length t and let G ∈ Gt(n). Woodall (1976) determined the maximum number of edges of G, ε(G) ≤ w(n,t), where w(n, t) = (n - 1) t/2 - r(t – r - 1)/2 and r = (n - 1 ) - (t - 1) ⎣(n - 1)/(t - 1)⎦. An alternative proof and characterization of the extremal (edge-maximal) graphs given by Caccetta and Vijayan (1991). The edge- maximal graphs have the property that their complements are either disconnected or have a cycle going through each vertex (i.e. they are hamiltonian). This motivates us to investigate connected graphs with prescribed circumference (length of the longest cycle) having connected complements with cycles . More specifically, we focus our investigations on : Let G(n, c, c ) denote the class of connected graphs on n vertices having circumference c and whose connected complements have circumference c . The problem of interest is that of determining the bounds of the number of edges of a graph G ∈ G(n, c, c ) and characterize the extremal graphs of G(n, c, c ). We discuss the class G(n, c, c ) and present some results for small c. In particular for c = 4 and c = n - 2, we provide a complete solution. Key words : extremal graph, circumferenc

The Modified CW1 Algorithm for the Degree Restricted Minimum Spanning Tree Problem

Given edge weighted graph G (all weights are non-negative), The Degree Constrained Minimum Spanning Tree Problem is concerned with finding the minimum weight spanning tree T satisfying specified degree restrictions on the vertices. This problem arises naturally in communication networks where the degree of a vertex represents the number of line interfaces available at a terminal (center). The applications of the Degree Constrained Minimum Spanning Tree problems that may arise in real-life include: the design of telecommunication, transportation, and energy networks. It is also used as a subproblem in the design of networks for computer communication, transportation, sewage and plumbing. Since, apart from some trivial cases, the problem is computationally difficult (NP-complete), a number of heuristics have been proposed. In this paper we will discuss the modification of CW1 Algorithm that already proposed by Wamiliana and Caccetta (2003). The results on540 random table problems will be discussed

Supporting Policy Definition in the e-Health domain: a QCA based method

eHealth is broadly considered as a promising strategy to improve the economic sustainability and quality of the healthcare service provision in Europe. Nevertheless, despite the enthusiastic declarations of eHealth potential, the adoption of IT in health care has progressed very slowly. A critical factor, not deeply addressed in literature, is related to the process of prioritization of the eHealth solution to adopt, in presence of financial constrains, external and internal pressure from a wide range of heterogeneous stakeholders, and conflicting information on different technological solutions. In this paper we introduce a method supporting policy definition in the eHealth domain. This method is based on a qualitative comparative analysis (QCA) of best practices and previous experiences performed through the lens of an analytic framework whose dimensions and categories are well situated in the eHealth context. This method could support policy-makers in the identification of the properties and characteristics of innovative projects at European level and to analyze the gap between the international scenario and the local context in order to understand trends and dynamics of development, to evaluate the best opportunities for innovation and, therefore, to assign priorities for the next investments by respecting the constraints of available resources.eHealth is broadly considered as a promising strategy to improve the economic sustainability and quality of the healthcare service provision in Europe. Nevertheless, despite the enthusiastic declarations of eHealth potential, the adoption of IT in health care has progressed very slowly. A critical factor, not deeply addressed in literature, is related to the process of prioritization of the eHealth solution to adopt, in presence of financial constrains, external and internal pressure from a wide range of heterogeneous stakeholders, and conflicting information on different technological solutions. In this paper we introduce a method supporting policy definition in the eHealth domain. This method is based on a qualitative comparative analysis (QCA) of best practices and previous experiences performed through the lens of an analytic framework whose dimensions and categories are well situated in the eHealth context. This method could support policy-makers in the identification of the properties and characteristics of innovative projects at European level and to analyze the gap between the international scenario and the local context in order to understand trends and dynamics of development, to evaluate the best opportunities for innovation and, therefore, to assign priorities for the next investments by respecting the constraints of available resources.Uninvited Submission

Accuracy assessment of a 300 m global land cover map : the GlobCover experience

The GlobCover project supported by ESA has developed an operational service dedicated to the generation of global land cover maps through an automated classification of MERIS FRS time series. This paper reports the independent accuracy assessment of the global GlobCover product as the first global exercise implemented according to the CEOS Land Product Validation group recommendations. Based on a network of 16 international experts and on-line tools, a unique, globally distributed reference data set was collected in a standardized manner and used to derive mapping accuracy figures. The overall accuracy, weighted by the area proportions of the various land cover classes, is 73 % based on a set of 3167 samples. These results are discussed with regards to the previous experiences. (Résumé d'auteur

Polylogarithmic Supports are required for Approximate Well-Supported Nash Equilibria below 2/3

In an epsilon-approximate Nash equilibrium, a player can gain at most epsilon in expectation by unilateral deviation. An epsilon well-supported approximate Nash equilibrium has the stronger requirement that every pure strategy used with positive probability must have payoff within epsilon of the best response payoff. Daskalakis, Mehta and Papadimitriou conjectured that every win-lose bimatrix game has a 2/3-well-supported Nash equilibrium that uses supports of cardinality at most three. Indeed, they showed that such an equilibrium will exist subject to the correctness of a graph-theoretic conjecture. Regardless of the correctness of this conjecture, we show that the barrier of a 2/3 payoff guarantee cannot be broken with constant size supports; we construct win-lose games that require supports of cardinality at least Omega((log n)^(1/3)) in any epsilon-well supported equilibrium with epsilon < 2/3. The key tool in showing the validity of the construction is a proof of a bipartite digraph variant of the well-known Caccetta-Haggkvist conjecture. A probabilistic argument shows that there exist epsilon-well-supported equilibria with supports of cardinality O(log n/(epsilon^2)), for any epsilon> 0; thus, the polylogarithmic cardinality bound presented cannot be greatly improved. We also show that for any delta > 0, there exist win-lose games for which no pair of strategies with support sizes at most two is a (1-delta)-well-supported Nash equilibrium. In contrast, every bimatrix game with payoffs in [0,1] has a 1/2-approximate Nash equilibrium where the supports of the players have cardinality at most two.Comment: Added details on related work (footnote 7 expanded

Multi-temporal Forest Cover Change and Forest Density Trend Detection in a Mediterranean Environment

The loss of forests along with the various types of shrubs in the Mediterranean region is seen as an important driver of climate change and has been repeatedly related with the observed land degradation and desertification in the region. Nevertheless, the extent of woody perennial vegetation cover (WPVC) and its density remain largely unclear. Here, we apply a series of algorithms and methods operationally used in Australia for large-scale WPVC mapping and monitoring and demonstrate their applicability in the Mediterranean region using a Spanish area as the trial site. Five Landsat TM and ETM+ images from various dates spanning 14 years are used to map changes in the extent of WPVC and to identify areas with a declining, stabilising or recovering trend. Results show that the applied methodology, which incorporates (i) preprocessing of the Landsat imagery, (ii) a canonical variate analysis to spectrally discriminate between woody and non-woody land cover types, (iii) a conditional probability network and (iv) spectral indices for mapping woody cover and density trend, is highly successful and well suited for use in Mediterranean environments. A rigorous accuracy assessment is undertaken producing overall accuracies above 97% for both woody and non-woody cover types and all dates. Results also show that in the area of study, the majority of WPVC disturbances were due to forest fires, which represent the region's most frequent natural and anthropogenic disturbance. This raises significant concerns about the future of the area's WPVC. Regeneration compensated to some degree for the high disturbance rates. Copyright © 2015 John Wiley & Sons, Ltd

Counting flags in triangle-free digraphs

Motivated by the Caccetta-Haggkvist Conjecture, we prove that every digraph on n vertices with minimum outdegree 0.3465n contains an oriented triangle. This improves the bound of 0.3532n of Hamburger, Haxell and Kostochka. The main new tool we use in our proof is the theory of flag algebras developed recently by Razborov.Comment: 19 pages, 7 figures; this is the final version to appear in Combinatoric

The Modified CW1 Algorithm For The Degree Restricted Minimum Spanning Tree Problem

Given edge weighted graph G (all weights are non-negative), The Degree Constrained Minimum Spanning Tree Problem is concerned with finding the minimum weight spanning tree T satisfying specified degree restrictions on the vertices. This problem arises naturally in communication networks where the degree of a vertex represents the number of line interfaces available at a terminal (center). The applications of the Degree Constrained Minimum Spanning Tree problems that may arise in real-life include: the design of telecommunication, transportation, and energy networks. It is also used as a subproblem in the design of networks for computer communication, transportation, sewage and plumbing. Since, apart from some trivial cases, the problem is computationally difficult (NP-complete), a number of heuristics have been proposed. In this paper we will discuss the modification of CW1 Algorithm that already proposed by Wamiliana and Caccetta (2003). The results on540 random table problems will be discussed