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Edge Density (edge + density)

Distribution by Scientific Domains

Mathematics and Statistics	50%

Selected Abstracts

Solving the minimum-weighted coloring problem

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2001
Massimiliano Caramia
Abstract Weighted coloring is a generalization of the well-known vertex (unweighted) coloring for which a number of exact algorithms have been presented in the literature. We are not aware of any optimal method specifically designed for the minimum-weighted coloring problem on arbitrary graphs. Only a few heuristics have been developed with the goal of finding tighter upper bounds for the maximum-weighted clique problem. Moreover, as shown in the paper, a straightforward reduction of a weighted instance into an unweighted one permits us to solve only very small instances. In this paper, we present a branch-and-bound algorithm for the weighted case capable of solving random graphs of up to 90 vertices for any edge density with integer weights uniformly drawn from the range [1, ,,10]. Likewise, we have used properly modified benchmark instances borrowed from vertex coloring as a further test bed for our algorithm. © 2001 John Wiley & Sons, Inc. [source]

What is the furthest graph from a hereditary property?

RANDOM STRUCTURES AND ALGORITHMS, Issue 1 2008
Noga Alon
Abstract For a graph property P, the edit distance of a graph G from P, denoted EP(G), is the minimum number of edge modifications (additions or deletions) one needs to apply to G to turn it into a graph satisfying P. What is the furthest graph on n vertices from P and what is the largest possible edit distance from P? Denote this maximal distance by ed(n,P). This question is motivated by algorithmic edge-modification problems, in which one wishes to find or approximate the value of EP(G) given an input graph G. A monotone graph property is closed under removal of edges and vertices. Trivially, for any monotone property, the largest edit distance is attained by a complete graph. We show that this is a simple instance of a much broader phenomenon. A hereditary graph property is closed under removal of vertices. We prove that for any hereditary graph property P, a random graph with an edge density that depends on P essentially achieves the maximal distance from P, that is: ed(n,P) = EP(G(n,p(P))) + o(n2) with high probability. The proofs combine several tools, including strengthened versions of the Szemerédi regularity lemma, properties of random graphs and probabilistic arguments. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008 [source]

Applying a continua landscape approach to evaluate plant response to fragmentation: Primula vulgaris in the Cantabrian mountains

APPLIED VEGETATION SCIENCE, Issue 4 2009
Alicia Valdés
Abstract Question: Continua landscape approaches conceptualize the effects of habitat fragmentation on the biota by considering fragmented landscapes as continuous gradients, departing from the view of habitat as either suitable (fragment) or unsuitable (matrix). They also consider the ecological gradients or the ,Umwelt' (species-specific perception of the landscape) to represent the processes that ultimately limit organisms' ability to colonize and persist within habitat remnants. Are these approaches suitable for evaluating the response of plant species to fragmentation? Location: Fragmented mid-elevation temperate forests, Cantabrian range, Spain. Methods: The presence, abundance and demographic structure of populations of the perennial herb Primula vulgaris were sampled across a continuous extent of 100 ha, subdivided into 400 50 m × 50 m sampling units. These variables were related to forest availability, forest subdivision and edge density, topography and the spatial clumpiness of populations (a measure of plant dispersal constraints and, hence, a major surrogate of plant Umwelt). Results: Fragmentation processes, especially habitat loss, negatively affect P. vulgaris, with a stronger effect on presence than on abundance and demography. Despite the importance of habitat availability, P. vulgaris does not occupy all potentially suitable forest habitat, mostly owing to dispersal constraints. A positive effect of slope on plant presence also suggests some effect of habitat quality in determining establishment and occupancy of forest landscape. Conclusions: Within-habitat dispersal constraints are as important as forest fragmentation in determining the landscape-scale distribution of P. vulgaris. By assessing the relative role of the diverse fragmentation processes, and of the species' landscape perception, a continua landscape approach proves to be a valuable tool for predicting plant response to landscape change. [source]

Multi-scale responses of plant species diversity in semi-natural buffer strips to agricultural landscapes

APPLIED VEGETATION SCIENCE, Issue 2 2008
Maohua Ma
Question: How does agricultural land usage affect plant species diversity in semi-natural buffer strips at multiple scales? Location: Lepsämä River watershed, Nurmijärvi, Southern Finland. Methods: Species diversity indicators included both richness and evenness. Plant communities in buffer strips were surveyed in 29 sampling sites. Using ArcGIS Desktop 9.0 (ArcInfo) and Fragstats 3.3 for GIS analysis, the landscape composition around each sampling site was characterized by seven parameters in square sectors at five scales: 4, 36, 100, 196, and 324ha. For each scale, Principle Component Analysis was used to examine the importance of each structural metric to diversity indicators using multiple regression and other simple analyses. Results: For all but the smallest scales (4 ha), two structural metrics including the diversity of land cover types and percentage of arable land were positively and negatively correlated with species richness, respectively. Both metrics had the highest correlation coefficients for species richness at the second largest scale (196 ha). The density of arable field edges between the fields was the only metric that correlated with species evenness for all scales, which had highest predictive power at the second smallest scale (36 ha). Conclusions: Species richness and evenness of buffer strips had scale-dependent relationships to land use in agricultural ecosystems. The results of this study indicated that species richness depends on the pattern of arable land use at large scales, which may relate to the regional species pool. Meanwhile, species evenness depended on the level of field edge density at small scales, which relates to how the nearby farmland was divided by the edges (e.g. many small-scale fields with high edge density or a few big-scale fields with low edge density). This implies that it is important to manage the biodiversity of buffer strips within a landscape context at multiple scales. [source]