scholarly journals Essential Constraints of Edge-Constrained Proximity Graphs

2017 ◽  
Vol 21 (4) ◽  
pp. 389-415
Author(s):  
Prosenjit Bose ◽  
Jean-Lou De Carufel ◽  
Alina Shaikhet ◽  
Michiel Smid
Keyword(s):  
Proximity Graphs

scholarly journals Data on cut-edge for spatial clustering based on proximity graphs

Data in Brief ◽  
2020 ◽  
Vol 28 ◽  
pp. 104899 ◽  
Author(s):  
Alper Aksac ◽  
Tansel Ozyer ◽  
Reda Alhajj
Keyword(s):  
Spatial Clustering ◽  
Cut Edge ◽  
Proximity Graphs

DEVELOPING PROXIMITY GRAPHS BY PHYSARUM POLYCEPHALUM: DOES THE PLASMODIUM FOLLOW THE TOUSSAINT HIERARCHY?

2009 ◽  
Vol 19 (01) ◽  
pp. 105-127 ◽  
Author(s):  
ANDREW ADAMATZKY
Keyword(s):  
Foraging Behavior ◽  
Delaunay Triangulation ◽  
Spanning Tree ◽  
Physarum Polycephalum ◽  
Minimum Spanning Tree ◽  
Nearest Neighbour ◽  
Minimal Spanning Tree ◽  
Proximity Graphs ◽  
Relative Neighborhood Graph ◽  
Plasmodium Of Physarum Polycephalum

Plasmodium of Physarum polycephalum spans sources of nutrients and constructs varieties of protoplasmic networks during its foraging behavior. When the plasmodium is placed on a substrate populated with sources of nutrients, it spans the sources with protoplasmic network. The plasmodium optimizes the network to deliver efficiently the nutrients to all parts of its body. How exactly does the protoplasmic network unfold during the plasmodium's foraging behavior? What types of proximity graphs are approximated by the network? Does the plasmodium construct a minimal spanning tree first and then add additional protoplasmic veins to increase reliability and through-capacity of the network? We analyze a possibility that the plasmodium constructs a series of proximity graphs: nearest-neighbour graph (NNG), minimum spanning tree (MST), relative neighborhood graph (RNG), Gabriel graph (GG) and Delaunay triangulation (DT). The graphs can be arranged in the inclusion hierarchy (Toussaint hierarchy): NNG ⊆ MST ⊆ RNG ⊆ GG ⊆ DT . We aim to verify if graphs, where nodes are sources of nutrients and edges are protoplasmic tubes, appear in the development of the plasmodium in the order NNG → MST → RNG → GG → DT , corresponding to inclusion of the proximity graphs.

scholarly journals Mechanisms Inducing Parallel Computation in a Model of Physarum polycephalum Transport Networks

2015 ◽  
Vol 25 (01) ◽  
pp. 1540004 ◽  
Author(s):  
Jeff Jones
Keyword(s):  
Physarum Polycephalum ◽  
Network Formation ◽  
Proximity Graphs ◽  
Complex Adaptive ◽  
Division Problems ◽  
Scaling Parameters ◽  
Angle Rotation ◽  
Multi Agent ◽  
Robotic Devices ◽  
Adaptive Behaviours

The giant amoeboid organism true slime mould Physarum polycephalum dynamically adapts its body plan in response to changing environmental conditions and its protoplasmic transport network is used to distribute nutrients within the organism. These networks are efficient in terms of network length and network resilience and are parallel approximations of a range of proximity graphs and plane division problems. The complex parallel distributed computation exhibited by this simple organism has since served as an inspiration for intensive research into distributed computing and robotics within the last decade. P. polycephalum may be considered as a spatially represented parallel unconventional computing substrate, but how can this ‘computer’ be programmed? In this paper we examine and catalogue individual low-level mechanisms which may be used to induce network formation and adaptation in a multi-agent model of P. polycephalum. These mechanisms include those intrinsic to the model (particle sensor angle, rotation angle, and scaling parameters) and those mediated by the environment (stimulus location, distance, angle, concentration, engulfment and consumption of nutrients, and the presence of simulated light irradiation, repellents and obstacles). The mechanisms induce a concurrent integration of chemoattractant and chemorepellent gradients diffusing within the 2D lattice upon which the agent population resides, stimulating growth, movement, morphological adaptation and network minimisation. Chemoattractant gradients, and their modulation by the engulfment and consumption of nutrients by the model population, represent an efficient outsourcing of spatial computation. The mechanisms may prove useful in understanding the search strategies and adaptation of distributed organisms within their environment, in understanding the minimal requirements for complex adaptive behaviours, and in developing methods of spatially programming parallel unconventional computers and robotic devices.

scholarly journals Spatial analyses of wildlife contact networks

2015 ◽  
Vol 12 (102) ◽  
pp. 20141004 ◽  
Author(s):  
Stephen Davis ◽  
Babak Abbasi ◽  
Shrupa Shah ◽  
Sandra Telfer ◽  
Mike Begon
Keyword(s):  
Critical Role ◽  
Host Density ◽  
Spatial Arrangement ◽  
Spatial Proximity ◽  
Contact Network ◽  
Spatial Constraints ◽  
Contact Networks ◽  
Proximity Graphs ◽  
Contact Rates ◽  
Pathogen Persistence

Datasets from which wildlife contact networks of epidemiological importance can be inferred are becoming increasingly common. A largely unexplored facet of these data is finding evidence of spatial constraints on who has contact with whom, despite theoretical epidemiologists having long realized spatial constraints can play a critical role in infectious disease dynamics. A graph dissimilarity measure is proposed to quantify how close an observed contact network is to being purely spatial whereby its edges are completely determined by the spatial arrangement of its nodes. Statistical techniques are also used to fit a series of mechanistic models for contact rates between individuals to the binary edge data representing presence or absence of observed contact. These are the basis for a second measure that quantifies the extent to which contacts are being mediated by distance. We apply these methods to a set of 128 contact networks of field voles ( Microtus agrestis ) inferred from mark–recapture data collected over 7 years and from four sites. Large fluctuations in vole abundance allow us to demonstrate that the networks become increasingly similar to spatial proximity graphs as vole density increases. The average number of contacts, , was (i) positively correlated with vole density across the range of observed densities and (ii) for two of the four sites a saturating function of density. The implications for pathogen persistence in wildlife may be that persistence is relatively unaffected by fluctuations in host density because at low density is low but hosts move more freely, and at high density is high but transmission is hampered by local build-up of infected or recovered animals.

Trans-Canada Slimeways

2014 ◽  
pp. 251-265
Author(s):  
Andrew Adamatzky ◽  
Selim G. Akl
Keyword(s):  
Urban Areas ◽  
Physarum Polycephalum ◽  
Minimum Energy ◽  
Extended Body ◽  
Slime Mould ◽  
Proximity Graphs ◽  
Maximum Coverage ◽  
National Highway ◽  
Highway Network ◽  
Similarities And Differences

Slime mould Physarum polycephalum builds up sophisticated networks to transport nutrients between distant parts of its extended body. The slime mould’s protoplasmic network is optimised for maximum coverage of nutrients yet minimum energy spent on transportation of the intra-cellular material. In laboratory experiments with P. polycephalum we represent Canadian major urban areas with rolled oats and inoculated slime mould in the Toronto area. The plasmodium spans the urban areas with its network of protoplasmic tubes. The authors uncover similarities and differences between the protoplasmic network and the Canadian national highway network, analyse the networks in terms of proximity graphs and evaluate slime mould’s network response to contamination.

A Low Arithmetic-Degree Algorithm for Computing Proximity Graphs

2018 ◽  
Vol 28 (03) ◽  
pp. 227-253
Author(s):  
Fabrizio d’Amore ◽  
Paolo G. Franciosa
Keyword(s):  
Minimum Spanning Tree ◽  
Optimal Time ◽  
Complex Data ◽  
Double Precision ◽  
Asymptotically Optimal ◽  
Neighborhood Graph ◽  
Proximity Graphs ◽  
Set Of Points ◽  
Region Approach ◽  
Relative Neighborhood Graph

In this paper, we study the problem of designing robust algorithms for computing the minimum spanning tree, the nearest neighbor graph, and the relative neighborhood graph of a set of points in the plane, under the Euclidean metric. We use the term “robust” to denote an algorithm that can properly handle degenerate configurations of the input (such as co-circularities and collinearities) and that is not affected by errors in the flow of control due to round-off approximations. Existing asymptotically optimal algorithms that compute such graphs are either suboptimal in terms of the arithmetic precision required for the implementation, or cannot handle degeneracies, or are based on complex data structures. We present a unified approach to the robust computation of the above graphs. The approach is a variant of the general region approach for the computation of proximity graphs based on Yao graphs, first introduced in Ref. 43 (A. C.-C. Yao, On constructing minimum spanning trees in [Formula: see text]-dimensional spaces and related problems, SIAM J. Comput. 11(4) (1982) 721–736). We show that a sparse supergraph of these geometric graphs can be computed in asymptotically optimal time and space, and requiring only double precision arithmetic, which is proved to be optimal. The arithmetic complexity of the approach is measured by using the notion of degree, introduced in Ref. 31 (G. Liotta, F. P. Preparata and R. Tamassia, Robust proximity queries: An illustration of degree-driven algorithm design, SIAM J. Comput. 28(3) (1998) 864–889) and Ref. 3 (J. D. Boissonnat and F. P. Preparata, Robust plane sweep for intersecting segments, SIAM J. Comput. 29(5) (2000) 1401–1421). As a side effect of our results, we solve a question left open by Katajainen27 (J. Katajainen, The region approach for computing relative neighborhood graphs in the [Formula: see text] metric, Computing 40 (1987) 147–161) about the existence of a subquadratic algorithm, based on the region approach, that computes the relative neighborhood graph of a set of points [Formula: see text] in the plane under the [Formula: see text] metric.

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