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# Bounceur A., Bezoui M., Euler R. Boundaries and Hulls of Euclidean Graphs

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Boca Raton: CRC Press, 2019. — 218 p.
Contents :
Cover
Half Title
Title
Dedication
Acknowledgments
Preface
Basic definitions
Partial graphs and subgraphs
Chains and cycles
Some classes of graphs
Hamiltonian graphs
Planar graphs
Minimum spanning trees
Non-graphical representations of a graph
Computational geometry
Delaunay triangulations
Planar straight-line graphs
Euclidean graphs
Polygons
Pseudo-polygons
Angles and visits
Visiting polar angles
Interior and exterior angles and polygons
Angle-based method
Minimum x-coordinate based method
Definitions and properties
Examples
Definitions and properties
Examples
Definition and properties
Relation between α-shape and Delaunay triangulation
Boundaries of graphs
Polygon hull of general Euclidean graphs
B-polygon hull
C-polygon hull
Finding the convex hull of a set of points in the plane
Jarvis' algorithm
The Quickhull algorithm
Andrew's algorithm
Kallay's algorithm
Chan's algorithm
Finding a concave hull of a set of points in the plane
Split and merge
Perceptual boundary extraction
K-nearest neighbor
Concaveness measure
LPCN: Least Polar-angle Connected Node algorithm to find a polygon hull of a connected Euclidean graph
A-polygon hull
B-polygon hull
C-polygon hull
Finding the polygon hull of a Euclidean graph without conditions on the starting vertex
What is a distributed algorithm?
Basic concepts
Complexity of distributed algorithms
Flooding and spanning tree
Flooding for Leaf Finding
Wait-Before-Starting
Minimum Finding
Local Minima Finding
Global Minimum Finding
The concept
The algorithm
The concept
The algorithm
The algorithm
Comparison of the leader election algorithms
The D-LPCN algorithm
The D-RRLPCN algorithm
The simulator CupCarbon and boundary detection
CupCarbon for network simulation
Sensor node
Analog events (Gas)
Marker
An introduction to SenScript
Sending and receiving messages
Routing
Flooding
Wait-Before-Starting (WBS)
Wait-Before-Starting with Flooding
Wait-Before-Starting with FLF
Global Minimum Finding
The R-LOGO algorithm
The R-BrOGO algorithm
The DoTRo algorithm
Version 1: fixing the starting node manually
Version 2: starting from Minimum Finding
Version 3: starting from R-BrOGO
Version 4: starting from DoTRo
Finding the boundary nodes of a WSN
Boundary node failure detection and reconfiguration
Finding voids and gaps in WSNs
Cluster finding and shape reconstruction
Image contour polygon
Polygon hull in an angle graph
Bibliography
Index
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