
Computational Geometry, Graphs and Applications
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Content
- Intro
- Title
- Preface
- Organization
- Table of Contents
- Determination of All Tessellation Polyhedra with Regular Polygonal Faces
- Introduction
- Regular Faced Tessellation Polyhedra
- Another Necessary Condition for Regular Faced Polyhedra to Have the Tessellation Property
- Main Theorem
- References
- Regular Graphs with Maximum Forest Number
- Introduction
- Connected Subclasses
- The Main Results
- $r+1\le n\le 2r-1$
- $n\ge 2r$
- References
- Semi Voronoi Diagrams
- Introduction
- Some Preliminary Results When the Visible Angle Is 180
- When the Visible Angle Is Not 180
- Area Not Controlled by Any Member in P
- Partition of the Plane by Two Sets
- Future Studies
- References
- Making Polygons by Simple Folds and One Straight Cut
- Introduction
- Definitions
- Passages
- Algorithm
- High-Level Algorithm
- Algorithmic Details
- Correctness
- Passage Invariant
- Shrinking Excess Paper
- Feasible Folds Are Safe
- Approaching the Convex Hull (Step 1)
- Approaching Limit Endpoints (Step 3)
- Convex Polygons
- Conclusion
- References
- Common Unfoldings of Polyominoes and Polycubes
- Introduction
- Unfolding Path-Like Polyominoes
- Unfolding Polycubes
- Path-Like Planar Polycubes
- Tree-Like Planar Polycubes
- Pentacubes
- References
- Affine Equivalent Classes of Parallelohedra
- Introduction, Basic Notions
- The Uniqueness Theorem
- References
- Fr\'{e} chet-Distance on Road Networks
- Introduction
- Preliminaries
- Computing the Fréchet-Distance Based on Network Distance
- Decision Problem
- Optimization Problem
- Variants of the Fréchet Distance Based on Network Distance
- The weak Fréchet-Distance Based on Network Distance
- The Discrete and Weak Discrete Frechét-Distance Based on Network Distance
- Conclusions
- References
- Acute Triangulations of the Cuboctahedral Surface
- Introduction
- Non-obtuse Triangulations
- Acute Triangulations
- No Acute Triangulation with Fewer Triangles
- References
- Edge Clique Partition of K4-Free and Planar Graphs
- Introduction
- Preliminaries
- K4-Free Graphs
- Planar Graphs
- Planar K4-Free Graphs
- Conclusions
- References
- Generation of Polyiamonds for p6 Tiling by the Reverse Search
- Introduction
- Preliminaries
- Generation Algorithms for p6 Tiling
- Family Trees
- Generating Polyiamonds
- Counting the Number of Polyiamonds
- Experimental Results
- Conclusions
- References
- Continuous Flattening of Platonic Polyhedra
- Introduction
- Lemma and Propositions
- Theorems and Proofs
- Further Research
- References
- Minimal Embedding of Hypercubic Graphs on Surface
- Introduction and Definition
- Lower Bound of (G)
- Upper Bound of (Qn)
- Minimal Embedding of Qn
- Conclusions
- References
- A Morphology Method for Determining the Number of Clusters Present in Spectral Co-clustering Documents and Words
- Introduction
- Typical Spectral Co-clustering Documents and Words
- Our Method for Determining the Number of Clusters Present in Spectral Co-clustering Documents and Words
- Generating a VAT Image
- Filtering the VAT Image
- Determination of Cluster Number
- Experimental Results and Comparisons
- Results on Different Methods for Automatically Determining the Number of Clusters
- Results for Modified Spectral Co-clustering Documents and Words Method
- Conclusion
- References
- A Property about the Convex Lattice Set in ZZ$^2$
- Introduction
- Proof of Main Result
- References
- On the Diameter of a Circle to Hold a Cube
- Introduction
- A Few Lemmas
- The Cube Case
- Outline of the Octahedron Case
- References
- An A* Algorithm Framework for the point-to-point Time-Dependent Shortest Path Problem
- Introduction
- Time-Dependent A* Algorithm Framework for TDSPP
- Time-Dependent ALT Algorithm for TDSPP
- Experimental Results
- Conclusion
- References
- Monotonic Polygons and Paths in Weighted Point Sets
- Introduction
- Monotonic Polygons in wp-sets
- wp-sets in Convex Position
- wp-sets in General Position
- Counting Monotonic Convex k-gons in PCn
- Monotonic Empty Quadrilaterals in PPn
- Lower Bound
- Upper Bound
- Monotonic Paths in wp-sets in Convex Position
- References
- Simple Characterization of LR-visibility Polygons
- Introduction
- Preliminary
- Characterizing LR-visibility Polygons
- Recognizing LR-visibility Polygons
- Shortest Path Trees in an LR-visibility Polygon
- Computing All Non-redundant Backward Components
- The Algorithm and Its Analysis
- References
- A 7/6-Approximation Algorithm for the Max-Min Connected Bipartition Problem on Grid Graphs
- Introduction
- Preliminaries
- Non-separating Connectors
- An Approximation Algorithm for GBCP2
- Concluding Remarks
- References
- Local Modification of Skin Surface Mesh: Towards Free-Form Skin Surface Deformation
- Introduction
- Background
- Delaunay and Voronoi Complexes
- Skin
- Skin Deformation and Local Modification
- Dynamic Skin Triangulation
- Local Modification of Skin Surface
- Updates on Delaunay and Voronoi Complexes
- Mixed Cells Deformation
- Surface Points Movements
- Maintaining the Mesh by Scheduling Algorithm
- Scheduling Edge Update
- Scheduling Triangle Update
- Handling Topology Changes
- Scheduling of Topology Preserving Operations
- Hyperboloid Warping
- Experiment Results and Conclusion
- References
- A Kind of Triangle Covering and Packing Problem
- Introduction
- Covering an Equilateral Triangle with Equilateral Triangles
- Packing an Equilateral Triangle by Equilateral Triangles
- References
- Consecutive Edge-Colorings of Generalized $\theta$ -Graphs
- Introduction and Preliminary
- Upper Bound of S($\theta$ m)
- CEC of m with Possible Spans
- Concluding Remarks
- References
- Author Index
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