Weighted CDS in Unit Disk Graph

2012 ◽  
pp. 77-104 ◽  
Author(s):  
Ding-Zhu Du ◽  
Peng-Jun Wan
Keyword(s):  
Unit Disk ◽  
Unit Disk Graph

scholarly journals A New Constant Factor Approximation to Construct Highly Fault-Tolerant Connected Dominating Set in Unit Disk Graph

2017 ◽  
Vol 25 (1) ◽  
pp. 18-28 ◽  
Author(s):  
Wei Wang ◽  
Bei Liu ◽  
Donghyun Kim ◽  
Deying Li ◽  
Jingyi Wang ◽  
...  
Keyword(s):  
Unit Disk ◽  
Fault Tolerant ◽  
Dominating Set ◽  
Constant Factor ◽  
Connected Dominating Set ◽  
Unit Disk Graph

scholarly journals Unit Disk Graph-Based Node Similarity Index for Complex Network Analysis

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-22
Author(s):  
Natarajan Meghanathan
Keyword(s):  
Coordinate System ◽  
Unit Disk ◽  
Complex Network ◽  
Search Algorithm ◽  
Similarity Index ◽  
Unit Disk Graph ◽  
Threshold Distance ◽  
Node Level ◽  
Centrality Metrics ◽  
Node Similarity

We seek to quantify the extent of similarity among nodes in a complex network with respect to two or more node-level metrics (like centrality metrics). In this pursuit, we propose the following unit disk graph-based approach: we first normalize the values for the node-level metrics (using the sum of the squares approach) and construct a unit disk graph of the network in a coordinate system based on the normalized values of the node-level metrics. There exists an edge between two vertices in the unit disk graph if the Euclidean distance between the two vertices in the normalized coordinate system is within a threshold value (ranging from 0 tok, where k is the number of node-level metrics considered). We run a binary search algorithm to determine the minimum value for the threshold distance that would yield a connected unit disk graph of the vertices. We refer to “1 − (minimum threshold distance/k)” as the node similarity index (NSI; ranging from 0 to 1) for the complex network with respect to the k node-level metrics considered. We evaluate the NSI values for a suite of 60 real-world networks with respect to both neighborhood-based centrality metrics (degree centrality and eigenvector centrality) and shortest path-based centrality metrics (betweenness centrality and closeness centrality).

scholarly journals DELAUNAY AND DIAMOND TRIANGULATIONS CONTAIN SPANNERS OF BOUNDED DEGREE

2009 ◽  
Vol 19 (02) ◽  
pp. 119-140 ◽  
Author(s):  
PROSENJIT BOSE ◽  
MICHIEL SMID ◽  
DAMING XU
Keyword(s):  
Unit Disk ◽  
Delaunay Triangulation ◽  
Maximum Degree ◽  
Time Algorithm ◽  
Connected Subgraph ◽  
Unit Disk Graph ◽  
Bounded Degree ◽  
Vertex Set ◽  
Range Of Values ◽  
Degree Bound

Given a triangulation G, whose vertex set V is a set of n points in the plane, and given a real number γ with 0 < γ < π, we design an O(n)-time algorithm that constructs a connected subgraph G' of G with vertex set V whose maximum degree is at most 14 + ⌈2π/γ⌉. If G is the Delaunay triangulation of V, and γ = 2π/3, we show that G' is a t-spanner of V (for some constant t) with maximum degree at most 17, thereby improving the previously best known degree bound of 23. If G is a triangulation satisfying the diamond property, then for a specific range of values of γ dependent on the angle of the diamonds, we show that G' is a t-spanner of V (for some constant t) whose maximum degree is bounded by a constant dependent on γ. If G is the graph consisting of all Delaunay edges of length at most 1, and γ = π/3, we show that a modified version of the algorithm produces a plane subgraph G' of the unit-disk graph which is a t-spanner (for some constant t) of the unit-disk graph of V, whose maximum degree is at most 20, thereby improving the previously best known degree bound of 25.

scholarly journals Unit disk graph recognition is NP-hard

1998 ◽  
Vol 9 (1-2) ◽  
pp. 3-24 ◽  
Author(s):  
Heinz Breu ◽  
David G. Kirkpatrick
Keyword(s):  
Unit Disk ◽  
Np Hard ◽  
Unit Disk Graph ◽  
Graph Recognition

scholarly journals Degree-bounded minimum spanning tree for unit disk graph

2012 ◽  
Vol 418 ◽  
pp. 92-105 ◽  
Author(s):  
Hongli Xu ◽  
Liusheng Huang ◽  
Wang Liu ◽  
Yindong Zhang ◽  
Yanjing Sun
Keyword(s):  
Unit Disk ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Unit Disk Graph
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