Numerical inversion of two-dimensional Laplace transforms—Fourier series representation
Applied Numerical Mathematics
On the connectivity of a random interval graph
Proceedings of the seventh international conference on Random structures and algorithms
Numerical Inversion of Laplace Transforms Using Laguerre Functions
Journal of the ACM (JACM)
On k-connectivity for a geometric random graph
Random Structures & Algorithms
Approximating layout problems on random geometric graphs
Journal of Algorithms
Random Geometric Problems on [0, 1]²
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks
IEEE Transactions on Mobile Computing
Stochastic properties of the random waypoint mobility model
Wireless Networks
The capacity of wireless networks
IEEE Transactions on Information Theory
Towards an information theory of large networks: an achievable rate region
IEEE Transactions on Information Theory
A network information theory for wireless communication: scaling laws and optimal operation
IEEE Transactions on Information Theory
Topological properties of the one dimensional exponential random geometric graph
Random Structures & Algorithms
Connectivity in a random interval graph with access points
Information Processing Letters
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Suppose that V = {v_{1,} v_{2,}\ldots v_n}is a set of nodes randomly (uniformly) distributed in the d dimensional cube[0,x_0 ]^d, and W = {w(i,j) 0 : 1 驴 i,j 驴 n} is a set of numbers chosen so that w(i,j) = w(j,i). Construct a graph G_{n,d,w} whose vertex set is V, and whose edge set consists of all pairs {u_i ,u_j}with \left\| {\{ u_i- u_j \} } \right\| \leqslant w(i,j). In the wireless network context, the set V is a set of labeled nodes in the network and W represents the maximum distances between the node pairs for them to be connected. We essentially addressed the following question: "If G is a graph with vertex set V, what is the probability that G appears as a subgraph in G_{n,d,w}?" Our main contribution is a closed form expression for this probability under the \iota _\infty norm for any dimension d and a suitably defined probability density function. As a corollary to the above answer, we also answer the question, "What is the probability that G_{n,d,w} is connected?"