Related papers: Counting k-Hop Paths in the Random Connection Mode…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
We consider a linear multi-hop network composed of multi-state discrete-time memoryless channels over each hop, with orthogonal time-sharing across hops under a half-duplex relaying protocol. We analyze the probability of error and…
The high-level contribution of this paper is a simulation-based analysis to evaluate the tradeoffs between lifetime and hop count of link-disjoint, node-disjoint and zone-disjoint multi-path routes vis-\`a-vis single-path minimum hop routes…
We consider a natural model of random knotting- choose a knot diagram at random from the finite set of diagrams with n crossings. We tabulate diagrams with 10 and fewer crossings and classify the diagrams by knot type, allowing us to…
In this paper, we investigate the exact asymptotic behavior of the connectivity probability in the Erdos-Renyi graph G(n,p), under different asymptotic assumptions on the edge probability p=p(n). We propose a novel approach based on the…
This paper proposes a new method for optimizing frequency-hopping ad hoc networks in the presence of Rayleigh fading. It is assumed that the system uses a capacity-approaching code (e.g., turbo or LDPC) and noncoherent binary…
We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is…
This paper considers the Hamiltonian walk problem in the multi-agent coordination framework, referred to as $k$-agents Hamiltonian walk problem ($k$-HWP). In this problem, a set of $k$ connected agents collectively compute a spanning walk…
Random intersection graphs have received much attention recently and been used in a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. For these graphs, each node is equipped…
The matching problem is a notorious combinatorial optimization problem that has attracted for many years the attention of the statistical physics community. Here we analyze the Euclidean version of the problem, i.e. the optimal matching…
Due to the computational complexity of finding almost shortest simple paths, we propose that identifying a larger collection of (nonbacktracking) paths is more efficient than finding almost shortest simple paths on positively weighted…
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad-hoc networks "soft" or "probabilistic"…
We study growth properties of the number of paths of lenght k for a variant of Cameo graphs introduced in an earlier paper. Sharp results are obtained for threshold for the k-path connectivity and the essential diameter.
The exact closed-form expressions for outage probability and bit error rate of spectrum sharing-based multi-hop decodeand- forward (DF) relay networks in non-identical Rayleigh fading channels are derived. We also provide the approximate…
Sampling random nodes is a fundamental algorithmic primitive in the analysis of massive networks, with many modern graph mining algorithms critically relying on it. We consider the task of generating a large collection of random nodes in…
A new network construction method is presented for building of scalable, high throughput, low latency networks. The method is based on the exact equivalence discovered between the problem of maximizing network throughput (measured as…
Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…
We present two complementary analytical approaches for calculating the distribution of shortest path lengths in Erdos-R\'enyi networks, based on recursion equations for the shells around a reference node and for the paths originating from…
Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present…
In discrete planar last passage percolation (LPP), random values are assigned independently to each vertex in $\mathbb Z^2$, and each finite upright path in $\mathbb Z^2$ is ascribed the weight given by the sum of values of its vertices.…