4 citations · 13 across the 58 of their papers we have counts for
63 papers
Criticality in Dissimilar Decomposition and Undersampling of Random Datasets with Anomalies
Ghurumuruhan Ganesan
Training datasets for upcoming LLMs would include a significant amount of AI text/image data generated from current LLMs. In such a scenario, it is important to understand how this…
Extremal Spanning Trees of Random Marked Graphs with Independent Edge Weights
Ghurumuruhan Ganesan
In this paper, we consider a Bernoulli random graph~\(G\) on~\(n\) vertices with non-uniform edge probabilities, where each vertex has an independent mark and each edge is equipped…
Constrained Maximum Weight Paths in Random Geometric Graphs
Ghurumuruhan Ganesan
In this paper, we consider a random geometric graph (RGG)~\(G\) formed by~\(n\) vertices distributed uniformly in the unit square~\(S\) on the plane and equip each edge of~\(G\) wi…
Maximum Spanning Trees of Random Geometric Graphs With Independent Edge Weights
Ghurumuruhan Ganesan
In this paper, we study maximum weight spanning trees of the random geometric graph (RGG)~\(G\) formed by~\(n\) vertices where each edge is independently either open or closed with…
Deviation Estimates for Extremal Relay Random Geometric Graphs
Ghurumuruhan Ganesan
In this paper, we consider a deterministic graph~\(Γ\) drawn on the unit square with straight line segments as edges and connect vertices of~\(Γ\) using edges of a random geometric…
Extremal Planar Matchings of Inhomogenous Random Bipartite Graphs
Ghurumuruhan Ganesan
In this paper we study maximum size and minimum weight planar matchings of inhomogenous random bipartite graphs. Our motivation for this study comes from efficient usage of cross e…
Dissimilar Batch Decompositions of Random Datasets
Ghurumuruhan Ganesan
For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probab…
Dirac-type Theorems for Inhomogenous Random Graphs
Ghurumuruhan Ganesan
In this paper, we study Dirac-type theorems for an inhomogenous random graph (G) whose edge probabilities are not necessarily all the same. We obtain sufficient conditions for the…
Tracking the Mean of a Piecewise Stationary Sequence
Ghurumuruhan Ganesan
In this paper we study the problem of tracking the mean of a piecewise stationary sequence of independent random variables. First we consider the case where the transition times ar…
Classification and Regression Error Bounds for Inhomogenous Data With Applications to Wireless Networks
Ghurumuruhan Ganesan
In this paper, we study classification and regression error bounds for inhomogenous data that are independent but not necessarily identically distributed. First, we consider classi…
Linearity and Local Correctness in Weighted Colourings of Random Graphs
Ghurumuruhan Ganesan
In this paper, we consider a weighted generalization of the chromatic number of a Binomial random graph~\(G.\) We equip each edge with a random weight and then colour the vertices…
Linearity Property of Unique Colourings in Random Graphs
Ghurumuruhan Ganesan
In this paper, we study unique colourings in random graphs as a generalization of both conflict-free and injective colourings. Specifically, we impose the condition that a fraction…
Critical Exponent for the Acyclic Chromatic Number of Random Graphs
Ghurumuruhan Ganesan
In this paper we study acyclic colouring in the random subgraph of the complete graph on vertices where each edge is present with probabili…
A Probabilistic Model for Data Redundancy in the Feature Domain
Ghurumuruhan Ganesan
In this paper, we use a probabilistic model to estimate the number of uncorrelated features in a large dataset. Our model allows for both pairwise feature correlation (collinearity…
Probabilistic Bounds for Data Storage with Feature Selection and Undersampling
Ghurumuruhan Ganesan
In this paper we consider data storage from a probabilistic point of view and obtain bounds for efficient storage in the presence of feature selection and undersampling, both of wh…
Linear Codes with Prescribed Hull Dimension and Minimum Distance
Ghurumuruhan Ganesan
The hull of a linear code (i.e., a finite field vector space)~\({\mathcal C}\) is defined to be the vector space formed by the intersection of~\({\mathcal C}\) with its dual~\({\ma…
Linear Eulerian Extensions of Inhomogenous Random Graphs
Ghurumuruhan Ganesan
The Eulerian extension number of any graph~\(H\) (i.e. the minimum number of edges needed to be added to make~\(H\) Eulerian) is at least~\(t(H),\) half the number of odd degree ve…
Euclidean minimum spanning trees with location dependent and power weighted edges
Ghurumuruhan Ganesan
Consider~\(n\) nodes~\(\{X_i\}_{1 \leq i \leq n}\) independently distributed in the unit square~\(S,\) each according to a distribution~\(f\) and let~\(K_n\) be the complete graph…
Robust Domination in Random Graphs
Ghurumuruhan Ganesan
In this paper, we study "robust" dominating sets of random graphs that retain the domination property even if a small \emph{deterministic} set of edges are removed. We motivate our…
Weighted Domination and Colouring in Random Graphs
Ghurumuruhan Ganesan
In the first part of this paper, we consider weighted domination in the case where the vertices of the complete graph on~\(n\) vertices are equipped with independent and identicall…
Edge Constrained Eulerian Extensions
Ghurumuruhan Ganesan
In this paper we study Eulerian extensions with edge constraints and use the probabilistic method to establish sufficient conditions for a given connected graph to be a subgraph of…
Redundancy of Codes with Graph Constraints
Ghurumuruhan Ganesan
In this paper, we study the redundancy of linear codes with graph constraints. First we consider linear parity check codes based on bipartite graphs with diversity and with general…
Minimum Weight Random Graphs with Edge Constraints
Ghurumuruhan Ganesan
In this paper, we study two examples of minimum weight random graphs with edge constraints. First we consider the complete graph on vertices equipped with uniformly heavy edg…
Coloured and Dependent Planar Matchings of Random Bipartite Graphs
Ghurumuruhan Ganesan
In this paper, we study two problems related to planar matchings in random bipartite graphs. First, we colour each edge of the complete bipartite graph uniformly randomly…