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Small depth networks arise in a variety of network related applications, often in the form of maximum flow and maximum weighted matching. Recent works have generalized such methods to include costs arising from concave functions. In this…
Real-world graphs are massive in size and we need a huge amount of space to store them. Graph compression allows us to compress a graph so that we need a lesser number of bits per link to store it. Of many techniques to compress a graph, a…
Compressed Counting (CC)} was recently proposed for approximating the $\alpha$th frequency moments of data streams, for $0<\alpha \leq 2$. Under the relaxed strict-Turnstile model, CC dramatically improves the standard algorithm based on…
We consider a routing problem which plays an important role in several applications, primarily in communication network planning and VLSI layout design. The original underlying graph algorithmic task is called Disjoint Paths problem. In…
Designing effective algorithms for community detection is an important and challenging problem in {\em large-scale} graphs, studied extensively in the literature. Various solutions have been proposed, but many of them are centralized with…
Reliable propagation of information through large networks, e.g., communication networks, social networks or sensor networks is very important in many applications concerning marketing, social networks, and wireless sensor networks.…
Data stream mining aims at extracting meaningful knowledge from continually evolving data streams, addressing the challenges posed by nonstationary environments, particularly, concept drift which refers to a change in the underlying data…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with…
We give an $\widetilde{O}({m^{3/2 - 1/762} \log (U+W))}$ time algorithm for minimum cost flow with capacities bounded by $U$ and costs bounded by $W$. For sparse graphs with general capacities, this is the first algorithm to improve over…
In a graph, a community may be loosely defined as a group of nodes that are more closely connected to one another than to the rest of the graph. While there are a variety of metrics that can be used to specify the quality of a given…
The capacity (or maximum flow) of an unicast network is known to be equal to the minimum s-t cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is dynamically changing or unknown, it is not…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
Data flow analysis and optimization is considered for homogeneous rectangular mesh networks. We propose a flow matrix equation which allows a closed-form characterization of the nature of the minimal time solution, speedup and a simple…
In this paper, we study the impact of edge weights on distances in diluted random graphs. We interpret these weights as delays, and take them as i.i.d exponential random variables. We analyze the weighted flooding time defined as the…
In real-world scenarios, large graphs represent relationships among entities in complex systems. Mining these large graphs often containing millions of nodes and edges helps uncover structural patterns and meaningful insights. Dividing a…
In this paper, we first introduce the weighted forward reduced volume of Ricci flow. The weighted forward reduced volume, which related to expanders of Ricci flow, is well-defined on noncompact manifolds and monotone non-increasing under…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
Community detection is a critical task in graph theory, social network analysis, and bioinformatics, where communities are defined as clusters of densely interconnected nodes. However, detecting communities in large-scale networks with…
In community detection, the exact recovery of communities (clusters) has been mainly investigated under the general stochastic block model with edges drawn from Bernoulli distributions. This paper considers the exact recovery of communities…
A fundamental problem in the analysis of network data is the detection of network communities, groups of densely interconnected nodes, which may be overlapping or disjoint. Here we describe a method for finding overlapping communities based…