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The quest for efficient sorting is ongoing, and we will explore a graph-based stable sorting strategy, in particular employing comparison graphs. We use the topological sort to map the comparison graph to a linear domain, and we can…
We study the problem of approximately simulating a $t$-step random walk on a graph where the input edges come from a single-pass stream. The straightforward algorithm using reservoir sampling needs $O(nt)$ words of memory. We show that this…
In many statistical applications, the dimension is too large to handle for standard high-dimensional machine learning procedures. This is particularly true for graphical models, where the interpretation of a large graph is difficult and…
As graphs continue to grow in size, we seek ways to effectively process such data at scale. The model of streaming graph processing, in which a compact summary is maintained as each edge insertion/deletion is observed, is an attractive one.…
Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
Where graphs are used for modelling and specifying systems, consistency is an important concern. To be a valid model of a system, the graph structure must satisfy a number of constraints. To date, consistency has primarily been viewed as a…
This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…
Real-time analysis of graphs containing temporal information, such as social media streams, Q&A networks, and cyber data sources, plays an important role in various applications. Among them, detecting patterns is one of the fundamental…
In this paper we present a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams (where the input graph is defined by a sequence of edge/hyperedge insertions…
The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…
Distances in a network capture relations between nodes and are the basis of centrality, similarity, and influence measures. Often, however, the relevance of a node $u$ to a node $v$ is more precisely measured not by the magnitude of the…
In the real world, data streams are ubiquitous -- think of network traffic or sensor data. Mining patterns, e.g., outliers or clusters, from such data must take place in real time. This is challenging because (1) streams often have high…
We study the problem of graph and hypergraph sparsification in insertion-only data streams. The input is a hypergraph $H=(V, E, w)$ with $n$ nodes, $m$ hyperedges, and rank $r$, and the goal is to compute a hypergraph $\widehat{H}$ that…
Part I of this paper considered optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network…
There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a…
A random walk on a directed graph gives a Markov chain on the vertices of the graph. An important question that arises often in the context of Markov chain is whether the uniform distribution on the vertices of the graph is a stationary…
In this work, we present the first efficient and practical algorithm for estimating the number of triangles in a graph stream using predictions. Our algorithm combines waiting room sampling and reservoir sampling with a predictor for the…
Graph processes exhibit a temporal structure determined by the sequence index and and a spatial structure determined by the graph support. To learn from graph processes, an information processing architecture must then be able to exploit…
Real-world graphs often manifest as a massive temporal stream of edges. The need for real-time analysis of such large graph streams has led to progress on low memory, one-pass streaming graph algorithms. These algorithms were designed for…