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Massive sizes of real-world graphs, such as social networks and web graph, impose serious challenges to process and perform analytics on them. These issues can be resolved by working on a small summary of the graph instead . A summary is a…
We introduce in this paper a new summarization method for large graphs. Our summarization approach retains only a user-specified proportion of the neighbors of each node in the graph. Our main aim is to simplify large graphs so that they…
We study distributed algorithms for some fundamental problems in data summarization. Given a communication graph $G$ of $n$ nodes each of which may hold a value initially, we focus on computing $\sum_{i=1}^N g(f_i)$, where $f_i$ is the…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
Are users of an online social network interested equally in all connections in the network? If not, how can we obtain a summary of the network personalized to specific users? Can we use the summary for approximate query answering? As…
Summarizing web graphs is challenging due to the heterogeneity of the modeled information and its changes over time. We investigate the use of neural networks for lifelong graph summarization. Assuming we observe the web graph at a certain…
This paper addresses the problem of finding a B-term wavelet representation of a given discrete function $f \in \real^n$ whose distance from f is minimized. The problem is well understood when we seek to minimize the Euclidean distance…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
Clustering trajectory data attracted considerable attention in the last few years. Most of prior work assumed that moving objects can move freely in an euclidean space and did not consider the eventual presence of an underlying road network…
Finding similar user pairs is a fundamental task in social networks, with numerous applications in ranking and personalization tasks such as link prediction and tie strength detection. A common manifestation of user similarity is based upon…
Let $G=(V,E)$ be a finite, connected graph. We consider a greedy selection of vertices: given a list of vertices $x_1, \dots, x_k$, take $x_{k+1}$ to be any vertex maximizing the sum of distances to the existing vertices and iterate: we…
A distributed network is modeled by a graph having $n$ nodes (processors) and diameter $D$. We study the time complexity of approximating {\em weighted} (undirected) shortest paths on distributed networks with a $O(\log n)$ {\em bandwidth…
We consider the following natural generalization of Binary Search: in a given undirected, positively weighted graph, one vertex is a target. The algorithm's task is to identify the target by adaptively querying vertices. In response to…
In network analysis and graph mining, closeness centrality is a popular measure to infer the importance of a vertex. Computing closeness efficiently for individual vertices received considerable attention. The NP-hard problem of group…
Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently…
Which one is better between two representative graph summarization models with and without edge weights? From web graphs to online social networks, large graphs are everywhere. Graph summarization, which is an effective graph compression…
Due to exponential growth of complex data, graph structure has become increasingly important to model various entities and their interactions, with many interesting applications including, bioinformatics, social network analysis, etc.…
In this paper, we propose a new method to compute the barycenter of large weighted graphs endowed with probability measures on their nodes. We suppose that the edge weights are distances between the nodes and that the probability measure on…
In Topological Data Analysis, a common way of quantifying the shape of data is to use a persistence diagram (PD). PDs are multisets of points in $\mathbb{R}^2$ computed using tools of algebraic topology. However, this multi-set structure…