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Random graph generation is an important tool for studying large complex networks. Despite abundance of random graph models, constructing models with application-driven constraints is poorly understood. In order to advance state-of-the-art…
The problem of recovering planted community structure in random graphs has received a lot of attention in the literature on the stochastic block model, where the input is a random graph in which edges crossing between different communities…
Karger (SIAM Journal on Computing, 1999) developed the first fully-polynomial approximation scheme to estimate the probability that a graph $G$ becomes disconnected, given that its edges are removed independently with probability $p$. This…
Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and a number of methods have been developed for scaling subgraph counting to large graphs. Many real-world networks carry a natural notion of strength of…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
Analyzing large graph data is an essential part of many modern applications, such as social networks. Due to its large computational complexity, distributed processing is frequently employed. This requires graph data to be divided across…
In this paper, we develop efficient exact and approximate algorithms for computing a maximum independent set in random graphs. In a random graph $G$, each pair of vertices are joined by an edge with a probability $p$, where $p$ is a…
We give an algorithm to find a minimum cut in an edge-weighted directed graph with $n$ vertices and $m$ edges in $\tilde O(n\cdot \max(m^{2/3}, n))$ time. This improves on the 30 year old bound of $\tilde O(nm)$ obtained by Hao and Orlin…
There exist many orthogonal graph drawing algorithms that minimize edge crossings or edge bends, however they produce unsatisfactory drawings in many practical cases. In this paper we present a grid-based algorithm for drawing orthogonal…
We explore the use of local algorithms in the design of streaming algorithms for the Maximum Directed Cut problem. Specifically, building on the local algorithm of Buchbinder et al. (FOCS'12) and Censor-Hillel et al. (ALGOSENSORS'17), we…
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. In this paper, we engineer the fastest known exact algorithm for the problem.…
The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network's graph. In this paper, we show that pre-processing can help in finding good triangulations forprobabilistic…
In this paper we present improved results on the problem of counting triangles in edge streamed graphs. For graphs with $m$ edges and at least $T$ triangles, we show that an extra look over the stream yields a two-pass treaming algorithm…
Designing distributed and scalable algorithms to improve network connectivity is a central topic in peer-to-peer networks. In this paper we focus on the following well-known problem: given an $n$-node $d$-regular network for $d=\Omega(\log…
Computing maximum independent sets in graphs is an important problem in computer science. In this paper, we develop an evolutionary algorithm to tackle the problem. The core innovations of the algorithm are very natural combine operations…
In $d$-Scattered Set we are given an (edge-weighted) graph and are asked to select at least $k$ vertices, so that the distance between any pair is at least $d$, thus generalizing Independent Set. We provide upper and lower bounds on the…
We study the problem of detecting local geometry in random graphs. We introduce a model $\mathcal{G}(n, p, d, k)$, where a hidden community of average size $k$ has edges drawn as a random geometric graph on $\mathbb{S}^{d-1}$, while all…
Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in…
Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely…
An $r$-cut of a $k$-uniform hypergraph is a partition of its vertex set into $r$ parts, and the size of the cut is the number of edges which have at least one vertex in each part. The study of the possible size of the largest $r$-cut in a…