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We prove the unexpected result that almost uniform sampling of independent sets in graphs is possible via a probabilistic polynomial time algorithm. Note that our sampling algorithm (if correct) has extremely surprising consequences; the…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to…
Dense subgraph discovery is an important problem in graph mining and network analysis with several applications. Two canonical problems here are to find a maxcore (subgraph of maximum min degree) and to find a densest subgraph (subgraph of…
We initiate a systematic study of algorithms that are both differentially private and run in sublinear time for several problems in which the goal is to estimate natural graph parameters. Our main result is a differentially-private…
Large data applications rely on storing data in massive, sparse graphs with millions to trillions of nodes. Graph-based methods, such as node prediction, aim for computational efficiency regardless of graph size. Techniques like localized…
Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…
For each $p \in (0,2]$, we present a randomized algorithm that returns an $\epsilon$-approximation of the $p$th frequency moment of a data stream $F_p = \sum_{i = 1}^n \abs{f_i}^p$. The algorithm requires space $O(\epsilon^{-2} \log…
In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…
In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets $X_m$ of the set $X_n$ (subset sum problem). Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly…
Coordination graph is a promising approach to model agent collaboration in multi-agent reinforcement learning. It conducts a graph-based value factorization and induces explicit coordination among agents to complete complicated tasks.…
The problem of graphical model selection is to correctly estimate the graph structure of a Markov random field given samples from the underlying distribution. We analyze the information-theoretic limitations of the problem of graph…
This paper makes three contributions to estimating the number of perfect matching in bipartite graphs. First, we prove that the popular sequential importance sampling algorithm works in polynomial time for dense bipartite graphs. More…
Notions of graph similarity provide alternative perspective on the graph isomorphism problem and vice-versa. In this paper, we consider measures of similarity arising from mismatch norms as studied in Gervens and Grohe: the edit distance…
Community detection is a fundamental task in graph analysis, with methods often relying on fitting models like the Stochastic Block Model (SBM) to observed networks. While many algorithms can accurately estimate SBM parameters when the…
We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning…
We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with…
In this paper, we design efficient algorithms to approximately count the number of edges of a given $k$-hypergraph, and to sample an approximately uniform random edge. The hypergraph is not given explicitly, and can be accessed only through…
Given a join with an acyclic set of degree constraints, we show how to draw a uniformly random sample from the join result in $O(\mathit{polymat}/ \max \{1, \mathrm{OUT} \})$ expected time after a preprocessing of $O(\mathrm{IN})$ expected…
In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…