Related papers: Online Algorithms for Spectral Hypergraph Sparsifi…
Wideband spectrum sensing is an essential part of cognitive radio systems. Exact spectrum estimation is usually inefficient as it requires sampling rates at or above the Nyquist rate. Using prior information on the structure of the signal…
A recent palette sparsification theorem of Assadi, Chen, and Khanna [SODA'19] states that in every $n$-vertex graph $G$ with maximum degree $\Delta$, sampling $O(\log{n})$ colors per each vertex independently from $\Delta+1$ colors almost…
We consider a basic problem in the general data streaming model, namely, to estimate a vector $f \in \Z^n$ that is arbitrarily updated (i.e., incremented or decremented) coordinate-wise. The estimate $\hat{f} \in \Z^n$ must satisfy…
In this paper, we initiate the study of the vertex coloring problem of a graph in the semi streaming model. In this model, the input graph is defined by a stream of edges, arriving in adversarial order and any algorithm must process the…
In recent years, hypergraph generalizations of many graph cut problems have been introduced and analyzed as a way to better explore and understand complex systems and datasets characterized by multiway relationships. Recent work has made…
We study the densest subgraph problem and give algorithms via multiplicative weights update and area convexity that converge in $O\left(\frac{\log m}{\epsilon^{2}}\right)$ and $O\left(\frac{\log m}{\epsilon}\right)$ iterations,…
We introduce a novel measure for quantifying the error in input predictions. The error is based on a minimum-cost hyperedge cover in a suitably defined hypergraph and provides a general template which we apply to online graph problems. The…
We present a spectral approach to design approximation algorithms for network design problems. We observe that the underlying mathematical questions are the spectral rounding problems, which were studied in spectral sparsification and in…
A seminal palette sparsification result of Assadi, Chen, and Khanna states that in every $n$-vertex graph of maximum degree $\Delta$, sampling $\Theta(\log n)$ colors per vertex from $\{1, \ldots, \Delta+1\}$ almost certainly allows for a…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
Depth first search is a fundamental graph problem having a wide range of applications. For a graph $G=(V,E)$ having $n$ vertices and $m$ edges, the DFS tree can be computed in $O(m+n)$ using $O(m)$ space where $m=O(n^2)$. In the streaming…
Decomposing hypergraphs is a key task in hypergraph analysis with broad applications in community detection, pattern discovery, and task scheduling. Existing approaches such as $k$-core and neighbor-$k$-core rely on vertex degree…
We study the algorithmic tractability of finding large independent sets in dense random hypergraphs. In the sparse regime, much of the natural algorithms can be formulated within either the local or the low-degree polynomial (LDP)…
Given a graph, an edge coloring assigns colors to edges so that no pairs of adjacent edges share the same color. We are interested in edge coloring algorithms under the W-streaming model. In this model, the algorithm does not have enough…
The iterations of many sparse estimation algorithms are comprised of a fixed linear filter cascaded with a thresholding nonlinearity, which collectively resemble a typical neural network layer. Consequently, a lengthy sequence of algorithm…
In this paper, we consider the problem of approximating the densest subgraph in the dynamic graph stream model. In this model of computation, the input graph is defined by an arbitrary sequence of edge insertions and deletions and the goal…
We study the complexity of local graph centrality estimation, with the goal of approximating the centrality score of a given target node while exploring only a sublinear number of nodes/arcs of the graph and performing a sublinear number of…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…
The Sparsest Cut is a fundamental optimization problem that has been extensively studied. For planar inputs the problem is in $P$ and can be solved in $\tilde{O}(n^3)$ time if all vertex weights are $1$. Despite a significant amount of…