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Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…
For very large values of $k$, we consider methods for fast $k$-means clustering of massive datasets with $10^7\sim10^9$ points in high-dimensions ($d\geq100$). All current practical methods for this problem have runtimes at least…
We present a universally-optimal distributed algorithm for the exact weighted min-cut. The algorithm is guaranteed to complete in $\widetilde{O}(D + \sqrt{n})$ rounds on every graph, recovering the recent result of Dory, Efron,…
We consider the streaming complexity of a fundamental task in approximate pattern matching: the $k$-mismatch problem. It asks to compute Hamming distances between a pattern of length $n$ and all length-$n$ substrings of a text for which the…
It has been shown that one can design distributed algorithms that are (nearly) singularly optimal, meaning they simultaneously achieve optimal time and message complexity (within polylogarithmic factors), for several fundamental global…
In this paper we study the hardness of the $k$-Center problem on inputs that model transportation networks. For the problem, a graph $G=(V,E)$ with edge lengths and an integer $k$ are given and a center set $C\subseteq V$ needs to be chosen…
A number of stations, independently activated over time, is able to communicate by transmitting and listening to a shared channel in discrete time slots, and a message is successfully delivered to all stations if and only if its source…
In the Feedback Vertex Set problem, one is given an undirected graph $G$ and an integer $k$, and one needs to determine whether there exists a set of $k$ vertices that intersects all cycles of $G$ (a so-called feedback vertex set). Feedback…
The \emph{maximal $k$-edge-connected subgraphs} problem is a classical graph clustering problem studied since the 70's. Surprisingly, no non-trivial technique for this problem in weighted graphs is known: a very straightforward…
In this work we study local computation with advice: the goal is to solve a graph problem $\Pi$ with a distributed algorithm in $T(\Delta)$ communication rounds, for some function $T$ that only depends on the maximum degree $\Delta$ of the…
The index coding problem is concerned with broadcasting encoded information to a collection of receivers in a way that enables each receiver to discover its required data based on its side information, which comprises the data required by…
Motivated by recent work in computational social choice, we extend the metric distortion framework to clustering problems. Given a set of $n$ agents located in an underlying metric space, our goal is to partition them into $k$ clusters,…
Massive device connectivity in Internet of Thing (IoT) networks with sporadic traffic poses significant communication challenges. To overcome this challenge, the serving base station is required to detect the active devices and estimate the…
We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes…
In this work, we propose an algorithm for solving exact sparse linear regression problems over a network in a distributed manner. Particularly, we consider the problem where data is stored among different computers or agents that seek to…
A team of mobile agents, starting from different nodes of an unknown network, possibly at different times, have to meet at the same node and declare that they have all met. Agents have different labels and move in synchronous rounds along…
We present an $n\Delta^{O(k^2)}$ time algorithm to obtain an optimal solution for $1$-dimensional cutting stock problem: the bin packing problem of packing $n$ items onto unit capacity bins under the restriction that the number of item…
This paper discusses distributed optimization over a directed graph. We begin with some well known algorithms which achieve consensus among agents including FROST [1], which possesses the quickest convergence to the optimum. It is a well…
Consider the problem: we are given $n$ boxes, labeled $\{1,2,\ldots, n\}$ by an adversary, each containing a single number chosen from an unknown distribution; these $n$ distributions are not necessarily identical. We are also given an…
Traditional graph-based semi-supervised learning (SSL) approaches, even though widely applied, are not suited for massive data and large label scenarios since they scale linearly with the number of edges $|E|$ and distinct labels $m$. To…