Related papers: (Noisy) Gap Cycle Counting Strikes Back: Random Or…
Subspace clustering is the problem of clustering data points into a union of low-dimensional linear/affine subspaces. It is the mathematical abstraction of many important problems in computer vision, image processing and machine learning. A…
We study the Telephone Broadcasting problem in graphs with restricted structure. Given a designated source in an undirected graph, the goal is to disseminate a message to all vertices in the minimum number of rounds, where in each round…
We consider the problem of detecting a cycle in a directed graph that grows by arc insertions, and the related problems of maintaining a topological order and the strong components of such a graph. For these problems, we give two…
We study the communication complexity of the Minimum Vertex Cover (MVC) problem on general graphs within the \(k\)-party one-way communication model. Edges of an arbitrary \(n\)-vertex graph are distributed among \(k\) parties. The…
A fundamental question that shrouds the emergence of massively parallel computing (MPC) platforms is how can the additional power of the MPC paradigm be leveraged to achieve faster algorithms compared to classical parallel models such as…
In standard number-in-hand multi-party communication complexity, performance is measured as the total number of bits transmitted globally in the network. In this paper, we study a variation called local communication complexity in which…
The problem of network-constrained averaging is to compute the average of a set of values distributed throughout a graph G using an algorithm that can pass messages only along graph edges. We study this problem in the noisy setting, in…
There has been a recent explosion in the size of stored data, partially due to advances in storage technology, and partially due to the growing popularity of cloud-computing and the vast quantities of data generated. This motivates the need…
We consider the minimal k-grouping problem: given a graph G=(V,E) and a constant k, partition G into subgraphs of diameter no greater than k, such that the union of any two subgraphs has diameter greater than k. We give a silent…
The Boolean Hidden Matching (BHM) problem, introduced in a seminal paper of Gavinsky et. al. [STOC'07], has played an important role in the streaming lower bounds for graph problems such as triangle and subgraph counting, maximum matching,…
We study the streaming complexity of $k$-counter approximate counting. In the $k$-counter approximate counting problem, we are given an input string in $[k]^n$, and we are required to approximate the number of each $j$'s ($j\in[k]$) in the…
Structural balance theory studies stability in networks. Given a $n$-vertex complete graph $G=(V,E)$ whose edges are labeled positive or negative, the graph is considered \emph{balanced} if every triangle either consists of three positive…
The problem of counting small subgraphs, and specifically cycles, in the streaming model received a lot of attention over the past few years. In this paper, we consider arbitrary order insertion-only streams, improving over the…
We prove tight network topology dependent bounds on the round complexity of computing well studied $k$-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing,…
We study the maximum $k$-set coverage problem in the following distributed setting. A collection of sets $S_1,\ldots,S_m$ over a universe $[n]$ is partitioned across $p$ machines and the goal is to find $k$ sets whose union covers the most…
Our work concerns algorithms for an unweighted variant of Maximum Flow. In the All-Pairs Connectivity (APC) problem, we are given a graph $G$ on $n$ vertices and $m$ edges, and are tasked with computing the maximum number of edge-disjoint…
We give unconditional parameterized complexity lower bounds on pure dynamic programming algorithms - as modeled by tropical circuits - for connectivity problems such as the Traveling Salesperson Problem. Our lower bounds are higher than the…
We resolve the space complexity of linear sketches for approximating the maximum matching problem in dynamic graph streams where the stream may include both edge insertion and deletion. Specifically, we show that for any $\epsilon > 0$,…
A key problem in random network coding (NC) lies in the complexity and energy consumption associated with the packet decoding processes, which hinder its application in mobile environments. Controlling and hence limiting such factors has…
As graphs continue to grow in size, we seek ways to effectively process such data at scale. The model of streaming graph processing, in which a compact summary is maintained as each edge insertion/deletion is observed, is an attractive one.…