Related papers: Planted Models for the Densest $k$-Subgraph Proble…
We give almost-linear-time algorithms for approximating rooted minimum cut and maximum arborescence packing in directed graphs, two problems that are dual to each other [Edm73]. More specifically, for an $n$-vertex, $m$-edge directed graph…
Recently [Bhattacharya et al., STOC 2015] provide the first non-trivial algorithm for the densest subgraph problem in the streaming model with additions and deletions to its edges, i.e., for dynamic graph streams. They present a…
For any given $\epsilon>0$ we provide an algorithm for the Densest $k$-Subhypergraph Problem with an approximation ratio of at most $O(n^{\theta_m+2\epsilon})$ for $\theta_m=\frac{1}{2}m-\frac{1}{2}-\frac{1}{2m}$ and run time at most…
The densest subgraph problem (DSG) aiming at finding an induced subgraph such that the average edge-weights of the subgraph is maximized, is a well-studied problem. However, when the input graph is a hypergraph, the existing notion of DSG…
We consider several problems related to packing forests in graphs. The first one is to find $k$ edge-disjoint forests in a directed graph $G$ of maximal size such that the indegree of each vertex in these forests is at most $k$. We describe…
In the k-edge connected directed Steiner tree (k-DST) problem, we are given a directed graph G on n vertices with edge-costs, a root vertex r, a set of h terminals T and an integer k. The goal is to find a min-cost subgraph H of G that…
Detection of planted subgraphs in Erd\"os-R\'enyi random graphs has been extensively studied, leading to a rich body of results characterizing both statistical and computational thresholds. However, most prior work assumes a purely random…
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 fair k-set selection problem where we aim to select $k$ sets from a given set system such that the (weighted) occurrence times that each element appears in these $k$ selected sets are balanced, i.e., the maximum (weighted)…
The Directed Steiner Network (DSN) problem takes as input a directed edge-weighted graph $G=(V,E)$ and a set $\mathcal{D}\subseteq V\times V$ of $k$ demand pairs. The aim is to compute the cheapest network $N\subseteq G$ for which there is…
We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main…
In the decremental $(1+\epsilon)$-approximate Single-Source Shortest Path (SSSP) problem, we are given a graph $G=(V,E)$ with $n = |V|, m = |E|$, undergoing edge deletions, and a distinguished source $s \in V$, and we are asked to process…
Packing disjoint subgraphs in a given graph is a fundamental problem with many applications. Motivated by political districting, we focus on connected subgraphs that are compact (e.g., having constant radius from a single center vertex) and…
Graph partitioning problems are a central topic of study in algorithms and complexity theory. Edge expansion and vertex expansion, two popular graph partitioning objectives, seek a $2$-partition of the vertex set of the graph that minimizes…
In the densest subgraph problem, given a weighted undirected graph $G(V,E,w)$, with non-negative edge weights, we are asked to find a subset of nodes $S\subseteq V$ that maximizes the degree density $w(S)/|S|$, where $w(S)$ is the sum of…
A graph is $k$-connected if it has $k$ internally-disjoint paths between every pair of nodes. A subset $S$ of nodes in a graph $G$ is a $k$-connected set if the subgraph $G[S]$ induced by $S$ is $k$-connected; $S$ is an $m$-dominating set…
The weighted $k$-center problem in graphs is a classical facility location problem where we place $k$ centers on the graph, which minimize the maximum weighted distance of a vertex to its nearest center. We study this problem when the…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…
The use of network based approaches to model and analyse large datasets is currently a growing research field. For instance in biology and medicine, networks are used to model interactions among biological molecules as well as relations…
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…