Related papers: Efficient $k$-Clique Listing: An Edge-Oriented Bra…
Finding dense substructures in a graph is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasiclique,…
Given a simple graph $G$ and an integer $k$, the goal of $k$-Clique problem is to decide if $G$ contains a complete subgraph of size $k$. We say an algorithm approximates $k$-Clique within a factor $g(k)$ if it can find a clique of size at…
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…
Consider the following "local" cut-detection problem in a directed graph: We are given a seed vertex $x$ and need to remove at most $k$ edges so that at most $\nu$ edges can be reached from $x$ (a "local" cut) or output $\bot$ to indicate…
Is detecting a $k$-clique in $k$-partite regular (hyper-)graphs as hard as in the general case? Intuition suggests yes, but proving this -- especially for hypergraphs -- poses notable challenges. Concretely, we consider a strong notion of…
In the $k$-Edge Connected Spanning Subgraph ($k$-ECSS) problem we are given a (multi-)graph $G=(V,E)$ with edge costs and an integer $k$, and seek a min-cost $k$-edge-connected spanning subgraph of $G$. The problem admits a…
This work considers the problem of output-sensitive listing of occurrences of $2k$-cycles for fixed constant $k\geq 2$ in an undirected host graph with $m$ edges and $t$ $2k$-cycles. Recent work of Jin and Xu (and independently Abboud,…
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…
The family of $(k,\ell)$-sparse graphs, introduced by Lorea, plays a central role in combinatorial optimization and has a wide range of applications, particularly in rigidity theory. A key algorithmic problem is to decide whether a given…
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…
Time series clustering poses a significant challenge with diverse applications across domains. A prominent drawback of existing solutions lies in their limited interpretability, often confined to presenting users with centroids. In…
Given a clique-width $k$-expression of a graph $G$, we provide $2^{O(k)}\cdot n$ time algorithms for connectivity constraints on locally checkable properties such as Node-Weighted Steiner Tree, Connected Dominating Set, or Connected Vertex…
Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel…
In the minimum $k$-edge-connected spanning subgraph ($k$-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to $k-1$ edge failures. This is a central problem in network design, and a natural generalization of the…
We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic…
In the family of clustering problems, we are given a set of objects (vertices of the graph), together with some observed pairwise similarities (edges). The goal is to identify clusters of similar objects by slightly modifying the graph to…
We show an $\tilde{O}(n^{p/(p+2)})$-round algorithm in the \congest model for \emph{listing} of $K_p$ (a clique with $p$ nodes), for all $p =4, p\geq 6$. For $p = 5$, we show an $\tilde{O}(n^{3/4})$-round algorithm. For $p=4$ and $p=5$, our…
Link streams offer a good model for representing interactions over time. They consist of links $(b,e,u,v)$, where $u$ and $v$ are vertices interacting during the whole time interval $[b,e]$. In this paper, we deal with the problem of…
Edge-centric distributed computations have appeared as a recent technique to improve the shortcomings of think-like-a-vertex algorithms on large scale-free networks. In order to increase parallelism on this model, edge partitioning -…
A \emph{Temporal Network} (also known as \emph{Link Stream} or \emph{Time-Varying Graph}) is often used to model a time-varying relationship among a group of agents. It is typically represented as a collection of triplets of the form…