Related papers: Fast Distributed Algorithms for Girth, Cycles and …
In Constrained Correlation Clustering, the goal is to cluster a complete signed graph in a way that minimizes the number of negative edges inside clusters plus the number of positive edges between clusters, while respecting hard constraints…
We show that the $(degree+1)$-list coloring problem can be solved deterministically in $O(D \cdot \log n \cdot\log^2\Delta)$ rounds in the \CONGEST model, where $D$ is the diameter of the graph, $n$ the number of nodes, and $\Delta$ the…
We establish that every monadic second-order logic (MSO) formula on graphs with bounded treedepth is decidable in a constant number of rounds within the CONGEST model. To our knowledge, this marks the first meta-theorem regarding…
We develop a general deterministic distributed method for locally rounding fractional solutions of graph problems for which the analysis can be broken down into analyzing pairs of vertices. Roughly speaking, the method can transform…
We propose a simple and time-optimal algorithm for property testing a graph for its conductance in the CONGEST model. Our algorithm takes only $O(\log n)$ rounds of communication (which is known to be optimal), and consists of simply…
Given query access to an undirected graph $G$, we consider the problem of computing a $(1\pm\epsilon)$-approximation of the number of $k$-cliques in $G$. The standard query model for general graphs allows for degree queries, neighbor…
Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small…
In the LOCAL model, low-diameter decomposition is a useful tool in designing algorithms, as it allows us to shift from the general graph setting to the low-diameter graph setting, where brute-force information gathering can be done…
We study the broadcast version of the CONGEST CLIQUE model of distributed computing. In this model, in each round, any node in a network of size $n$ can send the same message (i.e. broadcast a message) of limited size to every other node in…
The maximum independent set problem is a classic optimization problem that has also been studied quite intensively in the distributed setting. While the problem is hard to approximate in general, there are good approximation algorithms…
Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…
It is known that a better than $2$-approximation algorithm for the girth in dense directed unweighted graphs needs $n^{3-o(1)}$ time unless one uses fast matrix multiplication. Meanwhile, the best known approximation factor for a…
One of the most basic techniques in algorithm design consists of breaking a problem into subproblems and then proceeding recursively. In the case of graph algorithms, one way to implement this approach is through separator sets. Given a…
Graph coloring is fundamental to distributed computing. We give the first sub-logarithmic distributed algorithm for coloring cluster graphs. These graphs are obtained from the underlying communication network by contracting nodes and edges,…
Let $G = (V,E,\ell)$ be a $n$-node $m$-edge weighted undirected graph, where $\ell: E \rightarrow (0,\infty)$ is a real \emph{length} function defined on its edges, and let $g$ denote the girth of $G$, i.e., the length of its shortest…
Since counting subgraphs in general graphs is, by and large, a computationally demanding problem, it is natural to try and design fast algorithms for restricted families of graphs. One such family that has been extensively studied is that…
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…
We study the problem of approximating the number of $k$-cliques in a graph when given query access to the graph. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries and (3) pair queries. Let…
We give a distributed algorithm in the {\sf CONGEST} model for property testing of planarity with one-sided error in general (unbounded-degree) graphs. Following Censor-Hillel et al. (DISC 2016), who recently initiated the study of property…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…