Related papers: Improved Distributed Degree Splitting and Edge Col…
Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications…
In this paper, we consider distributed coloring for planar graphs with a small number of colors. We present an optimal (up to a constant factor) $O(\log{n})$ time algorithm for 6-coloring planar graphs. Our algorithm is based on a novel…
This paper introduces a natural generalization of the classical edge coloring problem in graphs that provides a useful abstraction for two well-known problems in multicast switching. We show that the problem is NP-hard and evaluate the…
In the past few years, a successful line of research has lead to lower bounds for several fundamental local graph problems in the distributed setting. These results were obtained via a technique called round elimination. On a high level,…
The dynamic scaling of distributed computations plays an important role in the utilization of elastic computational resources, such as the cloud. It enables the provisioning and de-provisioning of resources to match dynamic resource…
The availability of larger and larger graph datasets, growing exponentially over the years, has created several new algorithmic challenges to be addressed. Sequential approaches have become unfeasible, while interest on parallel and…
Vizing's theorem states that any $n$-vertex $m$-edge graph of maximum degree $\Delta$ can be {\em edge colored} using at most $\Delta + 1$ different colors [Diskret.~Analiz, '64]. Vizing's original proof is algorithmic and shows that such…
We provide a simple online $\Delta(1+o(1))$-edge-coloring algorithm for bipartite graphs of maximum degree $\Delta=\omega(\log n)$ under adversarial vertex arrivals on one side of the graph. Our algorithm slightly improves the result of…
An adjacent vertex distinguishing coloring of a graph G is a proper edge coloring of G such that any pair of adjacent vertices are incident with distinct sets of colors. The minimum number of colors needed for an adjacent vertex…
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…
We study the behavior of the Douglas-Rachford algorithm on the graph vertex-coloring problem. Given a graph and a number of colors, the goal is to find a coloring of the vertices so that all adjacent vertex pairs have different colors. In…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
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…
Vizing's celebrated theorem asserts that any graph of maximum degree $\Delta$ admits an edge coloring using at most $\Delta+1$ colors. In contrast, Bar-Noy, Naor and Motwani showed over a quarter century that the trivial greedy algorithm,…
This paper investigates the semi-streaming complexity of \textit{$k$-partial coloring}, a generalization of proper graph coloring. For $k \geq 1$, a $k$-partial coloring requires that each vertex $v$ in an $n$-node graph is assigned a color…
Let $\epsilon \in (0, 1)$ and $n, \Delta \in \mathbb N$ be such that $\Delta = \Omega\left(\max\left\{\frac{\log n}{\epsilon},\, \left(\frac{1}{\epsilon}\log \frac{1}{\epsilon}\right)^2\right\}\right)$. Given an $n$-vertex $m$-edge simple…
We show that the edges of any planar graph of maximum degree at most $9$ can be partitioned into $4$ linear forests and a matching. Combined with known results, this implies that the edges of any planar graph $G$ of odd maximum degree…
We prove new bounds on the distributed fractional coloring problem in the LOCAL model. Fractional $c$-colorings can be understood as multicolorings as follows. For some natural numbers $p$ and $q$ such that $p/q\leq c$, each node $v$ is…
We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…
The last five years of research on distributed graph algorithms have seen huge leaps of progress, both regarding algorithmic improvements and impossibility results: new strong lower bounds have emerged for many central problems and…