Related papers: Simpler and More General Distributed Coloring Base…
We present a simple deterministic distributed algorithm that computes a $(\Delta+1)$-vertex coloring in $O(\log^2 \Delta \cdot \log n)$ rounds. The algorithm can be implemented with $O(\log n)$-bit messages. The algorithm can also be…
Linial's famous color reduction algorithm reduces a given $m$-coloring of a graph with maximum degree $\Delta$ to a $O(\Delta^2\log m)$-coloring, in a single round in the LOCAL model. We show a similar result when nodes are restricted to…
Differential privacy is the gold standard in the problem of privacy preserving data analysis, which is crucial in a wide range of disciplines. Vertex colouring is one of the most fundamental questions about a graph. In this paper, we study…
The degree splitting problem requires coloring the edges of a graph red or blue such that each node has almost the same number of edges in each color, up to a small additive discrepancy. The directed variant of the problem requires…
We present a deterministic distributed algorithm that computes a $(2\Delta-1)$-edge-coloring, or even list-edge-coloring, in any $n$-node graph with maximum degree $\Delta$, in $O(\log^7 \Delta \log n)$ rounds. This answers one of the…
Vertex coloring is one of the classic symmetry breaking problems studied in distributed computing. In this paper we present a new algorithm for $(\Delta+1)$-list coloring in the randomized ${\sf LOCAL}$ model running in…
Given a graph $G$ with $n$ vertices and maximum degree $\Delta$, it is known that $G$ admits a vertex coloring with $\Delta + 1$ colors such that no edge of $G$ is monochromatic. This can be seen constructively by a simple greedy algorithm,…
Locally finding a solution to symmetry-breaking tasks such as vertex-coloring, edge-coloring, maximal matching, maximal independent set, etc., is a long-standing challenge in distributed network computing. More recently, it has also become…
This paper studies the fundamental problem of graph coloring in fully dynamic graphs. Since the problem of computing an optimal coloring, or even approximating it to within $n^{1-\epsilon}$ for any $\epsilon > 0$, is NP-hard in static…
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,…
There is a huge difference in techniques and runtimes of distributed algorithms for problems that can be solved by a sequential greedy algorithm and those that cannot. A prime example of this contrast appears in the edge coloring problem:…
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…
A defective $k$-coloring is a coloring on the vertices of a graph using colors $1,2, \dots, k$ such that adjacent vertices may share the same color. A $(d_1,d_2)$-\emph{coloring} of a graph $G$ is a defective $2$-coloring of $G$ such that…
We define the $d$-defective incidence chromatic number of a graph, generalizing the notion of incidence chromatic number, and determine it for some classes of graphs including trees, complete bipartite graphs, complete graphs, and…
Vizing's theorem states that any graph of maximum degree $\Delta$ can be properly edge colored with at most $\Delta+1$ colors. In the online setting, it has been a matter of interest to find an algorithm that can properly edge color any…
This paper explores the application of a new algebraic method of color exchanges to the edge coloring of simple graphs. Vizing's theorem states that the edge coloring of a simple graph $G$ requires either $\Delta$ or $\Delta+1$ colors,…
We consider the single-conflict coloring problem, a graph coloring problem in which each edge of a graph receives a forbidden ordered color pair. The task is to find a vertex coloring such that no two adjacent vertices receive a pair of…
Vizing showed that it suffices to color the edges of a simple graph using $\Delta + 1$ colors, where $\Delta$ is the maximum degree of the graph. However, up to this date, no efficient distributed edge-coloring algorithms are known for…
We present a general framework for constructing error-correcting codes using distributed graph coloring under the LOCAL model. Building on the correspondence between independent sets in the confusion graph and valid codes, we show that the…
Coloring unit-disk graphs efficiently is an important problem in the global and distributed setting, with applications in radio channel assignment problems when the communication relies on omni-directional antennas of the same power. In…