Related papers: Optimal Distributed Coloring Algorithms for Planar…
This paper is concerned with efficiently coloring sparse graphs in the distributed setting with as few colors as possible. According to the celebrated Four Color Theorem, planar graphs can be colored with at most 4 colors, and the proof…
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…
In 1994, Thomassen proved that every planar graph is 5-list-colorable. In 1995, Thomassen proved that every planar graph of girth at least five is 3-list-colorable. His proofs naturally lead to quadratic-time algorithms to find such…
This paper studies sufficient conditions to obtain efficient distributed algorithms coloring graphs optimally (i.e.\ with the minimum number of colors) in the LOCAL model of computation. Most of the work on distributed vertex coloring so…
The $\Delta$-vertex coloring problem has become one of the prototypical problems for understanding the complexity of local distributed graph problems on constant-degree graphs. The major open problem is whether the problem can be solved…
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,…
Graph coloring is one of the central problems in distributed graph algorithms. Much of the research on this topic has focused on coloring with $\Delta+1$ colors, where $\Delta$ denotes the maximum degree. Using $\Delta+1$ colors may be…
We provide novel deterministic distributed vertex coloring algorithms. As our main result, we give a deterministic distributed algorithm to compute a $(\Delta+1)$-coloring of an $n$-node graph with maximum degree $\Delta$ in…
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…
We give a new randomized distributed algorithm for $(\Delta+1)$-coloring in the LOCAL model, running in $O(\sqrt{\log \Delta})+ 2^{O(\sqrt{\log \log n})}$ rounds in a graph of maximum degree~$\Delta$. This implies that the…
The Four color problem is closely related to other branches of mathematics and practical applications. More than 20 of its reformulations are known, which connect this problem with problems of algebra, statistical mechanics and planning.…
Identifying the sets of operations that can be executed simultaneously is an important problem appearing in many parallel applications. By modeling the operations and their interactions as a graph, one can identify the independent…
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…
Distributed graph coloring is one of the most extensively studied problems in distributed computing. There is a canonical family of distributed graph coloring algorithms known as the locally-iterative coloring algorithms, first formalized…
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:…
Brooks' theorem states that all connected graphs but odd cycles and cliques can be colored with $\Delta$ colors, where $\Delta$ is the maximum degree of the graph. Such colorings have been shown to admit non-trivial distributed algorithms…
The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree $\Delta$. In this paper we explore the complexity of edge coloring in the LOCAL model in different palette size regimes. 1.…
We study the {edge-coloring} problem in the message-passing model of distributed computing. This is one of the most fundamental and well-studied problems in this area. Currently, the best-known deterministic algorithms for (2Delta…
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…
In this paper we present a deterministic CONGEST algorithm to compute an $O(k\Delta)$-vertex coloring in $O(\Delta/k)+\log^* n$ rounds, where $\Delta$ is the maximum degree of the network graph and $1\leq k\leq O(\Delta)$ can be freely…