相关论文: Deterministic Distributed Vertex Coloring: Simpler…
Vizing's theorem states that every graph $G$ of maximum degree $\Delta$ can be properly edge-colored using $\Delta + 1$ colors. The fastest currently known $(\Delta+1)$-edge-coloring algorithm for general graphs is due to Sinnamon and runs…
We provide new deterministic algorithms for the edge coloring problem, which is one of the classic and highly studied distributed local symmetry breaking problems. As our main result, we show that a $(2\Delta-1)$-edge coloring can be…
We present a simple polylogarithmic-time deterministic distributed algorithm for network decomposition. This improves on a celebrated $2^{O(\sqrt{\log n})}$-time algorithm of Panconesi and Srinivasan [STOC'92] and settles a central and…
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 present three sublinear randomized algorithms for vertex-coloring of graphs with maximum degree $\Delta$. The first is a simple algorithm that extends the idea of Morris and Song to color graphs with maximum degree $\Delta$ using…
We give an improved randomized CONGEST algorithm for distance-$2$ coloring that uses $\Delta^2+1$ colors and runs in $O(\log n)$ rounds, improving the recent $O(\log \Delta \cdot \log n)$-round algorithm in [Halld\'orsson, Kuhn, Maus; PODC…
In distributed network computing, a variant of the LOCAL model has been recently introduced, referred to as the SLEEPING model. In this model, nodes have the ability to decide on which round they are awake, and on which round they are…
A recent palette sparsification theorem of Assadi, Chen, and Khanna [SODA'19] states that in every $n$-vertex graph $G$ with maximum degree $\Delta$, sampling $O(\log{n})$ colors per each vertex independently from $\Delta+1$ colors almost…
Vizing's theorem guarantees that every graph with maximum degree $\Delta$ admits an edge coloring using $\Delta + 1$ colors. In online settings - where edges arrive one at a time and must be colored immediately - a simple greedy algorithm…
Vizing's celebrated theorem states that every simple graph with maximum degree $\Delta$ admits a $(\Delta+1)$ edge coloring which can be found in $O(m \cdot n)$ time on $n$-vertex $m$-edge graphs. This is just one color more than the…
In this paper, we consider algorithms for edge-coloring multigraphs $G$ of bounded maximum degree, i.e., $\Delta(G) = O(1)$. Shannon's theorem states that any multigraph of maximum degree $\Delta$ can be properly edge-colored with…
Graph coloring problems are among the most fundamental problems in parallel and distributed computing, and have been studied extensively in both settings. In this context, designing efficient deterministic algorithms for these problems has…
The problem of coloring the edges of an $n$-node graph of maximum degree $\Delta$ with $2\Delta - 1$ colors is one of the key symmetry breaking problems in the area of distributed graph algorithms. While there has been a lot of progress…
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 study the problem of bi-chromatic coloring of hypergraphs in the LOCAL distributed model of computation. This problem can easily be solved by a randomized local algorithm with no communication. However, it is not known how to solve it…
This paper improves and in two cases nearly settles, up to logarithmically lower-order factors, the deterministic complexity of some of the most central problems in distributed graph algorithms, which have been studied for over three…
We prove several new tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a $\Delta$-coloring on…
We give efficient randomized and deterministic distributed algorithms for computing a distance-$2$ vertex coloring of a graph $G$ in the CONGEST model. In particular, if $\Delta$ is the maximum degree of $G$, we show that there is a…
We obtain improved distributed algorithms in the CONGEST message-passing setting for problems on power graphs of an input graph $G$. This includes Coloring, Maximal Independent Set, and related problems. We develop a general deterministic…
We study the edge-colouring problem, and give efficient algorithms where the number of colours is parameterised by the graph's arboricity, $\alpha$. In a dynamic graph, subject to insertions and deletions, we give a deterministic algorithm…