Related papers: Efficient Parallel $(\Delta+1)$-Edge-Coloring
In the context of communication complexity, we explore protocols for graph coloring, focusing on the vertex and edge coloring problems in $n$-vertex graphs $G$ with a maximum degree $\Delta$. We consider a scenario where the edges of $G$…
Consider the following simple coloring algorithm for a graph on $n$ vertices. Each vertex chooses a color from $\{1, \dotsc, \Delta(G) + 1\}$ uniformly at random. While there exists a conflicted vertex choose one such vertex uniformly at…
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…
In this paper, we study the problem of computing an edge-coloring in the (one-pass) W-streaming model. In this setting, the edges of an $n$-node graph arrive in an arbitrary order to a machine with a relatively small space, and the goal is…
We consider the problem of designing deterministic graph algorithms for the model of Massively Parallel Computation (MPC) that improve with the sparsity of the input graph, as measured by the notion of arboricity. For the problems of…
We give a randomized algorithm that properly colors the vertices of a triangle-free graph G on n vertices using O(\Delta(G)/ log \Delta(G)) colors, where \Delta(G) is the maximum degree of G. The algorithm takes O(n\Delta2(G)log\Delta(G))…
We present the first parallel batch-dynamic algorithm for maintaining a proper $(\Delta + 1)$-vertex coloring. Our approach builds on a new sequential dynamic algorithm inspired by the work of Bhattacharya et al. (SODA'18). The resulting…
A streaming algorithm is considered to be adversarially robust if it provides correct outputs with high probability even when the stream updates are chosen by an adversary who may observe and react to the past outputs of the algorithm. We…
In recent years, there has been a growing interest in solving various graph coloring problems in the streaming model. The initial algorithms in this line of work are all crucially randomized, raising natural questions about how important a…
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…
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…
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 solve, in a fully decentralised way (\ie with no message passing), the classic problem of colouring a graph. We propose a novel algorithm that is automatically responsive to topology changes, and we prove that it converges quickly to a…
The problem of efficiently coloring $3$-colorable graphs with few colors has received much attention on both the algorithmic and inapproximability fronts. We consider exponential time approximations, in which given a parameter $r$, we aim…
For $n$-vertex $m$-edge graphs with integer polynomially-bounded costs and capacities, we provide a randomized parallel algorithm for the minimum cost flow problem with $\tilde O(m+n^ {1.5})$ work and $\tilde O(\sqrt{n})$ depth. On…
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…
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 study the maintenance of a $(\Delta+C)$-edge-coloring ($C\ge 1$) in a fully dynamic graph $G$ with maximum degree $\Delta$. We focus on minimizing \emph{recourse} which equals the number of recolored edges per edge updates. We present a…
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…
Let $\Delta(G)$ and $\chi'(G)$ be the maximum degree and chromatic index of a graph $G$, respectively. Appearing in different forms, Gupta\,(1967), Goldberg\,(1973), Andersen\,(1977), and Seymour\,(1979) made the following conjecture: Every…