Related papers: Dynamic Algorithms for Graph Coloring
Let $\mathcal{H}$ be a hypergraph of maximal vertex degree $\Delta$, such that each its hyperedge contains at least $\delta$ vertices. Let $k=\lceil\frac{2\Delta}{\delta}\rceil$. We prove that (i) The hypergraph $\mathcal{H}$ admits proper…
We obtain the following new coloring results: * A 3-colorable graph on $n$ vertices with maximum degree~$\Delta$ can be colored, in polynomial time, using $O((\Delta \log\Delta)^{1/3} \cdot\log{n})$ colors. This slightly improves an…
We develop the first parallel graph coloring heuristics with strong theoretical guarantees on work and depth and coloring quality. The key idea is to design a relaxation of the vertex degeneracy order, a well-known graph theory concept, and…
This paper presents a comprehensive study of algorithms for maintaining the number of all connected four-vertex subgraphs in a dynamic graph. Specifically, our algorithms maintain the number of paths of length three in deterministic…
In this paper we study the problem of fully dynamic maximal matching with lookahead. In a fully dynamic $n$-vertex graph setting, we have to handle updates (insertions and removals of edges), and answer queries regarding the current graph,…
We study the communication complexity of $(\Delta + 1)$ vertex coloring, where the edges of an $n$-vertex graph of maximum degree $\Delta$ are partitioned between two players. We provide a randomized protocol which uses $O(n)$ bits of…
Differential Privacy is the gold standard in privacy-preserving data analysis. This paper addresses the challenge of producing a differentially edge-private vertex coloring. In this paper, we present two novel algorithms to approach this…
We consider the problem of maintaining an approximate maximum integral matching in a dynamic graph $G$, while the adversary makes changes to the edges of the graph. The goal is to maintain a $(1+\epsilon)$-approximate maximum matching for…
Motivated by recent applications of dominator computations, we consider the problem of dynamically maintaining the dominators of flow graphs through a sequence of insertions and deletions of edges. Our main theoretical contribution is a…
Dynamically maintaining the minimum cut in a graph $G$ under edge insertions and deletions is a fundamental problem in dynamic graph algorithms for which no conditional lower bound on the time per operation exists. In an $n$-node graph the…
In the dynamic approximate maximum bipartite matching problem we are given bipartite graph $G$ undergoing updates and our goal is to maintain a matching of $G$ which is large compared the maximum matching size $\mu(G)$. We define a dynamic…
We present a polynomial-time algorithm that colors any 3-colorable $n$-vertex graph using $O(n^{0.19539})$ colors, improving upon the previous best bound of $\widetilde{O}(n^{0.19747})$ by Kawarabayashi, Thorup, and Yoneda [STOC 2024]. Our…
We present a randomized distributed algorithm that computes a $\Delta$-coloring in any non-complete graph with maximum degree $\Delta \geq 4$ in $O(\log \Delta) + 2^{O(\sqrt{\log\log n})}$ rounds, as well as a randomized algorithm that…
Given a simple $n$-vertex, $m$-edge graph $G$ undergoing edge insertions and deletions, we give two new fully dynamic algorithms for exactly maintaining the edge connectivity of $G$ in $\tilde{O}(n)$ worst-case update time and…
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…
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…
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…
Graph colouring is a fundamental problem for networks, serving as a tool for avoiding conflicts via symmetry breaking, for example, avoiding multiple computer processes simultaneously updating the same resource. This paper considers a…
We study a family of closely-related distributed graph problems, which we call degree splitting, where roughly speaking the objective is to partition (or orient) the edges such that each node's degree is split almost uniformly. Our findings…
A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…