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We prove the following asymptotically tight lower bound for $k$-color discrepancy: For any $k \geq 2$, there exists a hypergraph with $n$ hyperedges such that its $k$-color discrepancy is at least $\Omega(\sqrt{n})$. This improves on the…
Many graph problems are locally checkable: a solution is globally feasible if it looks valid in all constant-radius neighborhoods. This idea is formalized in the concept of locally checkable labelings (LCLs), introduced by Naor and…
The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error…
The local minimum degree of a graph is the minimum degree that can be reached by means of local complementation. For any n, there exist graphs of order n which have a local minimum degree at least 0.189n, or at least 0.110n when restricted…
The distributed coloring problem is arguably one of the key problems studied in the area of distributed graph algorithms. The most standard variant of the problem asks for a proper vertex coloring of a graph with $\Delta+1$ colors, where…
We revisit asynchronous computing in networks of crash-prone processes, under the asynchronous variant of the standard LOCAL model, recently introduced by Fraigniaud et al. [DISC 2022]. We focus on the vertex coloring problem, and our…
Locally Checkable Labeling (LCL) problems include essentially all the classic problems of $\mathsf{LOCAL}$ distributed algorithms. In a recent enlightening revelation, Chang and Pettie [arXiv 1704.06297] showed that any LCL (on bounded…
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,…
A graph is \textit{locally irregular} if the neighbors of every vertex $v$ have degrees distinct from the degree of $v$. \textit{locally irregular edge-coloring} of a graph $G$ is an (improper) edge-coloring such that the graph induced on…
Recent improvements on the deterministic complexities of fundamental graph problems in the LOCAL model of distributed computing have yielded state-of-the-art upper bounds of $\tilde{O}(\log^{5/3} n)$ rounds for maximal independent set (MIS)…
In the classic online graph balancing problem, edges arrive sequentially and must be oriented immediately upon arrival, to minimize the maximum in-degree. For adversarial arrivals, the natural greedy algorithm is $O(\log n)$-competitive,…
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 study the $k$-edge connectivity problem on undirected graphs in the distributed sketching model, where we have $n$ nodes and a referee. Each node sends a single message to the referee based on its 1-hop neighborhood in the graph, and the…
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…
Planar graphs are known to allow subexponential algorithms running in time $2^{O(\sqrt n)}$ or $2^{O(\sqrt n \log n)}$ for most of the paradigmatic problems, while the brute-force time $2^{\Theta(n)}$ is very likely to be asymptotically…
A graph is weakly $2$-colored if the nodes are labeled with colors black and white such that each black node is adjacent to at least one white node and vice versa. In this work we study the distributed computational complexity of weak…
The classic lower bound of Kuhn, Moscibroda and Wattenhofer [JACM 2016] states that approximate maximum matching and approximate vertex cover (among other problems) in the LOCAL model require $\Omega(\min\{\sqrt{\frac{\log n}{\log\log n}},…
In a recent breakthrough result, Balliu et al. [FOCS'19] proved a deterministic $\Omega(\min(\Delta,\log n /\log \log n))$-round and a randomized $\Omega(\min(\Delta,\log \log n/\log \log \log n))$-round lower bound for the complexity of…
In 2017 Day et al. introduced the notion of locality as a structural complexity-measure for patterns in the field of pattern matching established by Angluin in 1980. In 2019 Casel et al. showed that determining the locality of an arbitrary…
We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…