Yannic Maus
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View article: Nearly-Optimal Distributed Ruling Sets for Trees and high-girth graphs
Nearly-Optimal Distributed Ruling Sets for Trees and high-girth graphs Open
Given a graph G = (V, E), a β-ruling set is a subset S ⊆ V that is i) independent, and ii) every node υ ∈ V has a node of S within distance β. In this paper we present almost optimal distributed algorithms for finding ruling sets in trees …
View article: On Distributed Colouring of Hyperbolic Random Graphs
On Distributed Colouring of Hyperbolic Random Graphs Open
We analyse the performance of simple distributed colouring algorithms under the assumption that the input graph is a hyperbolic random graph (HRG), a generative model capturing key properties of real-world networks such as power-law degree…
View article: Towards Optimal Distributed Delta Coloring
Towards Optimal Distributed Delta Coloring Open
The $Δ$-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 determi…
View article: Exponential speedup over locality in MPC with optimal memory
Exponential speedup over locality in MPC with optimal memory Open
Locally Checkable Labeling () problems are graph problems in which a solution is correct if it satisfies some given constraints in the local neighborhood of each node. Example problems in this class include maximal matching, maximal indepe…
View article: Drawings of complete multipartite graphs up to triangle flips
Drawings of complete multipartite graphs up to triangle flips Open
For a drawing of a labeled graph, the rotation of a vertex or crossing is the cyclic order of its incident edges, represented by the labels of their other endpoints. The extended rotation system (ERS) of the drawing is the collection of th…
View article: On the Locality of Hall's Theorem
On the Locality of Hall's Theorem Open
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 exponen…
View article: Hyperbolic Random Graphs: Clique Number and Degeneracy with Implications for Colouring
Hyperbolic Random Graphs: Clique Number and Degeneracy with Implications for Colouring Open
Hyperbolic random graphs inherit many properties that are present in real-world networks. The hyperbolic geometry imposes a scale-free network with a strong clustering coefficient. Other properties like a giant component, the small world p…
View article: Distributed Delta-Coloring under Bandwidth Limitations
Distributed Delta-Coloring under Bandwidth Limitations Open
We consider the problem of coloring graphs of maximum degree $Δ$ with $Δ$ colors in the distributed setting with limited bandwidth. Specifically, we give a $\mathsf{poly}\log\log n$-round randomized algorithm in the CONGEST model. This is …
View article: Adaptive Massively Parallel Coloring in Sparse Graphs
Adaptive Massively Parallel Coloring in Sparse Graphs Open
Classic symmetry-breaking problems on graphs have gained a lot of attention in models of modern parallel computation. The Adaptive Massively Parallel Computation (AMPC) is a model that captures the central challenges in data center computa…
View article: Distributed Graph Coloring Made Easy
Distributed Graph Coloring Made Easy Open
In this article, we present a deterministic \(\mathsf {CONGEST}\) algorithm to compute an O ( k Δ)-vertex coloring in O (Δ / k )+log * n rounds, where Δ is the maximum degree of the network graph and k ≥ 1 can be freely chosen. The algorit…
View article: Distributed Symmetry Breaking on Power Graphs via Sparsification
Distributed Symmetry Breaking on Power Graphs via Sparsification Open
Funding Information: Saku Peltonen is supported by the Academy of Finland, Grant 334238. Publisher Copyright: © 2023 Owner/Author(s).
View article: Fast Dynamic Programming in Trees in the MPC Model
Fast Dynamic Programming in Trees in the MPC Model Open
Funding Information: We are grateful to Alkida Balliu, Darya Melnyk, and Dennis Olivetti for several fruitful discussions, and to the anonymous reviewers for their helpful feedback on prior versions of this work. This work was supported in…
View article: Adaptive Massively Parallel Connectivity in Optimal Space
Adaptive Massively Parallel Connectivity in Optimal Space Open
Funding Information: Supported by the Academy of Finland, Grant 334238 Publisher Copyright: © 2023 Owner/Author.
View article: Fast Dynamic Programming in Trees in the MPC Model
Fast Dynamic Programming in Trees in the MPC Model Open
We present a deterministic algorithm for solving a wide range of dynamic programming problems in trees in $O(\log D)$ rounds in the massively parallel computation model (MPC), with $O(n^δ)$ words of local memory per machine, for any given …
View article: Distributed Symmetry Breaking on Power Graphs via Sparsification
Distributed Symmetry Breaking on Power Graphs via Sparsification Open
In this paper, we present efficient distributed algorithms for classical symmetry breaking problems, maximal independent sets (MIS) and ruling sets, in power graphs. We work in the standard CONGEST model of distributed message passing, whe…
View article: Adaptive Massively Parallel Connectivity in Optimal Space
Adaptive Massively Parallel Connectivity in Optimal Space Open
We study the problem of finding connected components in the Adaptive Massively Parallel Computation (AMPC) model. We show that when we require the total space to be linear in the size of the input graph the problem can be solved in $O(\log…
View article: Optimal Deterministic Massively Parallel Connectivity on Forests
Optimal Deterministic Massively Parallel Connectivity on Forests Open
Publisher Copyright: Copyright © 2023 by SIAM.
View article: Conditionally Optimal Parallel Coloring of Forests
Conditionally Optimal Parallel Coloring of Forests Open
We show the first conditionally optimal deterministic algorithm for 3-coloring forests in the low-space massively parallel computation (MPC) model. Our algorithm runs in O(log log n) rounds and uses optimal global space. The best previous …
View article: Fast Distributed Brooks' Theorem
Fast Distributed Brooks' Theorem Open
We give a randomized $Δ$-coloring algorithm in the LOCAL model that runs in $\text{poly} \log \log n$ rounds, where $n$ is the number of nodes of the input graph and $Δ$ is its maximum degree. This means that randomized $Δ$-coloring is a r…
View article: Optimal Deterministic Massively Parallel Connectivity on Forests
Optimal Deterministic Massively Parallel Connectivity on Forests Open
We show fast deterministic algorithms for fundamental problems on forests in the challenging low-space regime of the well-known Massive Parallel Computation (MPC) model. A recent breakthrough result by Coy and Czumaj [STOC'22] shows that, …
View article: Exponential Speedup Over Locality in MPC with Optimal Memory
Exponential Speedup Over Locality in MPC with Optimal Memory Open
Locally Checkable Labeling (LCL) problems are graph problems in which a solution is correct if it satisfies some given constraints in the local neighborhood of each node. Example problems in this class include maximal matching, maximal ind…
View article: Fast Distributed Vertex Splitting with Applications
Fast Distributed Vertex Splitting with Applications Open
We present poly log log n-round randomized distributed algorithms to compute vertex splittings, a partition of the vertices of a graph into k parts such that a node of degree d(u) has ≈ d(u)/k neighbors in each part. Our techniques can be …
View article: Distributed Vertex Cover Reconfiguration
Distributed Vertex Cover Reconfiguration Open
Reconfiguration schedules, i.e., sequences that gradually transform one solution of a problem to another while always maintaining feasibility, have been extensively studied. Most research has dealt with the decision problem of whether a re…
View article: Efficient CONGEST Algorithms for the Lovasz Local Lemma
Efficient CONGEST Algorithms for the Lovasz Local Lemma Open
We present a poly $\log \log n$ time randomized CONGEST algorithm for a natural class of Lovasz Local Lemma (LLL) instances on constant degree graphs. This implies, among other things, that there are no LCL problems with randomized complex…
View article: Efficient randomized distributed coloring in CONGEST
Efficient randomized distributed coloring in CONGEST Open
Distributed vertex coloring is one of the classic problems and probably also the most widely studied problems in the area of distributed graph algorithms. We present a new randomized distributed vertex coloring algorithm for the standard C…
View article: Locally Checkable Labelings with Small Messages
Locally Checkable Labelings with Small Messages Open
A rich line of work has been addressing the computational complexity of locally checkable labelings (LCLs), illustrating the landscape of possible complexities. In this paper, we study the landscape of LCL complexities under bandwidth rest…