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Related papers: Towards Optimal Deterministic LOCAL Algorithms on …

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The landscape of the distributed time complexity is nowadays well-understood for subpolynomial complexities. When we look at deterministic algorithms in the LOCAL model and locally checkable problems (LCLs) in bounded-degree graphs, the…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-03-26 Alkida Balliu , Sebastian Brandt , Dennis Olivetti , Jukka Suomela

We describe a simple deterministic $O( \varepsilon^{-1} \log \Delta)$ round distributed algorithm for $(2\alpha+1)(1 + \varepsilon)$ approximation of minimum weighted dominating set on graphs with arboricity at most $\alpha$. Here $\Delta$…

Data Structures and Algorithms · Computer Science 2022-06-13 Michal Dory , Mohsen Ghaffari , Saeed Ilchi

We present a self-stabilizing leader election algorithm for arbitrary networks, with space-complexity $O(\max\{\log \Delta, \log \log n\})$ bits per node in $n$-node networks with maximum degree~$\Delta$. This space complexity is…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-02-27 Lélia Blin , Sébastien Tixeuil

The {\em edit distance} between two ordered trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as…

Data Structures and Algorithms · Computer Science 2010-12-01 Erik D. Demaine , Shay Mozes , Benjamin Rossman , Oren Weimann

Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…

Data Structures and Algorithms · Computer Science 2026-05-06 Juha Harviainen , Frank Sommer , Manuel Sorge

The $\Delta$-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…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-04-08 Manuel Jakob , Yannic Maus

The celebrated Time Hierarchy Theorem for Turing machines states, informally, that more problems can be solved given more time. The extent to which a time hierarchy-type theorem holds in the distributed LOCAL model has been open for many…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-04-24 Yi-Jun Chang , Seth Pettie

It is a well known fact that sequential algorithms which exhibit a strong "local" nature can be adapted to the distributed setting given a legal graph coloring. The running time of the distributed algorithm will then be at least the number…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-05-15 Ken-ichi Kawarabayashi , Gregory Schwartzman

In the implicit dynamic colouring problem, the task is to maintain a representation of a proper colouring as a dynamic graph is subject to insertions and deletions of edges, while facilitating interspersed queries to the colours of…

Data Structures and Algorithms · Computer Science 2022-03-14 Aleksander B. G. Christiansen , Eva Rotenberg

The study of optimal decision trees has gained increasing attention in recent years; however, despite substantial progress, it still suffers from two major challenges: First, trees constructed by existing optimal decision tree (ODT)…

Machine Learning · Computer Science 2026-05-04 Xi He

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-02-20 Sebastian Brandt , Dennis Olivetti

We investigate the connections between the fields of distributed computing and measurable combinatorics by considering complexity classes of locally checkable labeling problems on regular forests. We show that the most important…

We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-02-19 Alkida Balliu , Sebastian Brandt , Yuval Efron , Juho Hirvonen , Yannic Maus , Dennis Olivetti , Jukka Suomela

We give the first algorithm that maintains an approximate decision tree over an arbitrary sequence of insertions and deletions of labeled examples, with strong guarantees on the worst-case running time per update request. For instance, we…

Data Structures and Algorithms · Computer Science 2023-02-13 Marco Bressan , Mauro Sozio

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…

Data Structures and Algorithms · Computer Science 2023-07-03 Manuela Fischer , Jeff Giliberti , Christoph Grunau

This paper studies lower bounds for fundamental optimization problems in the CONGEST model. We show that solving problems exactly in this model can be a hard task, by providing $\tilde{\Omega}(n^2)$ lower bounds for cornerstone problems,…

Data Structures and Algorithms · Computer Science 2019-05-27 Nir Bachrach , Keren Censor-Hillel , Michal Dory , Yuval Efron , Dean Leitersdorf , Ami Paz

Graph coloring is one of the central problems in distributed graph algorithms. Much of the research on this topic has focused on coloring with $\Delta+1$ colors, where $\Delta$ denotes the maximum degree. Using $\Delta+1$ colors may be…

Data Structures and Algorithms · Computer Science 2017-08-24 Mohsen Ghaffari , Christiana Lymouri

Common definitions of the "standard" LOCAL model tend to be sloppy and even self-contradictory on one point: do the nodes update their state using an arbitrary function or a computable function? So far, this distinction has been safe to…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-02-26 Antonio Cruciani , Avinandan Das , Massimo Equi , Henrik Lievonen , Diep Luong-Le , Augusto Modanese , Jukka Suomela

Very recently, Khoury and Schild [FOCS 2025] showed that any randomized LOCAL algorithm that solves maximal matching requires $\Omega(\min\{\log \Delta, \log_\Delta n\})$ rounds, where $n$ is the number of nodes in the graph and $\Delta$ is…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-11-21 Alkida Balliu , Filippo Casagrande , Francesco d'Amore , Dennis Olivetti

We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…

Data Structures and Algorithms · Computer Science 2023-10-13 David G. Harris