Related papers: Local Mending
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…
We consider the distributed message-passing {LOCAL} model. In this model a communication network is represented by a graph where vertices host processors, and communication is performed over the edges. Computation proceeds in synchronous…
The present paper studies local distributed graph problems in highly dynamic networks. Communication and changes of the graph happen in synchronous rounds and our algorithms always, i.e., in every round, satisfy non-trivial guarantees, no…
In this work, we give a unifying view of locality in four settings: distributed algorithms, sequential greedy algorithms, dynamic algorithms, and online algorithms. We introduce a new model of computing, called the online-LOCAL model: the…
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…
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 establish that every monadic second-order logic (MSO) formula on graphs with bounded treedepth is decidable in a constant number of rounds within the CONGEST model. To our knowledge, this marks the first meta-theorem regarding…
An impressive recent line of work has charted the complexity landscape of distributed graph algorithms. For many settings, it has been determined which time complexities exist, and which do not (in the sense that no local problem could have…
Over the past decade, a long line of research has investigated the distributed complexity landscape of locally checkable labeling (LCL) problems on bounded-degree graphs, culminating in an almost-complete classification on general graphs…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
In this work we study local computation with advice: the goal is to solve a graph problem $\Pi$ with a distributed algorithm in $T(\Delta)$ communication rounds, for some function $T$ that only depends on the maximum degree $\Delta$ of the…
One of the central models in distributed computing is Linial's LOCAL model [SIAM J. Comp. 1992]. Over time, researchers have studied distributed graph problems in the LOCAL model under slightly different assumptions, such as whether nodes…
We study graph connectivity problem in MPC model. On an undirected graph with $n$ nodes and $m$ edges, $O(\log n)$ round connectivity algorithms have been known for over 35 years. However, no algorithms with better complexity bounds were…
We present a complete classification of the distributed computational complexity of local optimization problems in directed cycles for both the deterministic and the randomized LOCAL model. We show that for any local optimization problem…
Graph modification problems are typically asked as follows: is there a small set of operations that transforms a given graph to have a certain property. The most commonly considered operations include vertex deletion, edge deletion, and…
Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with $o(mn)$ total update time, where $m$ is the number of edges and $n$ is the…
In this paper we show a new algorithm for the decremental single-source reachability problem in directed planar graphs. It processes any sequence of edge deletions in $O(n\log^2{n}\log\log{n})$ total time and explicitly maintains the set of…
Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ to minimize the radius of the resulting graph. Previously, a similar problem for minimizing the diameter of the graph…
LCLs or locally checkable labelling problems (e.g. maximal independent set, maximal matching, and vertex colouring) in the LOCAL model of computation are very well-understood in cycles (toroidal 1-dimensional grids): every problem has a…
Solution discovery asks whether a given (infeasible) starting configuration to a problem can be transformed into a feasible solution using a limited number of transformation steps. This paper investigates meta-theorems for solution…