Related papers: Lower bounds for maximal matchings and maximal ind…
Linial's seminal result shows that any deterministic distributed algorithm that finds a $3$-colouring of an $n$-cycle requires at least $\log^*(n)/2 - 1$ communication rounds. We give a new simpler proof of this theorem.
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 $\Delta$…
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…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
This paper addresses the cornerstone family of \emph{local problems} in distributed computing, and investigates the curious gap between randomized and deterministic solutions under bandwidth restrictions. Our main contribution is in…
This paper improves and in two cases nearly settles, up to logarithmically lower-order factors, the deterministic complexity of some of the most central problems in distributed graph algorithms, which have been studied for over three…
There is a huge difference in techniques and runtimes of distributed algorithms for problems that can be solved by a sequential greedy algorithm and those that cannot. A prime example of this contrast appears in the edge coloring problem:…
The Maximal Independent Set (MIS) problem is one of the basics in the study of locality in distributed graph algorithms. This paper presents an extremely simple randomized algorithm providing a near-optimal local complexity for this…
We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…
In the distributed triangle detection problem, we have an $n$-vertex network $G=(V,E)$ with one player for each vertex of the graph who sees the edges incident on the vertex. The players communicate in synchronous rounds using the edges of…
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…
We explore the fundamental limits of distributed balls-into-bins algorithms. We present an adaptive symmetric algorithm that achieves a bin load of two in log* n+O(1) communication rounds using O(n) messages in total. Larger bin loads can…
We give a new randomized distributed algorithm for $(\Delta+1)$-coloring in the LOCAL model, running in $O(\sqrt{\log \Delta})+ 2^{O(\sqrt{\log \log n})}$ rounds in a graph of maximum degree~$\Delta$. This implies that the…
We present $O(\log\log n)$-round algorithms in the Massively Parallel Computation (MPC) model, with $\tilde{O}(n)$ memory per machine, that compute a maximal independent set, a $1+\epsilon$ approximation of maximum matching, and a…
Hella et al. (PODC 2012, Distributed Computing 2015) identified seven different models of distributed computing - one of which is the port-numbering model - and provided a complete classification of their computational power relative to…
This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree $\Delta$, and each node has up to $L$ units of load. The task is to distribute the load more evenly so that the loads of…
We consider the fundamental problem of multiple stations competing to transmit on a multiple access channel (MAC). We are given $n$ stations out of which at most $d$ are active and intend to transmit a message to other stations using MAC.…
We study the maximum $k$-set coverage problem in the following distributed setting. A collection of sets $S_1,\ldots,S_m$ over a universe $[n]$ is partitioned across $p$ machines and the goal is to find $k$ sets whose union covers the most…
The node-averaged complexity of a distributed algorithm running on a graph $G=(V,E)$ is the average over the times at which the nodes $V$ of $G$ finish their computation and commit to their outputs. We study the node-averaged complexity for…
We analyze the query complexity of finding a local minimum in $t$ rounds on general graphs. More precisely, given a graph $G = (V,E)$ and oracle access to an unknown function $f : V \to \mathbb{R}$, the goal is to find a local minimum--a…