Related papers: Distributed Maximal Matching: Greedy is Optimal
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,…
$ \renewcommand{\tilde}{\widetilde} $We present an $\tilde{O}(\log^2 n)$ round deterministic distributed algorithm for the maximal independent set problem. By known reductions, this round complexity extends also to maximal matching,…
Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
The greedy coloring algorithm shows that a graph of maximum degree at most $\Delta$ has chromatic number at most $\Delta + 1$, and this is tight for cliques. Much attention has been devoted to improving this "greedy bound" for graphs…
An unexpected difference between online and offline algorithms is observed. The natural greedy algorithms are shown to be worst case online optimal for Online Independent Set and Online Vertex Cover on graphs with 'enough' isolated…
In this paper we present a deterministic CONGEST algorithm to compute an $O(k\Delta)$-vertex coloring in $O(\Delta/k)+\log^* n$ rounds, where $\Delta$ is the maximum degree of the network graph and $1\leq k\leq O(\Delta)$ can be freely…
In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…
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…
In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a $(2/3)$-approximation for the Maximum Independent Set problem on interval graphs. We show that this is tight, even on unit interval…
The greedy algorithm A iterates over a set of uniformly sized independent sets of a given graph G and checks for each set S which non-neighbor of S, if any, is best suited to be added to S, until no more suitable non-neighbors are found for…
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…
We consider the problem of online graph colouring. Whenever a node is requested, a colour must be assigned to the node, and this colour must be different from the colours of any of its neighbours. According to the greedy algorithm the node…
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…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
We study the fully dynamic maximum matching problem. In this problem, the goal is to efficiently maintain an approximate maximum matching of a graph that is subject to edge insertions and deletions. Our focus is on algorithms that maintain…
We consider the communication complexity of finding an approximate maximum matching in a graph in a multi-party message-passing communication model. The maximum matching problem is one of the most fundamental graph combinatorial problems,…
Following a given ordering of the edges of a graph $G$, the greedy edge colouring procedure assigns to each edge the smallest available colour. The minimum number of colours thus involved is the chromatic index $\chi'(G)$, and the maximum…
We consider the problem of approximating a maximum weighted matching, when the edges of an underlying weighted graph $G(V,E)$ are revealed in a streaming fashion. We analyze a variant of the previously best-known…
Randomized greedy algorithms form one of the simplest yet most effective approaches for computing approximate matchings in graphs. In this paper, we focus on the class of vertex-iterative (VI) randomized greedy matching algorithms, which…
Collective communications are ubiquitous in parallel applications. We present two new algorithms for performing a reduction. The operation associated with our reduction needs to be associative and commutative. The two algorithms are…