Related papers: Distributed Maximal Matching: Greedy is Optimal
We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our…
We define and study greedy matchings in vertex-ordered bipartite graphs. It is shown that each vertex-ordered bipartite graph has a unique greedy matching. The proof uses (a weak form of) Newman's lemma. The vertex ordering is called a…
The dispersion problem has received much attention recently in the distributed computing literature. In this problem, $k\leq n$ agents placed initially arbitrarily on the nodes of an $n$-node, $m$-edge anonymous graph of maximum degree…
Wattenhofer [WW04] derive a complicated distributed algorithm to compute a weighted matching of an arbitrary weighted graph, that is at most a factor 5 away from the maximum weighted matching of that graph. We show that a variant of the…
We describe a new random greedy algorithm for generating regular graphs of high girth: Let $k\geq 3$ and $c \in (0,1)$ be fixed. Let $n \in \mathbb{N}$ be even and set $g = c \log_{k-1} (n)$. Begin with a Hamilton cycle $G$ on $n$ vertices.…
We consider a class of distributed submodular maximization problems in which each agent must choose a single strategy from its strategy set. The global objective is to maximize a submodular function of the strategies chosen by each agent.…
For a fixed integer $k\geqslant 2$, let $G\in \mathcal{G}(n,p)$ be a simple connected graph on $n\rightarrow\infty$ vertices with the expected degree $d=np$ satisfying $d\geqslant c$ and $d^{k-1}= o(n)$ for some large enough constant $c$.…
We study two-stage bipartite matching, in which the edges of a bipartite graph on vertices $(B_1 \cup B_2, I)$ are revealed in two batches. In stage one, a matching must be selected from among revealed edges $E \subseteq B_1 \times I$. In…
It is an easy observation that a natural greedy approach yields a $\left(d-O(1)\right)$-factor approximation algorithm for the maximum induced matching problem in $d$-regular graphs. The only considerable and non-trivial improvement of this…
Efficient marketing or awareness-raising campaigns seek to recruit $n$ influential individuals -- where $n$ is the campaign budget -- that are able to cover a large target audience through their social connections. So far most of the…
The greedy algorithm for approximating dominating sets is a simple method that is known to compute an $(\ln n+1)$-approximation of a minimum dominating set on any graph with $n$ vertices. We show that a small modification of the greedy…
A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective…
Motivated by online advertisement and exchange settings, greedy randomized algorithms for the maximum matching problem have been studied, in which the algorithm makes (random) decisions that are essentially oblivious to the input graph. Any…
We give deterministic distributed $(1+\epsilon)$-approximation algorithms for Minimum Vertex Coloring and Maximum Independent Set on chordal graphs in the LOCAL model. Our coloring algorithm runs in $O(\frac{1}{\epsilon} \log n)$ rounds,…
We prove exact bounds on the time complexity of distributed graph colouring. If we are given a directed path that is properly coloured with $n$ colours, by prior work it is known that we can find a proper 3-colouring in $\frac{1}{2}…
``Composable core-sets'' are an efficient framework for solving optimization problems in massive data models. In this work, we consider efficient construction of composable core-sets for the determinant maximization problem. This can also…
We solve, in a fully decentralised way (\ie with no message passing), the classic problem of colouring a graph. We propose a novel algorithm that is automatically responsive to topology changes, and we prove that it converges quickly to a…
Given $D$ and $\gamma>0$, whenever $c>0$ is sufficiently small and $n$ sufficiently large, if $\mathcal{G}$ is a family of $D$-degenerate graphs of individual orders at most $n$, maximum degrees at most $\tfrac{cn}{\log n}$, and total…
The random greedy algorithm for finding a maximal independent set in a graph constructs a maximal independent set by inspecting the graph's vertices in a random order, adding the current vertex to the independent set if it is not adjacent…
In this paper we study the maximum degree of interaction which may emerge in distributed systems. It is assumed that a distributed system is represented by a graph of nodes interacting over edges. Each node has some amount of data. The…