Related papers: Distributed Lower Bounds for Ruling Sets

Let $G$ be a finite group, and let ${\rm{cd}}(G)$ denote the set of degrees of the irreducible complex characters of $G$. The degree graph $\Delta(G)$ of $G$ is defined as the simple undirected graph whose vertex set ${\rm{V}}(G)$ consists…

We study lower bounds on information dissemination in adversarial dynamic networks. Initially, k pieces of information (henceforth called tokens) are distributed among n nodes. The tokens need to be broadcast to all nodes through a…

One of the fundamental open problems in the area of distributed graph algorithms is the question of whether randomization is needed for efficient symmetry breaking. While there are fast, $\text{poly}\log n$-time randomized distributed…

Let G = (V,E) be an n-vertex graph and M_d a d-vertex graph, for some constant d. Is M_d a subgraph of G? We consider this problem in a model where all n processes are connected to all other processes, and each message contains up to O(log…

A vertex subset S of a graph G is said to 2-dominate the graph if each vertex not in S has at least two neighbors in it. As usual, the associated parameter is the minimum cardinal of a 2-dominating set, which is called the 2-domination…

We provide novel deterministic distributed vertex coloring algorithms. As our main result, we give a deterministic distributed algorithm to compute a $(\Delta+1)$-coloring of an $n$-node graph with maximum degree $\Delta$ in…

A dominating set of a graph $G$ is a set $D \subseteq V(G)$ such that every vertex in $V(G) \setminus D$ is adjacent to at least one vertex in $D$. A set $L\subseteq V(G)$ is a locating set of $G$ if every vertex in $V(G) \setminus L$ has…

Let $G$ be a graph and ${\mathcal{\tau}}: V(G)\rightarrow \Bbb{N}\cup \{0\}$ be an assignment of thresholds to the vertices of $G$. A subset of vertices $D$ is said to be a dynamic monopoly corresponding to $(G, \tau)$ if the vertices of…

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…

Let $G$ be a simple $n$-vertex graph and $W\subseteq\V(G)$. We say that $W$ is a $\delta_k$-small set if $$ \sqrt[k]{\frac{\sum_{v\in W}d^k(v)}{\abs W}}\leq n-\abs W. $$ Let $\varphi^{(k)}(G)$ denote the smallest natural number $r$ such…

In this paper we present a deterministic $O(\log\log n)$-round algorithm for the 2-ruling set problem in the Massively Parallel Computation model with $\tilde{O}(n)$ memory; this algorithm also runs in $O(\log\log n)$ rounds in the…

Graph spanners are fundamental graph structures with a wide range of applications in distributed networks. We consider a standard synchronous message passing model where in each round $O(\log n)$ bits can be transmitted over every edge (the…

We study local symmetry breaking problems in the CONGEST model, focusing on ruling set problems, which generalize the fundamental Maximal Independent Set (MIS) problem. A $\beta$-ruling set is an independent set such that every node in the…

The $\Delta$-edge stability number ${\rm es}_{\Delta}(G)$ of a graph $G$ is the minimum number of edges of $G$ whose removal results in a subgraph $H$ with $\Delta(H) = \Delta(G)-1$. Sets whose removal results in a subgraph with smaller…

A set $S\subseteq V$ is a dominating set of $G$ if every vertex in $V - S$ is adjacent to at least one vertex in $S$. The domination number $\gamma(G)$ of $G$ equals the minimum cardinality of a dominating set $S$ in $G$; we say that such a…

Given a graph G, the domination number gamma(G) of G is the minimum order of a set S of vertices such that each vertex not in S is adjacent to some vertex in S. Equivalently, label the vertices from {0, 1} so that the sum over each closed…

A set $S$ of vertices in a graph $G(V,E)$ is called a dominating set if every vertex $v\in V$ is either an element of $S$ or is adjacent to an element of $S$. A set $S$ of vertices in a graph $G(V,E)$ is called a total dominating set if…

Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…

We present improved deterministic distributed algorithms for a number of well-studied matching problems, which are simpler, faster, more accurate, and/or more general than their known counterparts. The common denominator of these results is…

Let ${H}=(V, {E})$ be a hypergraph on the vertex set $V$ and edge set ${E}\subseteq 2^V$. We show that number of distinct {\it traces} on any $k-$ subset of $V$, is most $k.{\hat \alpha}(H)$, where ${\hat \alpha}(H)$ is the {\it degeneracy}…