相关论文: Computing a Maximal Independent Set Using Beeps
Maximum Independent Set (MIS for short) is in general graphs the paradigmatic $W[1]$-hard problem. In stark contrast, polynomial-time algorithms are known when the inputs are restricted to structured graph classes such as, for instance,…
We present randomized distributed algorithms for the maximal independent set problem (MIS) that, while keeping the time complexity nearly matching the best known, reduce the energy complexity substantially. These algorithms work in the…
The problem of distributed maximal independent set (MIS) is investigated on inhomogeneous random graphs with power-law weights by which the scale-free networks can be produced. Such a particular problem has been solved on graphs with $n$…
The Beeping Network (BN) model captures important properties of biological processes. Paradoxically, the extremely limited communication capabilities of such nodes has helped BN become one of the fundamental models for networks. Since in…
In many natural and engineered systems, agents interact through local contests that determine which individuals become dominant within their neighborhoods. These interactions are shaped by inherent differences in strength, and they often…
We investigate the distributed complexity of maximal matching and maximal independent set (MIS) in hypergraphs in the LOCAL model. A maximal matching of a hypergraph $H=(V_H,E_H)$ is a maximal disjoint set $M\subseteq E_H$ of hyperedges and…
In this paper, we study lower bounds for randomized solutions to the maximal independent set (MIS) and connected dominating set (CDS) problems in the dual graph model of radio networks---a generalization of the standard graph-based model…
This paper deals with the maximum independent set (M.I.S.) problem, also known as the stable set problem. The basic mathematical programming model that captures this problem is an Integer Program (I.P.) with zero-one variables $x_j$ and…
In broadcasting, one node of a network has a message that must be learned by all other nodes. We study deterministic algorithms for this fundamental communication task in a very weak model of wireless communication. The only signals sent by…
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…
Finding a maximal independent set (MIS) in a graph is a cornerstone task in distributed computing. The local nature of an MIS allows for fast solutions in a static distributed setting, which are logarithmic in the number of nodes or in…
We show that the maximum independent set problem (MIS) on an $n$-vertex graph can be solved in $1.1996^nn^{O(1)}$ time and polynomial space, which even is faster than Robson's $1.2109^{n}n^{O(1)}$-time exponential-space algorithm published…
We consider the classic maximal and maximum independent set problems in three models of graph streams: In the edge-arrival model we see a stream of edges which collectively define a graph, this model has been well-studied for a variety of…
Broadcasting and gossiping are fundamental communication tasks in networks. In broadcasting,one node of a network has a message that must be learned by all other nodes. In gossiping, every node has a (possibly different) message, and all…
We consider networks of processes which interact with beeps. In the basic model defined by Cornejo and Kuhn (2010), processes can choose in each round either to beep or to listen. Those who beep are unable to detect simultaneous beeps.…
In the semi-streaming model for processing massive graphs, an algorithm makes multiple passes over the edges of a given $n$-vertex graph and is tasked with computing the solution to a problem using $O(n \cdot \text{polylog}(n))$ space.…
We present the \emph{discrete beeping} communication model, which assumes nodes have minimal knowledge about their environment and severely limited communication capabilities. Specifically, nodes have no information regarding the local or…
We study the Maximum Independent Set (MIS) problem under the notion of stability introduced by Bilu and Linial (2010): a weighted instance of MIS is $\gamma$-stable if it has a unique optimal solution that remains the unique optimum under…
We investigate a special case of hereditary property that we refer to as {\em robustness}. A property is {\em robust} in a given graph if it is inherited by all connected spanning subgraphs of this graph. We motivate this definition in…
Two of the most fundamental distributed symmetry-breaking problems are that of finding a maximal independent set (MIS) and a maximal matching (MM) in a graph. It is a major open question whether these problems can be solved in constant…