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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…

The goal of this paper is to understand the complexity of symmetry breaking problems, specifically maximal independent set (MIS) and the closely related $\beta$-ruling set problem, in two computational models suited for large-scale graph…

Computing a maximum independent set (MaxIS) is a fundamental NP-hard problem in graph theory, which has important applications in a wide spectrum of fields. Since graphs in many applications are changing frequently over time, the problem of…

Map labeling is a classical problem in cartography and geographic information systems (GIS) that asks to place labels for area, line, and point features, with the goal to select and place the maximum number of independent, i.e.,…

We present improved results for approximating maximum-weight independent set ($\MaxIS$) in the CONGEST and LOCAL models of distributed computing. Given an input graph, let $n$ and $\Delta$ be the number of nodes and maximum degree,…

A $t$-ruling set of a graph $G = (V, E)$ is a vertex-subset $S \subseteq V$ that is independent and satisfies the property that every vertex $v \in V$ is at a distance of at most $t$ from some vertex in $S$. A \textit{maximal independent…

Given a graph, a maximal independent set (MIS) is a maximal subset of pairwise non-adjacent vertices. Finding an MIS is a fundamental problem in distributed computing. Although the problem is extensively studied and well understood in…

Maximal independent set (MIS), maximal matching (MM), and $(\Delta+1)$-coloring in graphs of maximum degree $\Delta$ are among the most prominent algorithmic graph theory problems. They are all solvable by a simple linear-time greedy…

We consider self-stabilizing algorithms to compute a Maximal Independent Set (MIS) in the extremely weak beeping communication model. The model consists of an anonymous network with synchronous rounds. In each round, each vertex can…

Symmetry breaking problems are among the most well studied in the field of distributed computing and yet the most fundamental questions about their complexity remain open. In this paper we work in the LOCAL model (where the input graph and…

Maximum weight independent set (MWIS) admits a $\frac1k$-approximation in inductively $k$-independent graphs and a $\frac{1}{2k}$-approximation in $k$-perfectly orientable graphs. These are a a parameterized class of graphs that generalize…

We study the Dominating set problem and Independent Set Problem for dynamic graphs in the vertex-arrival model. We say that a dynamic algorithm for one of these problems is $k$-stable when it makes at most $k$ changes to its output…

We study a natural extension of the Maximum Weight Independent Set Problem (MWIS), one of the most studied optimization problems in Graph algorithms. We are given a graph $G=(V,E)$, a weight function $w: V \rightarrow \mathbb{R^+}$, a…

A simple greedy algorithm to find a maximal independent set (MIS) in a graph starts with the empty set and visits every vertex, adding it to the set if and only if none of its neighbours are already in the set. In this paper, we consider…

The notion of {\em recoverable value} was advocated in work of Feige, Immorlica, Mirrokni and Nazerzadeh [Approx 2009] as a measure of quality for approximation algorithms. There this concept was applied to facility location problems. 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…

A graph $G$ with $n$ vertices is called an outerstring graph if it has an intersection representation of a set of $n$ curves inside a disk such that one endpoint of every curve is attached to the boundary of the disk. Given an outerstring…

We revisit the recent polynomial-time algorithm for the MAX WEIGHT INDEPENDENT SET (MWIS) problem in bounded-degree graphs that do not contain a fixed graph whose every component is a subdivided claw as an induced subgraph [Abrishami,…

The maximum independent set (MIS) problem of graph theory using the quantum alternating operator ansatz is studied. We perform simulations on the Rigetti Forest simulator for the square ring, $K_{2,3}$, and $K_{3,3}$ graphs and analyze the…

We address the realization of Maximum Weighted Independent Set (MWIS) and quantum Maximum Independent Set (MIS) problems under Pasqal's neutral-atom QPU constraints: limited qubit number, bounds on {\Omega} and {\Delta}, sequence duration,…