Related papers: Learning-augmented Maximum Independent Set
In the Graph Reconstruction (GR) problem, a player initially only knows the vertex set $V$ of an input graph $G=(V, E)$ and is required to learn its set of edges $E$. To this end, the player submits queries to an oracle and must deduce $E$…
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…
Max Independent Set (MIS) is a paradigmatic problem in theoretical computer science and numerous studies tackle its resolution by exact algorithms with non-trivial worst-case complexity. The best such complexity is, to our knowledge, the…
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 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…
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 present an approximation algorithm for the maximum independent set (MIS) problem over the class of equilateral $B_1$-VPG graphs. These are intersection graphs of $L$-shaped planar objects % (and their rotations by multiples of $90^o$)…
We study the approximability of the maximum size independent set (MIS) problem in bounded degree graphs. This is one of the most classic and widely studied NP-hard optimization problems. We focus on the well known minimum degree greedy…
We study the approximability of the Maximum Independent Set (MIS) problem in $H$-free graphs (that is, graphs which do not admit $H$ as an induced subgraph). As one motivation we investigate the following conjecture: for every fixed graph…
The Maximum Independent Set (MIS) problem is a fundamental combinatorial optimization task that can be naturally mapped onto the Ising Hamiltonian of neutral atom quantum processors. Given its connection to NP-hard problems and real-world…
The Maximal Independent Set (MIS) problem is one of the basics in the study of locality in distributed graph algorithms. This paper presents an extremely simple randomized algorithm providing a near-optimal local complexity for this…
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…
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…
Most graphs in real life keep changing with time. These changes can be in the form of insertion or deletion of edges or vertices. Such rapidly changing graphs motivate us to study dynamic graph algorithms. However, three important graph…
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…
Maximal Independent Set (MIS) is one of the fundamental and most well-studied problems in distributed graph algorithms. Even after four decades of intensive research, the best-known (randomized) MIS algorithms have $O(\log{n})$ round…
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,…
In the Maximum Independent Set problem we are asked to find a set of pairwise nonadjacent vertices in a given graph with the maximum possible cardinality. In general graphs, this classical problem is known to be NP-hard and hard to…
We consider the problem of finding a maximal independent set (MIS) in the discrete beeping model. At each time, a node in the network can either beep (i.e., emit a signal) or be silent. Silent nodes can only differentiate between no…
Finding a maximum independent set (MIS) of a given fam- ily of axis-parallel rectangles is a basic problem in computational geom- etry and combinatorics. This problem has attracted significant atten- tion since the sixties, when Wegner…