Related papers: Fast Algorithms for Max Independent Set in Graphs …
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 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 problem of finding a maximal independent set (MIS) in the standard LOCAL model of distributed computing. Classical algorithms by Luby [JACM'86] and Alon, Babai, and Itai [JALG'86] find an MIS in $O(\log n)$ rounds in $n$-node…
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 give an $O^*(1.0821^n)$-time, polynomial space algorithm for computing Maximum Independent Set in graphs with bounded degree 3. This improves all the previous running time bounds known for the problem.
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 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…
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…
We study the Maximum Independent Set (MIS) problem on general graphs within the framework of learning-augmented algorithms. The MIS problem is known to be NP-hard and is also NP-hard to approximate to within a factor of $n^{1-\delta}$ for…
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…
Maximal Independent Set (MIS) in a graph is a fundamental problem with applications in resource allocation, scheduling, and network optimization. Although graphs are inherently un-structured and challenging for GPU parallelism due to…
Maximal Independent Set (MIS) is one of the fundamental problems in distributed computing. The round (time) complexity of distributed MIS has traditionally focused on the \emph{worst-case time} for all nodes to finish. The best-known…
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…
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…
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…
A maximal independent set (MIS) can be maintained in an evolving $m$-edge graph by simply recomputing it from scratch in $O(m)$ time after each update. But can it be maintained in time sublinear in $m$ in fully dynamic graphs? We answer…
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,…
The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…
In this paper, we investigate the complexity of Maximum Independent Set (MIS) in the class of $H$-free graphs, that is, graphs excluding a fixed graph as an induced subgraph. Given that the problem remains $NP$-hard for most graphs $H$, we…
We present the first algorithm for maintaining a maximal independent set (MIS) of a fully dynamic graph---which undergoes both edge insertions and deletions---in polylogarithmic time. Our algorithm is randomized and, per update, takes…