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Related papers: Exact Algorithms for Maximum Independent Set

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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,…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-02-20 Ken-ichi Kawarabayashi , Seri Khoury , Aaron Schild , Gregory Schwartzman

We show that the Maximum Weight Independent Set problem (MWIS) can be solved in quasi-polynomial time on $H$-free graphs (graphs excluding a fixed graph $H$ as an induced subgraph) for every $H$ whose every connected component is a path or…

Data Structures and Algorithms · Computer Science 2025-09-24 Peter Gartland , Daniel Lokshtanov , Tomáš Masařík , Marcin Pilipczuk , Michał Pilipczuk , Paweł Rzążewski

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 Maximum Cut (Max-Cut) problem could be naturally expressed either in a Quadratic Unconstrained Binary Optimization (QUBO) formulation, or as an Ising model. It has long been known that the Maximum Independent Set (MIS) problem could…

Quantum Physics · Physics 2024-09-19 Chuixiong Wu , Jianan Wang , Fen Zuo

The Maximum Weight Independent Set (MWIS) problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. The complexity of the MWIS problem for $P_6$-free graphs is unknown. In this note, we…

Discrete Mathematics · Computer Science 2015-04-27 T. Karthick

We first devise a branching algorithm that computes a minimum independent dominating set on any graph with running time O*(2^0.424n) and polynomial space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A…

Data Structures and Algorithms · Computer Science 2015-05-13 Nicolas Bourgeois , Bruno Escoffier , Vangelis Th. Paschos

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-05-10 Fabian Kuhn , Chaodong Zheng

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…

Data Structures and Algorithms · Computer Science 2023-11-15 Maria Chudnovsky , Marcin Pilipczuk , Michał Pilipczuk , Stéphan Thomassé

In the Independent set problem, the input is a graph $G$, every vertex has a non-negative integer weight, and the task is to find a set $S$ of pairwise non-adjacent vertices, maximizing the total weight of the vertices in $S$. We give an…

Data Structures and Algorithms · Computer Science 2015-09-02 Daniel Lokshtanov , Marcin Pilipczuk , Erik Jan van Leeuwen

We consider the problem of maintaining a maximal independent set (MIS) in a dynamic graph subject to edge insertions and deletions. Recently, Assadi, Onak, Schieber and Solomon (STOC 2018) showed that an MIS can be maintained in sublinear…

Data Structures and Algorithms · Computer Science 2018-08-31 Krzysztof Onak , Baruch Schieber , Shay Solomon , Nicole Wein

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-12-20 Fabien Dufoulon , William K. Moses , Gopal Pandurangan

Finding maximum-weight independent sets in graphs is an important NP-hard optimization problem. Given a vertex-weighted graph $G$, the task is to find a subset of pairwise non-adjacent vertices of $G$ with maximum weight. Most recently…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-10-16 Jannick Borowitz , Ernestine Großmann , Mattthias Schimek

The Maximum Weight Independent Set (MWIS) problem is a well-known NP-hard problem. For graphs $G_1, G_2$, $G_1+G_2$ denotes the disjoint union of $G_1$ and $G_2$, and for a constant $l \ge 2$, $lG$ denotes the disjoint union of $l$ copies…

Discrete Mathematics · Computer Science 2016-02-19 Andreas Brandstadt , Raffaele Mosca

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.…

Data Structures and Algorithms · Computer Science 2023-12-21 Sepehr Assadi , Christian Konrad , Kheeran K. Naidu , Janani Sundaresan

This work addresses the well-known Maximum Independent Set problem in the context of hypergraphs. While this problem has been extensively studied on graphs, we focus on its strong extension to hypergraphs, where edges may connect any number…

Data Structures and Algorithms · Computer Science 2026-02-12 Ernestine Großmann , Christian Schulz , Darren Strash , Antonie Wagner

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-06-16 Soumyottam Chatterjee , Robert Gmyr , Gopal Pandurangan

For graphs $G$ and $H$, we say that $G$ is $H$-free if it does not contain $H$ as an induced subgraph. Already in the early 1980s Alekseev observed that if $H$ is connected, then the \textsc{Max Weight Independent Set} problem (MWIS)…

Data Structures and Algorithms · Computer Science 2022-02-09 Tara Abrishami , Maria Chudnovsky , Cemil Dibek , Paweł Rzążewski

We study the Maximum Bipartite Subgraph (MBS) problem, which is defined as follows. Given a set $S$ of $n$ geometric objects in the plane, we want to compute a maximum-size subset $S'\subseteq S$ such that the intersection graph of the…

Discrete Mathematics · Computer Science 2020-03-19 Satyabrata Jana , Anil Maheshwari , Saeed Mehrabi , Sasanka Roy

The maximum independent set problem is a classic optimization problem that has also been studied quite intensively in the distributed setting. While the problem is hard to approximate in general, there are good approximation algorithms…

Data Structures and Algorithms · Computer Science 2025-06-13 Salwa Faour , Fabian Kuhn

We study the algorithmic task of finding a large independent set in a sparse Erd\H{o}s-R\'{e}nyi random graph with $n$ vertices and average degree $d$. The maximum independent set is known to have size $(2 \log d / d)n$ in the double limit…

Computational Complexity · Computer Science 2020-11-13 Alexander S. Wein