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In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at…

Optimization and Control · Mathematics 2016-06-24 André Chassein , Marc Goerigk

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

Consider the Maximum Weight Independent Set problem for rectangles: given a family of weighted axis-parallel rectangles in the plane, find a maximum-weight subset of non-overlapping rectangles. The problem is notoriously hard both in the…

Data Structures and Algorithms · Computer Science 2016-11-22 Michał Pilipczuk , Erik Jan van Leeuwen , Andreas Wiese

Near ubiquitous mobile computing has led to intense interest in dynamic graph theory. This provides a new and challenging setting for algorithmics and complexity theory. For any graph-based problem, the rapid evolution of a (possibly…

Computational Complexity · Computer Science 2012-02-20 Arnaud Casteigts , Bernard Mans , Luke Mathieson

Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to…

Optimization and Control · Mathematics 2022-01-14 Marc Goerigk , Mohammad Khosravi

We consider the following NP-hard problem: in a weighted graph, find a minimum cost set of vertices whose removal leaves a graph in which no two cycles share an edge. We obtain a constant-factor approximation algorithm, based on the…

Data Structures and Algorithms · Computer Science 2015-05-14 Samuel Fiorini , Gwenaël Joret , Ugo Pietropaoli

We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version,…

Discrete Mathematics · Computer Science 2019-07-23 Maciej Drwal

In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the…

Optimization and Control · Mathematics 2024-04-30 Marc Goerigk , Mohammad Khosravi

The maximum independent set problem is a classical NP-hard problem in theoretical computer science. In this work, we study a special case where the family of graphs considered is restricted to intersection graphs of sets of axis-aligned…

Data Structures and Algorithms · Computer Science 2024-10-10 Rishi Advani , Abolfazl Asudeh

We provide an algorithm requiring only $O(N^2)$ time to compute the maximum weight independent set of interval filament graphs. This also implies an $O(N^4)$ algorithm to compute the maximum weight induced matching of interval filament…

Data Structures and Algorithms · Computer Science 2021-10-19 Darcy Best , Max Ward

We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…

Optimization and Control · Mathematics 2025-01-07 Xiaoyu Chen , Marc Goerigk , Michael Poss

The Maximum Weight Independent Set problem is a fundamental NP-hard problem in combinatorial optimization with several real-world applications. Given an undirected vertex-weighted graph, the problem is to find a subset of the vertices with…

Optimization and Control · Mathematics 2025-03-05 Ernestine Großmann , Kenneth Langedal , Christian Schulz

The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regev (2003) proved that the problem is NP-hard to approximate within a factor $2 - \epsilon$, assuming the Unique…

Computational Complexity · Computer Science 2015-11-30 Abbas Bazzi , Samuel Fiorini , Sebastian Pokutta , Ola Svensson

We consider robust combinatorial optimization problems with cost uncertainty where the decision maker can prepare K solutions beforehand and chooses the best of them once the true cost is revealed. Also known as min-max-min robustness (a…

Optimization and Control · Mathematics 2019-10-29 Marc Goerigk , Jannis Kurtz , Michael Poss

We provide a deterministic construction of hard instances for the maximum independent set problem (MIS). The constructed hard instances form an infinite graph sequence with increasing size, which possesses similar characteristics to sparse…

Data Structures and Algorithms · Computer Science 2019-11-11 Naoto Shiraishi , Jun Takahashi

This study considers online learning with general directed feedback graphs. For this problem, we present best-of-both-worlds algorithms that achieve nearly tight regret bounds for adversarial environments as well as poly-logarithmic regret…

Machine Learning · Computer Science 2022-12-29 Shinji Ito , Taira Tsuchiya , Junya Honda

Let $G(n,c/n)$ and $G_r(n)$ be an $n$-node sparse random graph and a sparse random $r$-regular graph, respectively, and let ${\cal I}(n,r)$ and ${\cal I}(n,c)$ be the sizes of the largest independent set in $G(n,c/n)$ and $G_r(n)$. The…

Probability · Mathematics 2007-05-23 David Gamarnik , Tomasz Nowicki , Grzegorz Swirscsz

This paper presents a fast and simple new 2-approximation algorithm for minimum weighted vertex cover. The unweighted version of this algorithm is equivalent to a well-known greedy maximal independent set algorithm. We prove that this…

Data Structures and Algorithms · Computer Science 2022-09-13 Nate Veldt

It is currently an unsolved problem to determine whether a $\triangle$-free planar graph $G$ contains an independent set $A$ such that $G[V_G\setminus A]$ is $2$-choosable. However, in this paper, we take a slightly different approach by…

Combinatorics · Mathematics 2023-05-22 Sounaka Mishra , Rohini S , Sagar S. Sawant

We consider the algorithm by Ferson et al. (Reliable computing 11(3), p. 207-233, 2005) designed for solving the NP-hard problem of computing the maximal sample variance over interval data, motivated by robust statistics (in fact, the…

Optimization and Control · Mathematics 2022-07-28 Miroslav Rada , Michal Černý , Ondřej Sokol