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Submodular maximization is a classic algorithmic problem with multiple applications in data mining and machine learning; there, the growing need to deal with massive instances motivates the design of algorithms balancing the quality of the…

Data Structures and Algorithms · Computer Science 2024-02-20 Georgios Amanatidis , Federico Fusco , Philip Lazos , Stefano Leonardi , Alberto Marchetti Spaccamela , Rebecca Reiffenhäuser

In this work we investigate the min-max-min robust optimization problem and the k-adaptability robust optimization problem for binary problems with uncertain costs. The idea of the first approach is to calculate a set of k feasible…

Optimization and Control · Mathematics 2023-08-16 Jannis Kurtz

Following recent advances in combining approximation algorithms with fixed-parameter tractability (FPT), we study FPT-time approximation algorithms for minimum-norm $k$-clustering problems, parameterized by the number $k$ of open…

Data Structures and Algorithms · Computer Science 2026-05-07 Han Dai , Shi Li , Sijin Peng

Multi-armed bandit models have proven to be useful in modeling many real world problems in the areas of control and sequential decision making with partial information. However, in many scenarios, such as those prevalent in healthcare and…

Optimization and Control · Mathematics 2024-08-27 Qinyang He , Yonatan Mintz

We study a tight Bennett-type concentration inequality for sums of heterogeneous and independent variables, defined as a one-dimensional minimization. We show that this refinement, which outperforms the standard known bounds, remains…

Optimization and Control · Mathematics 2022-11-23 Quentin Jacquet , Riadh Zorgati

We study algorithms for estimating the size of maximum matching. This problem has been subject to extensive research. For $n$-vertex graphs, Bhattacharya, Kiss, and Saranurak [FOCS'23] (BKS) showed that an estimate that is within…

Data Structures and Algorithms · Computer Science 2024-06-14 Soheil Behnezhad , Mohammad Roghani , Aviad Rubinstein

One of the most fundamental problems in Computer Science is the Knapsack problem. Given a set of n items with different weights and values, it asks to pick the most valuable subset whose total weight is below a capacity threshold T. Despite…

Data Structures and Algorithms · Computer Science 2018-07-16 Kyriakos Axiotis , Christos Tzamos

Recently, Cygan, Kowalik, and Wykurz [IPL 2009] gave sub-exponential-time approximation algorithms for the Set-Cover problem with approximation ratios better than ln(n). In light of this result, it is natural to ask whether such…

Combinatorics · Mathematics 2012-10-26 Eden Chlamtac , Zac Friggstad , Konstantinos Georgiou

We revisit the study of optimal regret rates in bandit combinatorial optimization---a fundamental framework for sequential decision making under uncertainty that abstracts numerous combinatorial prediction problems. We prove that the…

Machine Learning · Computer Science 2017-02-27 Alon Cohen , Tamir Hazan , Tomer Koren

We address a generalization of the bandit with knapsacks problem, where a learner aims to maximize rewards while satisfying an arbitrary set of long-term constraints. Our goal is to design best-of-both-worlds algorithms that perform…

Machine Learning · Computer Science 2024-05-28 Martino Bernasconi , Matteo Castiglioni , Andrea Celli , Federico Fusco

We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…

Data Structures and Algorithms · Computer Science 2008-10-29 Marek Cygan , Lukasz Kowalik , Marcin Pilipczuk , Mateusz Wykurz

Knapsack and Partition are two important additive problems whose fine-grained complexities in the $(1-\varepsilon)$-approximation setting are not yet settled. In this work, we make progress on both problems by giving improved algorithms. -…

Data Structures and Algorithms · Computer Science 2023-01-24 Mingyang Deng , Ce Jin , Xiao Mao

Detecting and counting copies of permutation patterns are fundamental algorithmic problems, with applications in the analysis of rankings, nonparametric statistics, and property testing tasks such as independence and quasirandomness…

Data Structures and Algorithms · Computer Science 2026-05-07 Michal Opler

In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more…

Data Structures and Algorithms · Computer Science 2023-08-30 Baris Can Esmer , Ariel Kulik , Daniel Marx , Daniel Neuen , Roohani Sharma

Bandits with knapsacks (BwK) constitute a fundamental model that combines aspects of stochastic integer programming with online learning. Classical algorithms for BwK with a time horizon $T$ achieve a problem-independent regret bound of…

Quantum Physics · Physics 2025-07-08 Yuexin Su , Ziyi Yang , Peiyuan Huang , Tongyang Li , Yinyu Ye

We investigate pseudopolynomial-time algorithms for Bounded Knapsack and Bounded Subset Sum. Recent years have seen a growing interest in settling their fine-grained complexity with respect to various parameters. For Bounded Knapsack, the…

Data Structures and Algorithms · Computer Science 2023-12-06 Lin Chen , Jiayi Lian , Yuchen Mao , Guochuan Zhang

We consider the adversarial multi-armed bandit problem under delayed feedback. We analyze variants of the Exp3 algorithm that tune their step-size using only information (about the losses and delays) available at the time of the decisions,…

Machine Learning · Computer Science 2020-10-14 András György , Pooria Joulani

We study pseudo-polynomial time algorithms for the fundamental \emph{0-1 Knapsack} problem. In terms of $n$ and $w_{\max}$, previous algorithms for 0-1 Knapsack have cubic time complexities: $O(n^2w_{\max})$ (Bellman 1957), $O(nw_{\max}^2)$…

Data Structures and Algorithms · Computer Science 2023-08-10 Ce Jin

We present a simple deterministic reduction which, assuming the Exponential Time Hypothesis ($\mathsf{ETH}$), yields tight lower bounds for approximating the parameterized Maximum Likelihood Decoding problem ($\mathsf{MLD}$) and the…

Computational Complexity · Computer Science 2026-05-12 Rishav Gupta , Bingkai Lin , Xin Zheng

We study the stochastic versions of a broad class of combinatorial problems where the weights of the elements in the input dataset are uncertain. The class of problems that we study includes shortest paths, minimum weight spanning trees,…

Data Structures and Algorithms · Computer Science 2016-11-18 Jian Li , Amol Deshpande