Optimization and Algorithms

Oct 13, 2025 by wbrum.org 144 views

Optimization and Algorithms

Knapsack

Knapsack problems are a classic example of combinatorial optimization problems. They involve finding the optimal subset of items to include in a knapsack of limited capacity, subject to certain constraints. In this section, we will discuss the latest papers on knapsack problems.

Constrained Bandwidth Observation Sharing for Multi-Robot Navigation in Dynamic Environments via Intelligent Knapsack: This paper proposes a novel approach to multi-robot navigation in dynamic environments using intelligent knapsack algorithms. The authors demonstrate the effectiveness of their approach through simulations and experiments.
Sum-Of-Squares To Approximate Knapsack: This paper presents a new approach to approximating knapsack problems using sum-of-squares techniques. The authors show that their approach can provide better approximations than existing methods.
Knapsack Optimization-based Schema Linking for LLM-based Text-to-SQL Generation: This paper proposes a novel approach to schema linking for LLM-based text-to-SQL generation using knapsack optimization. The authors demonstrate the effectiveness of their approach through experiments.
Generative-enhanced optimization for knapsack problems: an industry-relevant study: This paper presents a study on the application of generative-enhanced optimization to knapsack problems in industry settings. The authors demonstrate the effectiveness of their approach through case studies.
Bandits with Anytime Knapsacks: This paper proposes a novel approach to bandit problems with anytime knapsacks. The authors demonstrate the effectiveness of their approach through simulations and experiments.
A Nearly Quadratic-Time FPTAS for Knapsack: This paper presents a new algorithm for solving knapsack problems in nearly quadratic time. The authors demonstrate the effectiveness of their approach through experiments.
Hybrid Firefly-Genetic Algorithm for Single and Multi-dimensional 0-1 Knapsack Problems: This paper proposes a novel approach to solving single and multi-dimensional 0-1 knapsack problems using a hybrid firefly-genetic algorithm. The authors demonstrate the effectiveness of their approach through experiments.
Approximation Schemes for Geometric Knapsack for Packing Spheres and Fat Objects: This paper presents a new approach to approximating geometric knapsack problems for packing spheres and fat objects. The authors demonstrate the effectiveness of their approach through simulations and experiments.
The complexity of knapsack problems in wreath products: This paper studies the complexity of knapsack problems in wreath products. The authors demonstrate the hardness of the problem through reductions.
Approximation Algorithms for Correlated Knapsack Orienteering: This paper presents a new approach to approximating correlated knapsack orienteering problems. The authors demonstrate the effectiveness of their approach through simulations and experiments.
Shadoks Approach to Knapsack Polygonal Packing: This paper proposes a novel approach to knapsack polygonal packing using Shadoks algorithm. The authors demonstrate the effectiveness of their approach through simulations and experiments.
Online Unbounded Knapsack: This paper studies the online unbounded knapsack problem. The authors demonstrate the hardness of the problem through reductions.
Approximately Counting Knapsack Solutions in Subquadratic Time: This paper presents a new approach to approximately counting knapsack solutions in subquadratic time. The authors demonstrate the effectiveness of their approach through experiments.
Maximizing a Submodular Function with Bounded Curvature under an Unknown Knapsack Constraint: This paper studies the problem of maximizing a submodular function with bounded curvature under an unknown knapsack constraint. The authors demonstrate the hardness of the problem through reductions.
Packing a Knapsack with Items Owned by Strategic Agents: This paper proposes a novel approach to packing a knapsack with items owned by strategic agents. The authors demonstrate the effectiveness of their approach through simulations and experiments.

Minimum Cut

Minimum cut problems are a fundamental problem in graph theory and computer science. They involve finding the minimum cut in a graph, subject to certain constraints. In this section, we will discuss the latest papers on minimum cut problems.

Faster Global Minimum Cut with Predictions: This paper presents a new approach to finding the global minimum cut in a graph using predictions. The authors demonstrate the effectiveness of their approach through simulations and experiments.
An O(log n)-Approximation Algorithm for (p,q)-Flexible Graph Connectivity via Independent Rounding: This paper proposes a novel approach to finding the (p,q)-flexible graph connectivity using independent rounding. The authors demonstrate the effectiveness of their approach through simulations and experiments.
Fully Dynamic Approximate Minimum Cut in Subpolynomial Time per Operation: This paper presents a new approach to finding the fully dynamic approximate minimum cut in subpolynomial time per operation. The authors demonstrate the effectiveness of their approach through simulations and experiments.
Space Complexity of Minimum Cut Problems in Single-Pass Streams: This paper studies the space complexity of minimum cut problems in single-pass streams. The authors demonstrate the hardness of the problem through reductions.
Tree-Packing Revisited: Faster Fully Dynamic Min-Cut and Arboricity: This paper presents a new approach to finding the fully dynamic min-cut and arboricity using tree-packing. The authors demonstrate the effectiveness of their approach through simulations and experiments.
Approximating the Held-Karp Bound for Metric TSP in Nearly Linear Work and Polylogarithmic Depth: This paper proposes a novel approach to approximating the Held-Karp bound for metric TSP in nearly linear work and polylogarithmic depth. The authors demonstrate the effectiveness of their approach through simulations and experiments.
Linear-Time Algorithms for k-Edge-Connected Components, k-Lean Tree Decompositions, and More: This paper presents a new approach to finding the k-edge-connected components, k-lean tree decompositions, and more in linear time. The authors demonstrate the effectiveness of their approach through simulations and experiments.
A Simpler Approach for Monotone Parametric Minimum Cut: Finding the Breakpoints in Order: This paper proposes a novel approach to finding the monotone parametric minimum cut using a simpler approach. The authors demonstrate the effectiveness of their approach through simulations and experiments.
Graph Cuts with Arbitrary Size Constraints Through Optimal Transport: This paper presents a new approach to finding the graph cuts with arbitrary size constraints using optimal transport. The authors demonstrate the effectiveness of their approach through simulations and experiments.
Optimal Sensitivity Oracle for Steiner Mincut: This paper proposes a novel approach to finding the optimal sensitivity oracle for Steiner mincut. The authors demonstrate the effectiveness of their approach through simulations and experiments.
Mimicking Networks for Constrained Multicuts in Hypergraphs: This paper presents a new approach to finding the constrained multicuts in hypergraphs using mimicking networks. The authors demonstrate the effectiveness of their approach through simulations and experiments.
Finding Diverse Minimum s-t Cuts: This paper proposes a novel approach to finding the diverse minimum s-t cuts. The authors demonstrate the effectiveness of their approach through simulations and experiments.
The Parameterized Complexity Landscape of Two-Sets Cut-Uncut: This paper studies the parameterized complexity landscape of two-sets cut-uncut. The authors demonstrate the hardness of the problem through reductions.
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Q&A: Latest 15 Papers - March 13, 2025 =====================================

Optimization and Algorithms

Knapsack

Q: What is a knapsack problem? A: A knapsack problem is a classic example of a combinatorial optimization problem. It involves finding the optimal subset of items to include in a knapsack of limited capacity, subject to certain constraints.

Q: What are some common applications of knapsack problems? A: Knapsack problems have many real-world applications, including:

Resource allocation
Scheduling
Logistics
Finance

Q: What are some common techniques used to solve knapsack problems? A: Some common techniques used to solve knapsack problems include:

Dynamic programming
Linear programming
Greedy algorithms
Heuristics

Q: What are some recent advances in knapsack problem solving? A: Some recent advances in knapsack problem solving include:

The development of new algorithms for solving knapsack problems in near-linear time
The use of machine learning techniques to improve the performance of knapsack problem solvers
The development of new formulations for knapsack problems that can be solved more efficiently

Minimum Cut

Q: What is a minimum cut problem? A: A minimum cut problem is a fundamental problem in graph theory and computer science. It involves finding the minimum cut in a graph, subject to certain constraints.

Q: What are some common applications of minimum cut problems? A: Minimum cut problems have many real-world applications, including:

Network design
Communication networks
Logistics

Q: What are some common techniques used to solve minimum cut problems? A: Some common techniques used to solve minimum cut problems include:

Flow-based algorithms
Cut-based algorithms
Heuristics

Q: What are some recent advances in minimum cut problem solving? A: Some recent advances in minimum cut problem solving include:

The development of new algorithms for solving minimum cut problems in near-linear time
The use of machine learning techniques to improve the performance of minimum cut problem solvers
The development of new formulations for minimum cut problems that can be solved more efficiently

General Questions

Q: What are some common challenges in solving optimization problems? A: Some common challenges in solving optimization problems include:

Non-convexity
Non-linearity
High dimensionality

Q: What are some common techniques used to overcome these challenges? A: Some common techniques used to overcome these challenges include:

Relaxation methods
Approximation algorithms
Heuristics

Q: What are some recent advances in optimization problem solving? A: Some recent advances in optimization problem solving include:

The development of new algorithms for solving non-convex optimization problems
The use of machine learning techniques to improve the performance of optimization problem solvers
The development of new formulations for optimization problems that can be solved more efficiently

Conclusion

Optimization and algorithms are fundamental concepts in computer science and mathematics. They have many real-world applications and are used to solve a wide range of problems. In this article, we have discussed some of the latest papers on knapsack and minimum cut problems, as well as some general questions and answers on optimization and algorithms. We hope that this article has provided a useful overview of these topics and has inspired readers to learn more.

Additional Resources

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ArXiv for the latest papers on optimization and algorithms.
Google Scholar for a wide range of papers on optimization and algorithms.