Latest Research Papers Knapsack And Minimum Cut July 2025

by StackCamp Team 58 views

Hey guys! 👋 Check out the latest research papers in Knapsack and Minimum Cut, updated as of July 27, 2025. This compilation is brought to you by Scintilla06 and DailyArXiv. For a better reading experience and more papers, make sure to visit the Github page. Let's dive into these fascinating topics!

Knapsack

An In-Depth Look at Knapsack Problems

The knapsack problem is a classic optimization challenge with a wide range of applications, from resource allocation to cryptography. In this compilation, you'll find cutting-edge research on various aspects of the knapsack problem, including exact solvers, approximation algorithms, and quantum approaches. We're talking about some seriously cool stuff that could revolutionize how we solve these complex problems! The core idea of the knapsack problem involves selecting items with specific weights and values to maximize the total value while adhering to a weight constraint. Several papers address the optimization of this selection process under various conditions.

One intriguing paper, "An Exact Solver for Maximizing a Submodular Function Subject to a Knapsack Constraint," delves into maximizing submodular functions, which exhibit a diminishing returns property. This is super relevant in scenarios where adding more of something yields progressively smaller benefits. Then there's "Entropy Stable Nodal Discontinuous Galerkin Methods via Quadratic Knapsack Limiting," which explores numerical methods for solving partial differential equations using a knapsack-based limiting technique. It's a bit math-heavy, but essential for those working in computational science and engineering. For those interested in practical applications, "Efficient Branch-and-Bound for Submodular Function Maximization under Knapsack Constraint" presents an efficient algorithm accepted to ECAI 2025. Branch-and-bound is a powerful technique for solving combinatorial optimization problems, and this paper pushes the boundaries of what's possible.

Learning-augmented online knapsack problems are tackled in "Near-Optimal Consistency-Robustness Trade-Offs for Learning-Augmented Online Knapsack Problems," a fascinating study accepted at ICML 2025. This paper investigates how machine learning can improve online decision-making in knapsack scenarios. Moreover, "Episodic Contextual Bandits with Knapsacks under Conversion Models" explores the intersection of bandit algorithms and knapsack constraints in conversion modeling, which has significant implications for online advertising and recommendation systems. The paper "Dominating Set Knapsack Profit Optimization on Dominating Sets" introduces a novel twist by optimizing profits on dominating sets within a knapsack framework. This is particularly relevant in network design and resource allocation problems. Quantum computing enters the fray with "Quantum Algorithms for Bandits with Knapsacks with Improved Regret and Time Complexities," which presents quantum algorithms that outperform classical approaches for certain knapsack-related problems. This is cutting-edge research that could shape the future of optimization.

"On the Complexity of Knapsack under Explorable Uncertainty Hardness and Algorithms" dives into the computational complexity of the knapsack problem when faced with uncertainty. Understanding these limitations is crucial for designing effective algorithms. In the realm of number theory, "Unbounded knapsack problem and double partitions" explores the connections between the knapsack problem and number partitioning. The paper "Knapsack Optimization-based Schema Linking for LLM-based Text-to-SQL Generation" leverages knapsack optimization to improve the performance of text-to-SQL generation using large language models (LLMs). This is a hot topic right now, as LLMs are transforming how we interact with data. On the hardware front, "Energy Efficient Knapsack Optimization Using Probabilistic Memristor Crossbars" investigates using memristor crossbars to solve knapsack problems in an energy-efficient manner. This could lead to significant advances in embedded systems and edge computing. Then there's "Knapsack and Shortest Path Problems Generalizations From A Quantum-Inspired Tensor Network Perspective," which offers a quantum-inspired perspective on knapsack and shortest path problems. This interdisciplinary approach is pushing the boundaries of both quantum computing and optimization. "An extension of Dembo-Hammer's reduction algorithm for the 0-1 knapsack problem" provides further refinement of classical knapsack algorithms. The paper "Fair Submodular Maximization over a Knapsack Constraint" accepted to appear in IJCAI 2025, focuses on fairness considerations in submodular maximization under knapsack constraints. This is increasingly important as we deploy optimization algorithms in real-world settings. Finally, "Online Knapsack Problems with Estimates" addresses the challenges of online knapsack problems where estimates of item values are available. This is highly relevant in dynamic environments where information is incomplete.

Key Papers in Knapsack Problems

Here's a quick rundown of the key papers in this section:

  • An Exact Solver for Maximizing a Submodular Function Subject to a Knapsack Constraint
  • Entropy Stable Nodal Discontinuous Galerkin Methods via Quadratic Knapsack Limiting
  • Efficient Branch-and-Bound for Submodular Function Maximization under Knapsack Constraint
  • Near-Optimal Consistency-Robustness Trade-Offs for Learning-Augmented Online Knapsack Problems
  • Episodic Contextual Bandits with Knapsacks under Conversion Models
  • Dominating Set Knapsack: Profit Optimization on Dominating Sets
  • Quantum Algorithms for Bandits with Knapsacks with Improved Regret and Time Complexities
  • On the Complexity of Knapsack under Explorable Uncertainty: Hardness and Algorithms
  • Unbounded knapsack problem and double partitions
  • Knapsack Optimization-based Schema Linking for LLM-based Text-to-SQL Generation
  • Energy Efficient Knapsack Optimization Using Probabilistic Memristor Crossbars
  • Knapsack and Shortest Path Problems Generalizations From A Quantum-Inspired Tensor Network Perspective
  • An extension of Dembo-Hammer's reduction algorithm for the 0-1 knapsack problem
  • Fair Submodular Maximization over a Knapsack Constraint
  • Online Knapsack Problems with Estimates

Minimum Cut

Exploring Minimum Cut Algorithms and Applications

The minimum cut problem is another fundamental concept in graph theory and combinatorial optimization. It involves finding the smallest set of edges (or vertices) that, when removed, disconnect a graph. Applications range from network reliability to image segmentation. This section highlights the latest advancements in minimum cut algorithms and their applications. The minimum cut problem is a core concept in network analysis and graph theory. It aims to identify the smallest set of edges whose removal disconnects the graph. This has broad applications, from network design to image processing. Several papers in this compilation present innovative approaches to solving minimum cut problems and related challenges.

For instance, "Dual Charging for Half-Integral TSP" explores techniques relevant to the Traveling Salesperson Problem (TSP), which often involves minimum cut considerations. "Fast Algorithms for Graph Arboricity and Related Problems," accepted to FOCS 2025, presents algorithms that efficiently compute graph arboricity, a measure of how sparsely a graph can be covered by forests. This is closely related to minimum cut problems. "Bicriteria Polygon Aggregation with Arbitrary Shapes" tackles the problem of aggregating polygons while optimizing two criteria, which may involve minimum cut computations. "Cut-Query Algorithms with Few Rounds" focuses on algorithms that efficiently answer queries about cuts in a graph, using a minimal number of rounds of interaction. This is particularly relevant in distributed computing settings. Approximating the Held-Karp bound for Metric TSP is the focus of "Approximating the Held-Karp Bound for Metric TSP in Nearly Linear Work and Polylogarithmic Depth." This bound is a crucial ingredient in solving the TSP, and this paper offers significant performance improvements. A major breakthrough is presented in "Breaking the O(mn)-Time Barrier for Vertex-Weighted Global Minimum Cut," which offers a faster algorithm for computing the global minimum cut in vertex-weighted graphs. This could have a significant impact on various applications. "A Framework for the Design of Efficient Diversification Algorithms to NP-Hard Problems" introduces a general framework for designing diversification algorithms, which can be applied to minimum cut and other NP-hard problems. This paper provides valuable tools for tackling computationally challenging tasks. The paper "Spectral Clustering for Directed Graphs via Likelihood Estimation on Stochastic Block Models" leverages spectral clustering techniques for directed graphs, which can be used to identify clusters of nodes that are weakly connected to other clusters. This is valuable in social network analysis and community detection.

"An Effective Flow-based Method for Positive-Unlabeled Learning 2-HNC" introduces a flow-based method for positive-unlabeled learning, a machine learning paradigm where only positive examples and unlabeled data are available. This has applications in various domains, such as fraud detection and medical diagnosis. "Near-Optimal Minimum Cuts in Hypergraphs at Scale" addresses the challenge of computing minimum cuts in hypergraphs, which are generalizations of graphs where edges can connect more than two vertices. This is important in modeling complex relationships. "The Case for External Graph Sketching" argues for the use of external graph sketching techniques, which are particularly useful for processing massive graphs that don't fit in memory. The paper "Multicut Problems in Embedded Graphs The Dependency of Complexity on the Demand Pattern" delves into the complexity of multicut problems in embedded graphs, showing how the difficulty depends on the demand pattern. "Minimum Cut Representability of Stable Matching Problems" explores the connections between minimum cuts and stable matching problems, which arise in areas such as economics and resource allocation. This interdisciplinary approach yields interesting insights. "Informed Greedy Algorithm for Scalable Bayesian Network Fusion via Minimum Cut Analysis" presents an informed greedy algorithm for fusing Bayesian networks, leveraging minimum cut analysis to guide the fusion process. Bayesian networks are used to model probabilistic relationships, and this paper offers a scalable method for combining them. A significant theoretical result is presented in "Network Unreliability in Almost-Linear Time," which provides an algorithm for computing network unreliability in nearly linear time. This has implications for designing robust and fault-tolerant networks.

Key Papers in Minimum Cut Problems

Here's a summary of the key papers in this section:

  • Dual Charging for Half-Integral TSP
  • Fast Algorithms for Graph Arboricity and Related Problems
  • Bicriteria Polygon Aggregation with Arbitrary Shapes
  • Cut-Query Algorithms with Few Rounds
  • Approximating the Held-Karp Bound for Metric TSP in Nearly Linear Work and Polylogarithmic Depth
  • Breaking the O(mn)-Time Barrier for Vertex-Weighted Global Minimum Cut
  • A Framework for the Design of Efficient Diversification Algorithms to NP-Hard Problems
  • Spectral Clustering for Directed Graphs via Likelihood Estimation on Stochastic Block Models
  • An Effective Flow-based Method for Positive-Unlabeled Learning: 2-HNC
  • Near-Optimal Minimum Cuts in Hypergraphs at Scale
  • The Case for External Graph Sketching
  • Multicut Problems in Embedded Graphs: The Dependency of Complexity on the Demand Pattern
  • Minimum Cut Representability of Stable Matching Problems
  • Informed Greedy Algorithm for Scalable Bayesian Network Fusion via Minimum Cut Analysis
  • Network Unreliability in Almost-Linear Time

Stay tuned for more updates, and don't forget to check out the Github page for the latest papers and resources! Happy reading! 📚