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Policy Split: Incentivizing Dual-Mode Exploration in LLM Reinforcement with Dual-Mode Entropy Regularization METER: Evaluating Multi-Level Contextual Causal Reasoning in Large Language Models Think Before you Write: QA-Guided Reasoning for Character Descriptions in Books METRO: Towards Strategy Induction from Expert Dialogue Transcripts for Non-collaborative Dialogues Retrieval as Generation: A Unified Framework with Self-Triggered Information Planning Do LLMs Know Tool Irrelevance? Demystifying Structural Alignment Bias in Tool Invocations Enhancing Multimodal Large Language Models for Ancient Chinese Character Evolution Analysis via Glyph-Driven Fine-Tuning Exploring Knowledge Conflicts for Faithful LLM Reasoning: Benchmark and Method CocoaBench: Evaluating Unified Digital Agents in the Wild MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical Reasoning Data Synthesis Efficient Training for Cross-lingual Speech Language Models Shared Emotion Geometry Across Small Language Models: A Cross-Architecture Study of Representation, Behavior, and Methodological Confounds A Systematic Analysis of the Impact of Persona Steering on LLM Capabilities Uncertainty-Aware Web-Conditioned Scientific Fact-Checking When Valid Signals Fail: Regime Boundaries Between LLM Features and RL Trading Policies When Verification Fails: How Compositionally Infeasible Claims Escape Rejection Mem$^2$Evolve: Towards Self-Evolving Agents via Co-Evolutionary Capability Expansion and Experience Distillation AOP-Smart: A RAG-Enhanced Large Language Model Framework for Adverse Outcome Pathway Analysis Advancing Polish Language Modeling through Tokenizer Optimization in the Bielik v3 7B and 11B Series TInR: Exploring Tool-Internalized Reasoning in Large Language Models Do BERT Embeddings Encode Narrative Dimensions? A Token-Level Probing Analysis of Time, Space, Causality, and Character in Fiction Generating Multiple-Choice Knowledge Questions with Interpretable Difficulty Estimation using Knowledge Graphs and Large Language Models Deep-Reporter: Deep Research for Grounded Multimodal Long-Form Generation Too Nice to Tell the Truth: Quantifying Agreeableness-Driven Sycophancy in Role-Playing Language Models Learning and Enforcing Context-Sensitive Control for LLMs Efficient Process Reward Modeling via Contrastive Mutual Information Computational Lesions in Multilingual Language Models Separate Shared and Language-specific Brain Alignment Bridging Linguistic Gaps: Cross-Lingual Mapping in Pre-Training and Dataset for Enhanced Multilingual LLM Performance Early Decisions Matter: Proximity Bias and Initial Trajectory Shaping in Non-Autoregressive Diffusion Language Models LLMs Should Incorporate Explicit Mechanisms for Human Empathy
A Clustering-Based Variable Ordering Framework for Relaxe...
Mohsen Nafar, Michael Römer, Lin Xie · 2025-12-17 · via cs.AI updates on arXiv.org

Efficient exact algorithms for Discrete Optimization (DO) rely heavily on strong primal and dual bounds. Relaxed Decision Diagrams (DDs) provide a versatile mechanism for deriving such dual bounds by compactly over-approximating the solution space through node merging. However, the quality of these relaxed diagrams, i.e. the tightness of the resulting dual bounds, depends critically on the variable ordering and the merging decisions executed during compilation. While dynamic variable ordering heuristics effectively tighten bounds, they often incur computational overhead when evaluated globally across the entire variable set. To mitigate this trade-off, this work introduces a novel clustering-based framework for variable ordering. Instead of applying dynamic ordering heuristics to the full set of unfixed variables, we first partition variables into clusters. We then leverage this structural decomposition to guide the ordering process, significantly reducing the heuristic's search space. Within this framework, we investigate two distinct strategies: Cluster-to-Cluster, which processes clusters sequentially using problem-specific aggregate criteria (such as cumulative vertex weights in the Maximum Weighted Independent Set Problem (MWISP)), and Pick-and-Sort, which iteratively selects and sorts representative variables from each cluster to balance local diversity with heuristic guidance. Later on, developing some theoretical results on the growth of the size of DDs for MWISP we propose two different policies for setting the number of clusters within the proposed framework. We embed these strategies into a DD-based branch-and-bound algorithm and evaluate them on the MWISP. Across benchmark instances, the proposed methodology consistently reduces computational costs compared to standard dynamic variable ordering baseline.