Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.41081

Optimization Techniques for Solving the Minimum Red--Blue Separating Set Problem with an Application to Human--AI Text Separation

Marko Djukanović·Staša Vujičić Stanković·Žiga Zebec·Christian Blum
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the so-called Minimum Red''Blue Separating Set Problem (MRBSSP) which arises from computational geometry. In particular, we propose a compact Set-Cover ILP formulation, safe preprocessing rules, a Greedy Randomized Adaptive Search Procedure (GRASP), and two exact approaches: one is based on Logic-Based Benders Decomposition (LBBD) approach, and the second represents a novel Branch-and-Benders-Cut (BBC) approach. These two exact approaches are compared to ILP--alongside GRASP and the Variable Neighborhood Search (VNS) from literature. Experiments on 250 random graphs with up to 500 vertices reveal complementary strengths: ILP yields the best feasible solutions, LBBD provides the strongest lower bounds and smallest mean optimality gap, and BBC certifies optimality most frequently. We further introduce an NLP application distinguishing human- and AI-generated texts through vocabulary-based graph features. On 42 instances, BBC achieves the smallest mean optimality gap, certifying 16 optima, while GRASP outperforms VNS. Structural analysis of optimal vocabulary separators identifies 113 mandatory and 151 replaceable features across 272 tests, highlighting substantial variability among optimal solutions. Overall, our results demonstrate the effectiveness of complementary optimization strategies and the interpretability of optimal vocabulary-based discrimination.

Explore related subjects

cs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Marko Djukanović, Staša Vujičić Stanković, Žiga Zebec, Christian Blum. 2026-10-29. Optimization Techniques for Solving the Minimum Red--Blue Separating Set Problem with an Application to Human--AI Text Separation. https://arxiv.org/abs/2610.41081

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Failure-Driven Workflow Refinement

Optimizing LLM-based workflows is typically formulated as a global search, where candidate workflows are evaluated based on a scalar metric. This paradigm, however, suffers from a critical flaw: information collapse. By reducing rich, multi-step execution traces to simple success/failure signals, existing methods are rendered blind to the underlying structure of failures, fundamentally preventing them from modeling the workflow's failure distribution. We reconceptualize this challenge as a distributional problem. We propose a new paradigm where the optimization goal is not to maximize a scalar score, but to directly minimize a workflow's Expected Failure Mass, i.e., the integral of its failure probability density function defined over a high-dimensional Failure Signature Space (FSS). This distributional lens allows us to move from inefficient, zero-order optimization to a principled, gradient-like descent on the failure landscape itself. We introduce CE-Graph, a framework that operationalizes this paradigm through a novel, failure-driven refinement process. CE-Graph approximates the failure distribution from a pool of counterexamples, identifies its densest regions as recurring failure modes, and applies targeted, operator-constrained graph edits via a Propose-and-Verify mechanism to greedily reduce the failure mass. On math, code, and QA benchmarks, our CE-Graph achieves higher robustness at a significantly lower cost than strong baselines. This suggests that a system's reliability emerges not from avoiding failures, but from systematically learning and reshaping the geometric structure of its failure distributions.

cs.AI↗
arXiv2026

Payoff scaling shapes cooperation in LLM agents across languages

Large language models (LLMs) are increasingly deployed as autonomous agents that negotiate, coordinate, and make decisions on behalf of human users. Understanding how they cooperate is therefore important for AI governance and machine behaviour research. We examine two factors: payoff magnitude and interaction language. Classical game theory predicts that multiplying all payoffs by a positive constant should not change behaviour because the underlying strategic incentives remain unchanged. We test this prediction using five widely adopted commercial LLMs playing an iterated prisoner's dilemma across ten payoff scales and five languages (English, French, Vietnamese, Chinese and Arabic). Contrary to theoretical expectations, changing only the numerical scale of payoffs substantially alters cooperation. Models respond differently, often in opposite directions, meaning that averages across models can conceal important behavioural heterogeneity. Sensitivity to payoff scale also depends strongly on prompt language. Moreover, payoff scale modifies the effects of persona instructions: at sub-unit stakes, where no payoff shown exceeds 1, all five models cooperate more under a selfish than a cooperative persona, whereas Claude and Gemini reverse this pattern at larger scales. These findings show that cooperation measures depend critically on payoff scale and language and should not be treated as fixed model traits.

cs.AI↗
arXiv2026

An Alternative Trajectory for Generative AI

The generative artificial intelligence (AI) ecosystem is undergoing rapid transformations that threaten its sustainability. As models transition from research prototypes to high-traffic products, the energetic burden has shifted from one-time training to recurring, unbounded inference. This is exacerbated by reasoning models that inflate compute costs by orders of magnitude per query. The prevailing pursuit of artificial general intelligence through scaling of monolithic models is colliding with hard physical constraints: grid failures, water consumption, and diminishing returns on data scaling. This trajectory yields models with impressive factual recall but struggles in domains requiring in-depth reasoning, possibly due to insufficient abstractions in training data. Current large language models (LLMs) exhibit genuine reasoning depth only in domains like mathematics and coding, where rigorous, pre-existing abstractions provide structural grounding. In other fields, the current approach fails to generalize well. We propose an alternative trajectory based on domain-specific superintelligence (DSS). We argue for first constructing explicit symbolic abstractions (knowledge graphs, ontologies, and formal logic) to underpin synthetic curricula enabling small language models to master domain-specific reasoning without the model collapse problem typical of LLM-based synthetic data methods. Rather than a single generalist giant model, we envision "societies of DSS models": dynamic ecosystems where orchestration agents route tasks to distinct DSS back-ends. This paradigm shift decouples capability from size, enabling intelligence to migrate from energy-intensive data centers to secure, on-device experts. By aligning algorithmic progress with physical constraints, DSS societies move generative AI from an environmental liability to a sustainable force for economic empowerment.

cs.AI↗