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1,248 claims from 785 papers are on the record. 45 have been checked so far; the other 1,203 have no check with a result yet.

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Status: Unchecked ×Keyword: combinatorial optimization ×Clear all

17 claims from 10 papers

1. Arts and Humanities › Digital Humanities and Scholarship

   HISTORIAE, History of Socio-Cultural Transformation as Linguistic Data Science. A Humanities Use Case

   Yinhan, Myle, Naman et al. · arXiv (Cornell University) · 2019

   A replication study of BERT pretraining measured the effect of key hyperparameters and training data size, and reports that BERT was undertrained and that a better-trained version reached state-of-the-art results.

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   1. UncheckedComparing pretrained language models is hard: training is costly, data are private and vary in size, and hyperparameters matter greatly.“Training is computationally expensive, often done on private datasets of different sizes, and, as we will show, hyperparameter choices have significant impact on the final results.”
   2. UncheckedThe authors' best retrained BERT-style model reports state-of-the-art results on three language-understanding benchmarks: GLUE, RACE and SQuAD.“Our best model achieves state-of-the-art results on GLUE, RACE and SQuAD.”

2. Computer Science › Metaheuristic Optimization Algorithms Research

   Hyper-heuristics: a survey of the state of the art

   Burke, Gendreau, Hyde et al. · Journal of the Operational Research Society · 2013

   A survey of the hyper-heuristics literature: its origins, the main types of approach, related areas, and current and future research directions.

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   1. UncheckedThe paper says hyper-heuristics fall into two main categories: those that select existing heuristics and those that generate new ones.“Two main hyper-heuristic categories can be considered: heuristic selection and heuristic generation.”
   2. UncheckedHyper-heuristics are defined by searching over heuristics or heuristic components, not directly over the possible solutions to the problem being addressed.“The distinguishing feature of hyper-heuristics is that they operate on a search space of heuristics (or heuristic components) rather than directly on the search space of solutions to the underlying problem that is being addressed.”

3. Computer Science › Metaheuristic Optimization Algorithms Research

   A review of metaheuristic algorithms for solving TSP-based scheduling optimization problems

   Toaza and Esztergár‐Kiss · Applied Soft Computing · 2023

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   1. Unchecked“The results demonstrate that the most applied metaheuristic algorithm is the genetic algorithm, but the ant colony optimization algorithm is the most popular one based on the number of citations.”

4. Computer Science › Constraint Satisfaction and Optimization

   On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms

   Ricci-Tersenghi and Semerjian · Journal of Statistical Mechanics Theory and Experiment · 2009

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   1. Unchecked“We introduce a version of the cavity method for diluted mean-field spin models that allows the computation of thermodynamic quantities similar to the Franz-Parisi quenched potential in sparse random graph models.”

5. Computer Science › Constraint Satisfaction and Optimization

   Locked Constraint Satisfaction Problems

   Zdeborová and Mézard · Physical Review Letters · 2008

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   1. Unchecked“While the phase diagram can be found easily, these problems, in their clustered phase, are extremely hard from the algorithmic point of view: the best known algorithms all fail to find solutions.”

6. Computer Science › Constraint Satisfaction and Optimization

   The freezing threshold for k-colourings of a random graph

   Molloy · ACM Symposium on Theory of Computing (STOC) · 2012

   Unchecked2 claims
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   1. Unchecked“We prove that for random graphs with density above rkf, almost every colouring is such that a linear number of variables are frozen, meaning that their colours cannot be changed by a sequence of alterations whereby we change the colours of o(n) vertices at a…
   2. Unchecked“When the density is below rkf, then almost every colouring has at most o(n) frozen variables.”

7. Computer Science › Constraint Satisfaction and Optimization

   An Analysis of Phase Transition in NK Landscapes

   Gao and Culberson · Journal of Artificial Intelligence Research · 2002

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   1. Unchecked“For the fixed ratio model, we establish several upper bounds for the solubility threshold, and prove that random instances with parameters above these upper bounds can be solved polynomially.”
   2. Unchecked“For the uniform probability model, we prove that the phase transition is easy in the sense that there is a polynomial algorithm that can solve a random instance of the problem with the probability asymptotic to 1 as the problem size tends to infinity.”

8. Computer Science › Constraint Satisfaction and Optimization

   The Freezing Threshold for k -Colourings of a Random Graph

   Molloy · Journal of the ACM · 2018

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   1. Unchecked“We prove that for random graphs with density above r f k , almost every colouring is such that a linear number of vertices are frozen, meaning that their colour cannot be changed by a sequence of alterations whereby we change the colours of o ( n ) vertices…
   2. Unchecked“When the density is below r f k , then almost every colouring is such that every vertex can be changed by a sequence of alterations where we change O (log n ) vertices at a time.”

9. Physics and Astronomy › Theoretical and Computational Physics

   Coloring Random Graphs

   Mulet, Pagnani, Weigt and Zecchina · Physical Review Letters · 2002

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   1. Unchecked“Moreover, we show that below $c_q$ there exist a clustering phase $c\in [c_d,c_q]$ in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity…

10. Computer Science › Metaheuristic Optimization Algorithms Research

    Efficient Heuristics Generation for Solving Combinatorial Optimization Problems Using Large Language Models

    Wu, Di Wang, Wu et al. · arXiv (Cornell University) · 2025

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    1. Unchecked“We theoretically prove the effectiveness of CAP in reducing unspecificity and provide empirical results in this work.”
    2. Unchecked“The use of PPP makes Hercules more resource-efficient and we name this variant Hercules-P.”
    3. Unchecked“Extensive experiments across four HG tasks, five COPs, and eight LLMs demonstrate that Hercules outperforms the state-of-the-art LLM-based HG algorithms, while Hercules-P excels at minimizing required computing resources.”