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Related Experiment Video

Updated: Jun 26, 2025

Mimicking a Space Mission to Mars Using Hindlimb Unloading and Partial Weight Bearing in Rats
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Large-W limit of the knapsack problem.

Mobolaji Williams1

  • 1Jellyfish, 225 Franklin St, 20th Floor, Boston, Massachusetts 02110, USA and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.

Physical Review. E
|May 17, 2024
PubMed
Summary

This study models the knapsack problem (KP) using statistical physics, developing new algorithms. While not always outperforming existing methods, the approach reveals a link between dynamic programming and greedy solutions for the KP.

Area of Science:

  • Statistical Physics
  • Combinatorial Optimization

Background:

  • The knapsack problem (KP) is a classic optimization challenge.
  • Existing solutions include dynamic programming, annealing, and greedy algorithms.

Purpose of the Study:

  • To formulate the knapsack problem (KP) as a statistical physics system.
  • To derive novel KP algorithms based on statistical physics principles.
  • To explore the relationship between different KP solution methodologies.

Main Methods:

  • Formulating the KP as a statistical physics system.
  • Computing the partition function as a complex plane integral.
  • Developing three algorithms based on different limits of the partition function.

Main Results:

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  • Three statistical-physics-based algorithms for the KP were derived.
  • These algorithms did not consistently outperform established methods in runtime or accuracy.
  • The exact partition function reproduced the dynamic programming solution.
  • The zero-temperature algorithm yielded a greedy solution.

Conclusions:

  • A statistical physics formalism reveals a connection between dynamic programming and greedy solutions for the KP.
  • The large weight-constraint limit of dynamic programming leads to a greedy solution.
  • The formalism can be extended for more accurate algorithms and other optimization problems.