Short Communication: Optimally Solving the Unit-Demand Envy-Free Pricing Problem with Metric Substitutability in Cubic Time
Abstract
:1. Introduction
2. Materials and Methods
2.1. Literature Review
2.2. The Algorithms’ Design Scheme
3. Results
3.1. Clearing Prices
3.1.1. Reduction of the Udefp with Metric Substitutability into the Efpm
3.1.2. Allocation
3.1.3. Pricing
3.1.4. The Algorithm
Algorithm 1 Find an optimal clearing envy-free pricing. |
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3.2. General Scenario
Algorithm 2 Find an optimal envy-free pricing. |
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4. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Problem Properties | Result | Author, Year |
---|---|---|
The number of items n is constant | -approximation algorithm | Hartline and Koltun, 2005 [11] |
The consumers’ valuations satisfy the Monge property | exact algorithm | Günlük, 2008 [12] |
Consumers grouped into segments | Heuristic algorithms | Shioda et al., 2011 [13] |
Every buyer evaluates at most two items with a positive valuation | exact algorithm | Chen and Deng, 2014 [14] |
Consumers grouped into segments | Heuristic algorithms | Mykelbust et al., 2016 [15] |
; the valuations of every buyer type come from the same support | 1.88-approximation algorithm | Anshelevich et al., 2017 [16] |
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Salvatierra, M.M.; Salvatierra, M., Jr.; Colonna, J.G. Short Communication: Optimally Solving the Unit-Demand Envy-Free Pricing Problem with Metric Substitutability in Cubic Time. Algorithms 2021, 14, 279. https://doi.org/10.3390/a14100279
Salvatierra MM, Salvatierra M Jr., Colonna JG. Short Communication: Optimally Solving the Unit-Demand Envy-Free Pricing Problem with Metric Substitutability in Cubic Time. Algorithms. 2021; 14(10):279. https://doi.org/10.3390/a14100279
Chicago/Turabian StyleSalvatierra, Marcos M., Mario Salvatierra, Jr., and Juan G. Colonna. 2021. "Short Communication: Optimally Solving the Unit-Demand Envy-Free Pricing Problem with Metric Substitutability in Cubic Time" Algorithms 14, no. 10: 279. https://doi.org/10.3390/a14100279
APA StyleSalvatierra, M. M., Salvatierra, M., Jr., & Colonna, J. G. (2021). Short Communication: Optimally Solving the Unit-Demand Envy-Free Pricing Problem with Metric Substitutability in Cubic Time. Algorithms, 14(10), 279. https://doi.org/10.3390/a14100279