Simultaneous eating algorithm and greedy algorithm in assignment problems

The simultaneous eating algorithm (SEA) and probabilistic serial (PS) mechanism are well known for allocating a set of divisible or indivisible goods to agents with ordinal preferences. The PS mechanism is SEA at the same eating speed. The prominent property of SEA is ordinal efficiency. Recently, w...

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Bibliographic Details
Published in:Journal of combinatorial optimization 2023-07, Vol.45 (5), Article 137
Main Author: Zhan, Ping
Format: Article
Language:English
Subjects:
Algorithms
Combinatorics
Convex and Discrete Geometry
Eating
Efficiency
Greedy algorithms
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
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Summary:The simultaneous eating algorithm (SEA) and probabilistic serial (PS) mechanism are well known for allocating a set of divisible or indivisible goods to agents with ordinal preferences. The PS mechanism is SEA at the same eating speed. The prominent property of SEA is ordinal efficiency. Recently, we extended the PS mechanism (EPS) from a fixed quota of each good to a variable varying in a polytope constrained by submodular functions. In this article, we further generalized some results on SEA. After formalizing the extended ESA (ESEA), we show that it can be characterized by ordinal efficiency. We established a stronger summation optimization than the Pareto type of ordinal efficiency by an introduced weight vector. The weights in the summation optimization coincide with agents’ preferences at the acyclic positive values of an allocation. Hence, the order of goods selected to eat in ESEA is exactly the one chosen in the execution of the well-known greedy algorithm.
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-023-01063-0