1/2-Approximate MMS Allocation for Separable Piecewise Linear Concave Valuations

Authors: Chandra Chekuri, Pooja Kulkarni , Rucha Kulkarni, Ruta Mehta

AAAI 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We show that 1/2-MMS allocation exists and can be computed in polynomial time, significantly improving the state-of-the-art. We use a relax-and-round paradigm that goes through competitive equilibrium and LP relaxation. First, we design an LP-relaxation-based method to find a 1/2-MMS allocation for SPLC valuations in polynomial time. Our result is in fact stronger; the algorithm outputs an allocation that gives each agent a value at least 1/2-APSi (for symmetric agents). Second, we show that a simple greedy algorithm achieves 1/3-APS allocation for submodular valuations.
Researcher Affiliation Academia Chandra Chekuri, Pooja Kulkarni, Rucha Kulkarni, Ruta Mehta University of Illinois at Urbana-Champaign 201 N Goodwin Ave Urbana, Illinois 61801 USA chekuri@illinois.edu, poojark2@illinois.edu, ruchark2@illinois.edu, rutameht@illinois.edu
Pseudocode Yes Algorithm 1: Rounding the Fractional Optimal of LP (6), Algorithm 2: Existence of 1/2-MMS Algorithm for SPLC valuations, Algorithm 3: Greedy Procedure for APS with Submodular Valuations
Open Source Code No The paper does not provide any concrete access information (specific repository link, explicit code release statement, or code in supplementary materials) for the methodology described.
Open Datasets No This is a theoretical paper that does not use or reference any public or open datasets for training or evaluation.
Dataset Splits No This is a theoretical paper and does not involve empirical data partitioning or validation splits.
Hardware Specification No The paper does not provide any specific hardware details used for running experiments.
Software Dependencies No The paper does not provide specific ancillary software details (e.g., library or solver names with version numbers) needed to replicate experiments.
Experiment Setup No This is a theoretical paper and does not include specific experimental setup details such as hyperparameters or training configurations.