On the PTAS for Maximin Shares in an Indivisible Mixed Manna

Authors: Rucha Kulkarni, Ruta Mehta, Setareh Taki5523-5530

AAAI 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical In this paper, we complement the hardness result by obtaining a PTAS to compute the MMS value, when its absolute value is at least 1/p times either the total value of all the goods or total cost of all the chores, for some constant p valued at least 1. The algorithm runs in time O(mn L), where m,n are the number of items and agents, and L is the bit-length of the input. One of the key tools used by our algorithm is a carefully designed Integer Program (IP) that can be solved in polynomial-time.
Researcher Affiliation Academia 1 University of Illinois at Urbana-Champaign ruchark2@illinois.edu, rutameht@illinois.edu, staki2@illinois.edu
Pseudocode Yes Algorithm 1: Algorithm for GC-MMS
Open Source Code No The paper does not contain any statement about open-sourcing their code or providing a link to a repository.
Open Datasets No The paper is theoretical, focusing on algorithmic design and proofs, and does not involve empirical training on datasets. It defines an abstract 'MMS instance' but does not use empirical data.
Dataset Splits No The paper is theoretical and does not describe any experimental setup involving training, validation, or test dataset splits.
Hardware Specification No The paper is theoretical and describes algorithms and proofs; it does not specify any hardware used for experiments.
Software Dependencies No The paper is theoretical and discusses algorithms (e.g., 'Lenstra’s algorithm') but does not specify software dependencies with version numbers needed for experimental reproducibility.
Experiment Setup No The paper is theoretical and describes algorithms and proofs; it does not provide details on an experimental setup with hyperparameters or system-level training settings.