Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Convexity of b-matching Games
Authors: Soh Kumabe, Takanori Maehara
IJCAI 2020 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this study, we give a necessary and sufficient condition of the convexity of a b-matching game (Lemma 3.6). Based on this characterization, we propose a polynomial-time algorithm to check the convexity of a given b-matching game. Formally, the following is our main theorem. Theorem 1.1. There is an O(n log n + mα(n)) time algorithm to check whether a given b-matching game is convex, where α is the inverse Ackermann function1. As an application of our characterization, we derive a polynomial-time algorithm to compute the Shapley value of a convex b-matching game. |
| Researcher Affiliation | Academia | Soh Kumabe1,2 and Takanori Maehara2 1The University of Tokyo 2RIKEN AIP |
| Pseudocode | Yes | Algorithm 1 Checking the supermodularity of ν |
| Open Source Code | No | The paper does not provide any explicit statement about releasing source code or a link to a code repository. |
| Open Datasets | No | This paper is theoretical and does not use or analyze any datasets. |
| Dataset Splits | No | This paper is theoretical and does not involve data splits for training, validation, or testing. |
| Hardware Specification | No | This paper is theoretical and focuses on mathematical proofs and algorithm complexity; therefore, it does not describe any specific hardware used for experiments. |
| Software Dependencies | No | This paper is theoretical and does not mention any specific software dependencies with version numbers required for implementation or reproduction. |
| Experiment Setup | No | This paper is theoretical and does not include details on experimental setup, hyperparameters, or training configurations. |