no code implementations • 8 May 2024 • Yixin Chen, Ankur Nath, Chunli Peng, Alan Kuhnle
For constrained, not necessarily monotone submodular maximization, guiding the measured continuous greedy algorithm with a local search algorithm currently obtains the state-of-the-art approximation factor of 0. 401 \citep{buchbinder2023constrained}.
no code implementations • 30 Oct 2023 • Ankur Nath, Alan Kuhnle
In recent years, combining neural networks with local search heuristics has become popular in the field of combinatorial optimization.
no code implementations • 11 Apr 2023 • Yuanhang Shao, Tonmoy Dey, Nikola Vuckovic, Luke Van Popering, Alan Kuhnle
Combinatorial optimization (CO) aims to efficiently find the best solution to NP-hard problems ranging from statistical physics to social media marketing.
no code implementations • 9 Mar 2023 • Alan Kuhnle, Jeffrey Richley, Darleen Perez-Lavin
For general-sum, n-player, strategic games with transferable utility, the Harsanyi-Shapley value provides a computable method to both 1) quantify the strategic value of a player; and 2) make cooperation rational through side payments.
no code implementations • 20 Jun 2022 • Tonmoy Dey, Yixin Chen, Alan Kuhnle
Distributed maximization of a submodular function in the MapReduce (MR) model has received much attention, culminating in two frameworks that allow a centralized algorithm to be run in the MR setting without loss of approximation, as long as the centralized algorithm satisfies a certain consistency property - which had previously only been known to be satisfied by the standard greedy and continous greedy algorithms.
1 code implementation • NeurIPS 2021 • Yixin Chen, Tonmoy Dey, Alan Kuhnle
For the problem of maximizing a monotone, submodular function with respect to a cardinality constraint $k$ on a ground set of size $n$, we provide an algorithm that achieves the state-of-the-art in both its empirical performance and its theoretical properties, in terms of adaptive complexity, query complexity, and approximation ratio; that is, it obtains, with high probability, query complexity of $O(n)$ in expectation, adaptivity of $O(\log(n))$, and approximation ratio of nearly $1-1/e$.
no code implementations • 27 Oct 2020 • Alan Kuhnle
In general, our algorithm achieves ratio $\alpha / (1 + \alpha) - \varepsilon$, for any $\varepsilon > 0$, where $\alpha$ is the ratio of an offline (deterministic) algorithm for SMCC used for post-processing.
no code implementations • 10 Sep 2020 • Alan Kuhnle
In addition, we propose a deterministic, multi-pass streaming algorithm with a constant number of passes that achieves nearly the optimal ratio with linear query and time complexities.
1 code implementation • 3 Sep 2020 • Yixin Chen, Alan Kuhnle
In this version, we propose a fixed and improved subroutine to add a set with high average marginal gain, ThreshSeq, which returns a solution in $O( \log(n) )$ adaptive rounds with high probability.