arXiv subjects

George Li

Publications and source records attributed to George Li.

5 recordsLinked to original sources

arXiv2026

Is Four Enough? Automated Reasoning Approaches and Dual Bounds for Condorcet Dimensions of Elections

In an election where $n$ voters rank $m$ candidates, a Condorcet winning set is a committee of $k$ candidates such that for any outside candidate, a majority of voters prefer some committee member. Condorcet's paradox shows that some elections admit no Condorcet winning sets with a single candidate (i.e., $k=1$), and the same can be shown for $k=2$. On the other hand, recent work proves that a set of size $k=5$ exists for every election. This leaves an important theoretical gap between the best known lower bound $(k\geq 3)$ and upper bound $(k \leq 5)$ for the number of candidates needed to guarantee existence. We aim to close the gap between the existence guarantees and impossibility results for Condorcet winning sets. We explore an automated reasoning approach to tighten these bounds. We design a mixed-integer linear program (MILP) to search for elections that would serve as counter-examples to conjectured bounds. We employ a number of optimizations, such as symmetry breaking, subsampling, and constraint generation, to enhance the search and model effectively infinite electorates. Furthermore, we analyze the dual of the linear programming relaxation as a path towards obtaining a new upper bound. Despite extensive search on moderate-sized elections, we fail to find any election requiring a committee larger than size 3. Motivated by our experimental results in this direction, we simplify the dual linear program and formulate a conjecture which, if true, implies that a winning set of size 4 always exists. Our automated reasoning results provide strong empirical evidence that the Condorcet dimension of any election may be smaller than currently known upper bounds, at least for small instances. We offer a general-purpose framework for searching elections in ranked voting and a new, concrete analytical path via duality toward proving that smaller committees suffice.

cs.GT↗

arXiv2025

Inverse-designed nanophotonic neural network accelerators for ultra-compact optical computing

Inverse-designed nanophotonic devices offer promising solutions for analog optical computation. High-density photonic integration is critical for scaling such architectures toward more complex computational tasks and large-scale applications. Here, we present an inverse-designed photonic neural network (PNN) accelerator on a high-index contrast material platform, enabling ultra-compact and energy-efficient optical computing. Our approach introduces a wave-based inverse-design method based on three dimensional finite-difference time-domain (3D-FDTD) simulations, exploiting the linearity of Maxwell's equations to reconstruct arbitrary spatial fields through optical coherence. By decoupling the forward-pass process into linearly separable simulations, our approach is highly amenable to computational parallelism, making it particularly well suited for acceleration using graphics processing units (GPUs) and other parallel computing platforms, thereby enhancing scalability across large problem domains. We fabricate and experimentally validate two inverse-designed PNN accelerators on the silicon-on-insulator platform, achieving on-chip MNIST and MedNIST classification accuracies of 89% and 90% respectively, within ultra-compact footprints of just 20 $\times$ 20 $\mu$m$^{2}$ and 30 $\times$ 20 $\mu$m$^{2}$. Our results establish a scalable and energy-efficient platform for analog photonic computing, effectively bridging inverse nanophotonic design with high-performance optical information processing.

physics.optics↗

arXiv2022

Fine-Grained Buy-Many Mechanisms Are Not Much Better Than Bundling

Multi-item revenue-optimal mechanisms are known to be extremely complex, often offering buyers randomized lotteries of goods. In the standard buy-one model, it is known that optimal mechanisms can yield revenue infinitely higher than that of any "simple" mechanism -- the ones with size polynomial in the number of items -- even with just two items and a single buyer (Briest et al. 2015, Hart and Nisan 2017). We introduce a new parameterized class of mechanisms, buy-$k$ mechanisms, which smoothly interpolate between the classical buy-one mechanisms and the recently studied buy-many mechanisms (Chawla et al. 2019, Chawla et al. 2020, Chawla et al. 2022). Buy-$k$ mechanisms allow the buyer to buy up to $k$ many menu options. We show that restricting the seller to the class of buy-$n$ incentive-compatible mechanisms suffices to overcome the bizarre, infinite revenue properties of the buy-one model. Our main result is that the revenue gap with respect to bundling, an extremely simple mechanism, is bounded by $O(n^2)$ for any arbitrarily correlated distribution $\mathcal{D}$ over $n$ items for the case of an additive buyer. Our techniques also allow us to prove similar upper bounds for arbitrary monotone valuations, albeit with an exponential factor in the approximation. On the negative side, we show that allowing the buyer to purchase a small number of menu options does not suffice to guarantee sub-exponential approximations, even when we weaken the benchmark to the optimal buy-$k$ deterministic mechanism. If an additive buyer is only allowed to buy $k = \Theta(n^{1/2-\varepsilon})$ many menu options, the gap between the revenue-optimal deterministic buy-$k$ mechanism and bundling may be exponential in $n$. In particular, this implies that no "simple" mechanism can obtain a sub-exponential approximation in this regime.

cs.GT↗

arXiv2022

Deploying Vaccine Distribution Sites for Improved Accessibility and Equity to Support Pandemic Response

In response to COVID-19, many countries have mandated social distancing and banned large group gatherings in order to slow down the spread of SARS-CoV-2. These social interventions along with vaccines remain the best way forward to reduce the spread of SARS CoV-2. In order to increase vaccine accessibility, states such as Virginia have deployed mobile vaccination centers to distribute vaccines across the state. When choosing where to place these sites, there are two important factors to take into account: accessibility and equity. We formulate a combinatorial problem that captures these factors and then develop efficient algorithms with theoretical guarantees on both of these aspects. Furthermore, we study the inherent hardness of the problem, and demonstrate strong impossibility results. Finally, we run computational experiments on real-world data to show the efficacy of our methods.

cs.AI↗

arXiv2021

A Markov Decision Process Framework for Efficient and Implementable Contact Tracing and Isolation

Efficient contact tracing and isolation is an effective strategy to control epidemics. It was used effectively during the Ebola epidemic and successfully implemented in several parts of the world during the ongoing COVID-19 pandemic. An important consideration in contact tracing is the budget on the number of individuals asked to quarantine -- the budget is limited for socioeconomic reasons. In this paper, we present a Markov Decision Process (MDP) framework to formulate the problem of using contact tracing to reduce the size of an outbreak while asking a limited number of people to quarantine. We formulate each step of the MDP as a combinatorial problem, MinExposed, which we demonstrate is NP-Hard; as a result, we develop an LP-based approximation algorithm. Though this algorithm directly solves MinExposed, it is often impractical in the real world due to information constraints. To this end, we develop a greedy approach based on insights from the analysis of the previous algorithm, which we show is more interpretable. A key feature of the greedy algorithm is that it does not need complete information of the underlying social contact network. This makes the heuristic implementable in practice and is an important consideration. Finally, we carry out experiments on simulations of the MDP run on real-world networks, and show how the algorithms can help in bending the epidemic curve while limiting the number of isolated individuals. Our experimental results demonstrate that the greedy algorithm and its variants are especially effective, robust, and practical in a variety of realistic scenarios, such as when the contact graph and specific transmission probabilities are not known. All code can be found in our GitHub repository: https://github.com/gzli929/ContactTracing.

cs.CY↗