arXiv subjects

Changyeol Lee

Publications and source records attributed to Changyeol Lee.

8 recordsLinked to original sources

arXiv2026

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis

Modular arithmetic is central to quantum algorithms for cryptographic problems, including Shor's algorithm and Grover-based cryptanalysis, with modular reduction contributing substantially to circuit cost. Pseudo-Mersenne moduli $q=2^n-c$ allow classical Crandall reduction to replace division with folding and constant arithmetic, providing a structural opportunity for more efficient quantum modular reduction than Barrett reduction. We translate this advantage into a reversible quantum setting by deriving explicit folding and normalization conditions for $2n$-bit inputs. To the best of our knowledge, this constitutes the first exact reversible quantum circuit formulation of Crandall reduction. Based on this formulation, we develop two variants: Crandall reduction-1 is designed to minimize execution cost through one-step normalization, whereas Crandall reduction-2 uses two-step normalization to support a wider range of $c$ with limited overhead. Logical resource estimates show that both variants require fewer qubits and lower T-count and T-depth than optimized folding Barrett reduction. At $n=10$, Crandall reduction-1 reduces both T-count and T-depth by approximately 46.9% relative to optimized folding Barrett reduction. Surface-code analysis further shows that, at $n=20$ under the Sparse Blossom decoder, the estimated runtimes of the two variants are 30.05 ms and 35.39 ms, respectively, compared with 53.77 ms for optimized folding Barrett reduction. These results demonstrate the practical value of exploiting modulus-specific arithmetic structure in fault-tolerant quantum circuit design.

quant-ph↗

arXiv2026

Approximating (Weighted) Chromatic Correlation Clustering via Cluster LP

Correlation Clustering is a fundamental clustering problem that is generalized to Chromatic Correlation Clustering to incorporate categorical data. Both problems have been intensively studied, and recently, substantial improvements were obtained in the approximation algorithms for Correlation Clustering. At the heart of this success lies a new linear program (LP) formulation called the cluster LP; a natural question was whether this LP can be extended to Chromatic Correlation Clustering to enable similar success. We answer this question in the affirmative by presenting a $(2+\varepsilon)$-approximation algorithm for the problem using a chromatic cluster LP. We then consider Weighted Chromatic Correlation Clustering, in which edges have fractional weights satisfying the probability constraints, to show that our algorithm extends to this weighted version to yield the same approximation guarantee.

cs.DS↗

arXiv2026

Optimal Learning-Augmented Algorithm for Online Bidding

Recent advances in machine learning have spurred significant interest in learning-augmented algorithms, particularly for online optimization. A growing body of work has studied online bidding in this framework, aiming to characterize the trade-off between robustness and consistency. While this trade-off is fully understood for deterministic algorithms, a gap between upper and lower bounds remains in the randomized setting. In this paper, we close this gap by presenting a Pareto-optimal randomized learning-augmented algorithm for this problem. Our approach introduces the notion of a bidding profile, a novel framework for representing the distribution over bids generated by an algorithm. We show that any bidding algorithm can be reduced, without loss of generality, to one driven by a bidding profile, and we characterize the optimal profile via a system of delayed differential equations. Finally, we demonstrate the broader applicability of our approach by extending it to the linear search problem, yielding a significant improvement over prior learning-augmented algorithms for linear search.

cs.DS↗

arXiv2025

Structural encoding with classical codes for computational-basis bit-flip correction in the early fault-tolerant regime

Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the functionality of classical error correction. In this approach, quantum computation is performed within the codeword subspace defined by a classical error correction code. The correction of various types of errors that manifest as bit flips is carried out based on the final measurement outcomes. The approach leverages the asymmetric structure of many key algorithms, where problem-defining diagonal operators (e.g., oracles) are paired with fixed non-diagonal operators (e.g., diffusion operators). The proposed encoding maps computational basis states to classical codewords. This approach commutes with diagonal operators, obviating their overhead and confining the main computational cost to simpler non-diagonal components. Noisy simulations corroborate this analysis, demonstrating that the proposed scheme serves as a viable protocol-level layer for enhancing performance in the early fault-tolerant regime.

quant-ph↗

arXiv2025

Improved Algorithms for Overlapping and Robust Clustering of Edge-Colored Hypergraphs: An LP-Based Combinatorial Approach

Clustering is a fundamental task in both machine learning and data mining. Among various methods, edge-colored clustering (ECC) has emerged as a useful approach for handling categorical data. Given a hypergraph with (hyper)edges labeled by colors, ECC aims to assign vertex colors to minimize the number of edges where the vertex color differs from the edge's color. However, traditional ECC has inherent limitations, as it enforces a nonoverlapping and exhaustive clustering. To tackle these limitations, three versions of ECC have been studied: Local ECC and Global ECC, which allow overlapping clusters, and Robust ECC, which accounts for vertex outliers. For these problems, both linear programming (LP) rounding algorithms and greedy combinatorial algorithms have been proposed. While these LP-rounding algorithms provide high-quality solutions, they demand substantial computation time; the greedy algorithms, on the other hand, run very fast but often compromise solution quality. In this paper, we present an algorithmic framework that combines the strengths of LP with the computational efficiency of combinatorial algorithms. Both experimental and theoretical analyses show that our algorithms efficiently produce high-quality solutions for all three problems: Local, Global, and Robust ECC. We complement our algorithmic contributions with complexity-theoretic inapproximability results and integrality gap bounds, which suggest that significant theoretical improvements are unlikely. Our results also answer two open questions previously raised in the literature.

cs.LG↗

arXiv2025

Handling LP-Rounding for Hierarchical Clustering and Fitting Distances by Ultrametrics

We consider the classic correlation clustering problem in the hierarchical setting. Given a complete graph $G=(V,E)$ and $\ell$ layers of input information, where the input of each layer consists of a nonnegative weight and a labeling of the edges with either + or -, this problem seeks to compute for each layer a partition of $V$ such that the partition for any non-top layer subdivides the partition in the upper-layer and the weighted number of disagreements over the layers is minimized. Hierarchical correlation clustering is a natural formulation of the classic problem of fitting distances by ultrametrics, which is further known as numerical taxonomy in the literature. While single-layer correlation clustering received wide attention since it was introduced and major progress evolved in the past three years, few is known for this problem in the hierarchical setting. The lack of understanding and adequate tools is reflected in the large approximation ratio known for this problem originating from 2021. In this work we make both conceptual and technical contributions towards the hierarchical clustering problem. We present a simple paradigm that greatly facilitates LP-rounding in hierarchical clustering, illustrated with an algorithm providing a significantly improved approximation guarantee of 25.7846 for the hierarchical correlation clustering problem. Our techniques reveal surprising new properties of the formulation presented and subsequently used in previous works for hierarchical clustering over the past two decades. This provides an interpretation on the core problem in hierarchical clustering as the problem of finding cuts with prescribed properties regarding average distances. We further illustrate this perspective by showing that a direct application of the techniques gives a simple alternative to the state-of-the-art result for the ultrametric violation distance problem.

cs.DS↗

arXiv2023

On Optimal Consistency-Robustness Trade-Off for Learning-Augmented Multi-Option Ski Rental

The learning-augmented multi-option ski rental problem generalizes the classical ski rental problem in two ways: the algorithm is provided with a prediction on the number of days we can ski, and the ski rental options now come with a variety of rental periods and prices to choose from, unlike the classical two-option setting. Subsequent to the initial study of the multi-option ski rental problem (without learning augmentation) due to Zhang, Poon, and Xu, significant progress has been made for this problem recently in particular. The problem is very well understood when we relinquish one of the two generalizations -- for the learning-augmented classical ski rental problem, algorithms giving best-possible trade-off between consistency and robustness exist; for the multi-option ski rental problem without learning augmentation, deterministic/randomized algorithms giving the best-possible competitiveness have been found. However, in presence of both generalizations, there remained a huge gap between the algorithmic and impossibility results. In fact, for randomized algorithms, we did not have any nontrivial lower bounds on the consistency-robustness trade-off before. This paper bridges this gap for both deterministic and randomized algorithms. For deterministic algorithms, we present a best-possible algorithm that completely matches the known lower bound. For randomized algorithms, we show the first nontrivial lower bound on the consistency-robustness trade-off, and also present an improved randomized algorithm. Our algorithm matches our lower bound on robustness within a factor of e/2 when the consistency is at most 1.086.

cs.DS↗

arXiv2023

Improved Learning-Augmented Algorithms for the Multi-Option Ski Rental Problem via Best-Possible Competitive Analysis

In this paper, we present improved learning-augmented algorithms for the multi-option ski rental problem. Learning-augmented algorithms take ML predictions as an added part of the input and incorporates these predictions in solving the given problem. Due to their unique strength that combines the power of ML predictions with rigorous performance guarantees, they have been extensively studied in the context of online optimization problems. Even though ski rental problems are one of the canonical problems in the field of online optimization, only deterministic algorithms were previously known for multi-option ski rental, with or without learning augmentation. We present the first randomized learning-augmented algorithm for this problem, surpassing previous performance guarantees given by deterministic algorithms. Our learning-augmented algorithm is based on a new, provably best-possible randomized competitive algorithm for the problem. Our results are further complemented by lower bounds for deterministic and randomized algorithms, and computational experiments evaluating our algorithms' performance improvements.

cs.DS↗