arXiv subjects

Dahoon Lee

Publications and source records attributed to Dahoon Lee.

3 recordsLinked to original sources

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

1.64-Approximation for Chromatic Correlation Clustering via Chromatic Cluster LP

Chromatic Correlation Clustering (CCC) generalizes Correlation Clustering by assigning multiple categorical relationships (colors) to edges and imposing chromatic constraints on the clusters. Unlike traditional Correlation Clustering, which only deals with binary $(+/-)$ relationships, CCC captures richer relational structures. Despite its importance, improving the approximation for CCC has been difficult due to the limitations of standard LP relaxations. We present a randomized $1.64$-approximation algorithm to the CCC problem, significantly improving the previous factor of $2.15$. Our approach extends the cluster LP framework to the chromatic setting by introducing a chromatic cluster LP relaxation and an rounding algorithm that utilizes both a cluster-based and a greedy pivot-based strategy. The analysis bypasses the integrality gap of $2$ for the CCC version of standard LP and highlights the potential of the cluster LP framework to address other variants of clustering problems.

cs.DS↗

arXiv2025

Improved Approximation Algorithms for Chromatic and Pseudometric-Weighted Correlation Clustering

Correlation Clustering (CC) is a foundational problem in unsupervised learning that models binary similarity relations using labeled graphs. While classical CC has been widely studied, many real-world applications involve more nuanced relationships, either multi-class categorical interactions or varying confidence levels in edge labels. To address these, two natural generalizations have been proposed: Chromatic Correlation Clustering (CCC), which assigns semantic colors to edge labels, and pseudometric-weighted CC, which allows edge weights satisfying the triangle inequality. In this paper, we develop improved approximation algorithms for both settings. Our approach leverages LP-based pivoting techniques combined with problem-specific rounding functions. For the pseudometric-weighted correlation clustering problem, we present a tight $10/3$-approximation algorithm, matching the best possible bound achievable within the framework of standard LP relaxation combined with specialized rounding. For the Chromatic Correlation Clustering (CCC) problem, we improve the approximation ratio from the previous best of $2.5$ to $2.15$, and we establish a lower bound of $2.11$ within the same analytical framework, highlighting the near-optimality of our result.

cs.DS↗