Chi Luo | Searcharxiv

arXiv2026

Approximate Butterfly Counting in Sublinear Time

Bipartite graphs serve as a natural model for representing relationships between two different types of entities. When analyzing bipartite graphs, butterfly counting is a fundamental research problem that aims to count the number of butterflies (i.e., 2x2 bicliques) in a given bipartite graph. While this problem has been extensively studied in the literature, existing algorithms usually necessitate access to a large portion of the entire graph, presenting challenges in real scenarios where graphs are extremely large and I/O costs are expensive. In this paper, we study the butterfly counting problem under the query model, where the following query operations are permitted: degree query, neighbor query, and vertex-pair query. We propose TLS, a practical two-level sampling algorithm that can estimate the butterfly count accurately while accessing only a limited graph structure, achieving significantly lower query costs under the standard query model. TLS also incorporates several key techniques to control the variance, including "small-degree-first sampling" and "wedge sampling via small subsets". To ensure theoretical guarantees, we further introduce two novel techniques: "heavy-light partition" and "guess-and-prove", integrated into TLS. With these techniques, we prove that the algorithm can achieve a (1+eps) accuracy for any given approximation parameter 0 < eps < 1 on general bipartite graphs with a promised time and query complexity. In particular, the promised time is sublinear when the input graph is dense enough. Extensive experiments on 15 datasets demonstrate that TLS delivers robust estimates with up to three orders of magnitude lower query costs and runtime compared to existing solutions.

cs.DB↗

arXiv2024

LaMP-Val: Large Language Models Empower Personalized Valuation in Auction

Auctions are a vital economic mechanism used to determine the market value of goods or services through competitive bidding within a specific framework. However, much of the current research primarily focuses on the bidding algorithms used within auction mechanisms. This often neglects the potential benefits of incorporating individual users' unique preferences into the valuation process. Our theoretical and empirical analysis demonstrates that valuation errors can significantly impact the overall utility. To bridge this gap, we propose a personalized valuation framework, namely Large \underline{La}nguage \underline{M}odels-powered \underline{P}ersonalized \underline{Val}uation (LaMP-Val), which integrates Large Language Models to incorporate personalized semantic preference into users valuation process. LaMP-Val integrating three components: data, learning, and evaluation. The data component tackles the challenge of building a novel dataset specifically for LLMs fine-tuning in personalized valuation modeling. The learning component introduces a diversity template to enhance LLMs' capacity for modeling fine-grained personal valuation patterns. The evaluation component establishes a closed-loop system where LLM-generated valuations interact with bidding strategies and auction. It proposes two novel metrics to quantify valuation precision and bidding intention accuracy in personalized scenarios. Extensive experiments show that LaMP-Val more accurately captures personalized values and achieves greater profits than baseline approaches.

cs.CE↗