arXiv subjects

Xiaowei Ye

Publications and source records attributed to Xiaowei Ye.

6 recordsLinked to original sources

arXiv2026

MCI: A Maximal Clique Index for Efficient Arbitrary-Filtered Approximate Nearest Neighbor Search

Approximate Nearest Neighbor Search with arbitrary filtering predicates (AFANNS) is essential for modern data applications, yet existing methods often incur substantial storage and computational costs. In this work, we introduce the Maximal Clique Index (\mci), a novel graph-based index designed for robust and efficient AFANNS. The core idea of \mci is to approximate a dense Nearest Neighbor Graph (NNG) through a compact, clique-based representation. We propose two key techniques: (1) Maximal Clique Cover (\mcc), which exploits the geometric transitivity of high-dimensional spaces to encode dense neighborhoods as maximal cliques, achieving an index with high compression and connectivity; and (2) Local Neighborhood Graph Geometric Densification, a strategy that constructs an index approximating a large NNG from a sparse initial NNG, recovers global connectivity by progressively increasing distance thresholds to locally densify the structure. The index is built in a lock-free parallel manner for scalability and queried via a carefully-designed multi-seed strategy to handle fragmented predicate-induced subgraphs. Extensive experiments on 10 datasets show that \mci significantly outperforms state-of-the-art methods by up to one order of magnitude in QPS at high recall while using substantially smaller space, and remains competitive even on range/keyword filtering tasks, demonstrating robust general-purpose performance.

cs.DB↗

arXiv2026

A Provable Expressiveness Hierarchy in Hybrid Linear-Full Attention

Transformers serve as the foundation of most modern large language models. To mitigate the quadratic complexity of standard full attention, various efficient attention mechanisms, such as linear and hybrid attention, have been developed. A fundamental gap remains: their expressive power relative to full attention lacks a rigorous theoretical characterization. In this work, we theoretically characterize the performance differences among these attention mechanisms. Our theory applies to all linear attention variants that can be formulated as a recurrence, including Mamba, DeltaNet, etc. Specifically, we establish an expressiveness hierarchy: for the sequential function composition-a multi-step reasoning task that must occur within a model's forward pass, an ($L+1$)-layer full attention network is sufficient, whereas any hybrid network interleaving $L-1$ layers of full attention with a substantially larger number ($2^{3L^2}$) of linear attention layers cannot solve it. This result demonstrates a clear separation in expressive power between the two types of attention. Our work provides the first provable separation between hybrid attention and standard full attention, offering a theoretical perspective for understanding the fundamental capabilities and limitations of different attention mechanisms.

cs.LG↗

arXiv2024

Fast Biclique Counting on Bipartite Graphs: A Node Pivot-based Approach

Counting the number of $(p, q)$-bicliques (complete bipartite subgraphs) in a bipartite graph is a fundamental problem which plays a crucial role in numerous bipartite graph analysis applications. However, existing algorithms for counting $(p, q)$-bicliques often face significant computational challenges, particularly on large real-world networks. In this paper, we propose a general biclique counting framework, called \npivot, based on a novel concept of node-pivot. We show that previous methods can be viewed as specific implementations of this general framework. More importantly, we propose a novel implementation of \npivot based on a carefully-designed minimum non-neighbor candidate partition strategy. We prove that our new implementation of \npivot has lower worst-case time complexity than the state-of-the-art methods. Beyond basic biclique counting, a nice feature of \npivot is that it also supports local counting (computing bicliques per node) and range counting (simultaneously counting bicliques within a size range). Extensive experiments on 12 real-world large datasets demonstrate that our proposed \npivot substantially outperforms state-of-the-art algorithms by up to two orders of magnitude.

cs.DS↗

arXiv2024

Counting Cohesive Subgraphs with Hereditary Properties

Counting small cohesive subgraphs in a graph is a fundamental operation with numerous applications in graph analysis. Previous studies on cohesive subgraph counting are mainly based on the clique model, which aim to count the number of $k$-cliques in a graph with a small $k$. However, the clique model often proves too restrictive for practical use. To address this issue, we investigate a new problem of counting cohesive subgraphs that adhere to the hereditary property. Here the hereditary property means that if a graph $G$ has a property $\mathcal{P}$, then any induced subgraph of $G$ also has a property $\mathcal{P}$. To count these hereditary cohesive subgraphs (\hcss), we propose a new listing-based framework called \hcslist, which employs a backtracking enumeration procedure to count all \hcss. A notable limitation of \hcslist is that it requires enumerating all \hcss, making it intractable for large and dense graphs due to the exponential growth in the number of \hcss with respect to graph size. To overcome this limitation, we propose a novel pivot-based framework called \hcspivot, which can count most \hcss in a combinatorial manner without explicitly listing them. Two additional noteworthy features of \hcspivot is its ability to (1) simultaneously count \hcss of any size and (2) simultaneously count \hcss for each vertex or each edge, while \hcslist is only capable of counting a specific size of \hcs and obtaining a total count of \hcss in a graph. We focus specifically on two \hcs: $s$-defective clique and $s$-plex, with several non-trivial pruning techniques to enhance the efficiency. We conduct extensive experiments on 8 large real-world graphs, and the results demonstrate the high efficiency and effectiveness of our solutions.

cs.DS↗

arXiv2024

Scalable $k$-clique Densest Subgraph Search

In this paper, we present a collection of novel and scalable algorithms designed to tackle the challenges inherent in the $k$-clique densest subgraph problem (\kcdsp) within network analysis. We propose \psctl, a novel algorithm based on the Frank-Wolfe approach for addressing \kcdsp, effectively solving a distinct convex programming problem. \textcolor{black}{\psctl is able to approximate \kcdsp with near optimal guarantees.} The notable advantage of \psctl lies in its time complexity, which is independent of the count of $k$-cliques, resulting in remarkable efficiency in practical applications. Additionally, we present \spath, a sampling-based algorithm with the capability to handle networks on an unprecedented scale, reaching up to $1.8\times 10^9$ edges. By leveraging the \ccpath algorithm as a uniform $k$-clique sampler, \spath ensures the efficient processing of large-scale network data, accompanied by a detailed analysis of accuracy guarantees. Together, these contributions represent a significant advancement in the field of $k$-clique densest subgraph discovery. In experimental evaluations, our algorithms demonstrate orders of magnitude faster performance compared to the current state-of-the-art solutions.

cs.DS↗

arXiv2024

Strong Spatial Mixing for General 2-Spin Systems: A Unified Approach from Zero-Freeness

We study the algorithmic implications of zero-free regions for the partition functions of 2-spin systems. While Barvinok's algorithm yields FPTASes in such regions, the applicability of Weitz's algorithm is limited to parameter regimes where strong spatial mixing (SSM) can be established. It remains open whether Weitz's algorithm can be applied to general zero-free regions, particularly in settings where no standard tree-recurrence-based proof of SSM is known. We establish new SSM results and thereby extend the applicability of Weitz's FPTAS to all currently known zero-free regions of 2-spin systems with pinned vertices. We achieve this through a unified approach to deriving SSM from zero-freeness in the most general settings of 2-spin systems. Our work features two key innovations. 1.Our SSM results cover parts of the celebrated Lee-Yang zero-free region for the ferromagnetic Ising model, where no tree-recurrence-based proof of SSM is currently known or considered feasible. The tree recurrence method typically relies on carefully designed potential functions, the construction and analysis of which can be highly challenging. For ferromagnetic 2-spin systems, it remains an open challenge whether such potential functions can be constructed. We circumvent this difficulty by deriving SSM directly from zero-freeness. 2.The prior approach to deriving SSM from zero-freeness relies on cluster expansions, which are model-specific and known only for a few restricted parameter settings such as the hard-core model near vertex activity $\lambda=1$. We overcome this obstacle by introducing a purely combinatorial approach based on a novel Christoffel-Darboux-type identity that holds universally for 2-spin systems. This provides a broadly applicable framework for handling general 2-spin systems with arbitrary multivariate parameters and zero-free regions of arbitrary shape in a unified manner.

math-ph↗