The evaluation of Kleene Closure Property Path Queries (KPPQs) over RDF graphs presents a fundamental trade-off. Under the intuitive simple path semantics, which forbids node repetition, the problem is NP-complete. This forces practical systems to adopt existential path semantics, which admits tractable evaluation but produces result sets bloated with redundant and often semantically meaningless paths due to unnecessary detours through cycles. This paper introduces a novel indexing framework that effectively navigates this trade-off. Our key insight is that while enumerating all simple paths is intractable, a carefully selected, compact set of representative simple paths is sufficient to correctly and completely answer connectivity queries in practice. We propose the Node Clustered Index (NCI), which pre-materializes such paths—including the longest acyclic chains and fundamental cycles —transforming online query processing from a costly graph traversal into an efficient index lookup and expansion operation. Crucially, our method guarantees that every result conforms to simple path semantics. Extensive experiments demonstrate that our approach achieves near-perfect recall, outperforming state-of-the-art systems by up to an order of magnitude. This work establishes that for NP-complete path problems, seeking polynomial-time, empirically perfect approximations is a viable and powerful paradigm, delivering both performance and quality without compromise.

This paper tackles the challenges of physics-based simulation of rigid bodies in neural rendering, with a focus on 3D model representation and collision handling. We propose Physics and Geometry-Augmented Neural Implicit Surfaces (PGA-NeuS), a novel approach that combines neural implicit surfaces with a differentiable physics solver. In the pre-processing stage, PGA-NeuS reconstructs static scene and object geometry from multi-view images using signed distance fields (SDFs). For dynamic scenes captured in monocular videos, these SDFs, along with the initial position and orientation of moving rigid bodies, are fed into a differentiable rigid body solver to optimize physical parameters, such as initial velocity and friction coefficients. Subsequently, PGA-NeuS leverages color loss, physics loss, and object mask supervision to iteratively refine the neural implicit surface, ensuring the target object's alignment with the predicted motion sequence. We evaluate PGA-NeuS on five real-world scenes, demonstrating its ability to accurately reconstruct realistic motion sequences and estimate physical parameters such as position and velocity. Dataset and source code are available at https://github.com/Raining00/PGA-NeuS . • PGA-NeuS reconstructs moving rigid objects from monocular videos using physics-aware neural surfaces. • Joint optimization of color, physics, and mask losses enables dynamic scene reconstruction from monocular videos. • We introduce a dataset with synthetic and real scenes featuring sliding, rolling, and collision motions.

Abstract As the core operator of regular path query (RPQ), the Kleene closure is essentially a recursive operation based on predicates. It has more expressive power than first-order logic, but its algorithmic complexity is an NP-hard problem and expensive to execute. Most approaches implement Kleene closure via online recursive queries (inefficient for large-scale data), yet significant reusable intermediate results emerge during execution. This paper proposes an efficient query optimization method based on offline preprocessing and tree-structured strategies to address the challenges of NP-hard complexity and low execution efficiency caused by the recursive nature of Kleene closure RPQs (KRPQs). The core contributions of this work include: (i) recursive index tree: by precomputing and materializing intermediate results of predicate paths offline, Kleene closure queries are transformed into non-recursive SPARQL queries. This allows direct retrieval of answer branches from the preconstructed index tree, eliminating redundant computations and reducing online complexity. (ii) Selectivity-driven dynamic optimization: a heuristic cost model estimates intermediate result sizes to guide query plan generation, minimizing redundant operations. (3) Query decomposition tree for nested KRPQs: a hierarchical decomposition algorithm processes nested Kleene closures layer-by-layer from inner to outer expressions, overcoming limitations of existing methods in handling complex nested structures. Experiments on large-scale RDF datasets demonstrate that the method reduces average response times by 50%–70% for single-predicate and expression-based Kleene closure queries compared to systems like Virtuoso, Jena, and KRPQ, with over 60% improvement for complex nested queries. Additionally, multithreaded preprocessing and path pool optimizations achieve up to a 76$\times $ reduction in index construction time. Experiments show that the method can significantly reduce the time of KRPQs based on large RDF graphs.