arXiv subjects

Hang Liao

Publications and source records attributed to Hang Liao.

6 recordsLinked to original sources

arXiv2026

Query Complexity of Hypergraph Connectivity and Learnability using CUT Oracles

We investigate the power of CUT queries to reveal the structure of unknown hypergraphs. While simple graphs allow for optimal $O(n)$-query connectivity algorithms, hypergraphs face a fundamental identifiability barrier in that distinct hypergraphs can share identical cut-profiles, making exact edge learning impossible in general, a primitive crucial in the graph connectivity algorithms. We first present a zero-error randomized algorithm that identifies the connected components of any weighted hypergraph using $O(n)$ expected queries, matching the $\Omega(n)$ lower bound. This approach bypasses the reconstruction barrier by introducing the notion of ``independent families'' -- vertex subpartitions that do not share hyperedges -- and iteratively coarsening them using auxiliary weighted graph connectivity techniques [Liao-Chakrabarty, 2024]. Second, we demonstrate that the impossibility of exact learning depends on hyperedge parity. For even-parity hypergraphs, we show that the structure is reconstructible using a M\"obius transform on the CUT function to implement binary-search-style vertex identification. This yields deterministic algorithms for obtaining $k$-connectivity certificates for $r$-bounded even hypergraphs in $\tilde{O}_r(kn)$ queries. Finally, we bypass parity and rank constraints for linear hypergraphs, achieving a subquadratic $\tilde{O}(kn^{1.5})$ query complexity for $k$-connectivity. This significantly improves upon the general $\tilde{O}(n^2)$ bound derived via symmetric submodular function minimization.

cs.DS↗

arXiv2026

WikiKV: Schema-Evolving Path-Indexed Storage for Hierarchical Knowledge Navigation

LLM-curated hierarchical knowledge bases, namely a tree-structured wiki whose nodes summarize an underlying corpus, have become a dominant substrate for retrieval-augmented applications, yet their storage layer is still treated as an implementation detail. This workload is hierarchical, query-intensive, and continuously evolving, and no existing storage model natively captures all three properties at once. We present WikiKV, a path-indexed key-value storage model purpose-built for this workload, comprising three components: (i) a data-driven schema that bootstraps the hierarchy via Intent-Anchored Schema Induction and refines it through Continuous Evolution Operators; (ii) a consistency protocol for the path-indexed storage model that precludes partial-read observations under concurrent offline rewrites without read-path locking; and (iii) a budgeted navigation operator whose search-accelerated routing reduces the expected number of LLM-assisted descent steps from d to O(1) while preserving anytime semantics with progressively refined answers. We evaluate WikiKV through real-world deployment for the WeChat Official Account AI Assistant and benchmark it against diverse baselines on the AuthTrace dataset, where it achieves balanced low per-operator latency across four query operators against relational, graph, and FS backends, and reaches 63.2% end-to-end answer correctness, exceeding multiple RAG baselines, with the gap widening on low- and high-fan-in multi-document questions. Ablation study further confirms the effectiveness of WikiKV's components.

cs.DB↗

arXiv2024

Gated-Channel Conductivity Modulation by Hole Storage Effect Under Pulsed Conditions in p-GaN Gate Double Channel HEMT

Recently, a p-GaN gate double channel HEMT (DC-HEMT) with conductivity modulation has been reported. The conductivity modulation is realized by hole storage in the gate stack and observed under quasi-static measurements. In this work, pulsed measurement and transient simulations of the DC-HEMT are carried out to disclose the conductivity modulation at high frequency and build-up time of hole storage. It takes 150 ns for the hole storage to be completely established despite a Schottky gate in the DC-HEMT with low gate leakage. The fast build-up of hole storage is attributed to the AlN insertion layer's strong confinement capability of holes and suppressed electron-hole recombination in the DC structure.

physics.app-ph↗

arXiv2024

Learning Partitions using Rank Queries

We consider the problem of learning an unknown partition of an $n$ element universe using rank queries. Such queries take as input a subset of the universe and return the number of parts of the partition it intersects. We give a simple $O(n)$-query, efficient, deterministic algorithm for this problem. We also generalize to give an $O(n + k\log r)$-rank query algorithm for a general partition matroid where $k$ is the number of parts and $r$ is the rank of the matroid.

cs.DS↗

arXiv2023

Learning Spanning Forests Optimally using CUT Queries in Weighted Undirected Graphs

In this paper we describe a randomized algorithm which returns a maximal spanning forest of an unknown {\em weighted} undirected graph making $O(n)$ $\mathsf{CUT}$ queries in expectation. For weighted graphs, this is optimal due to a result in [Auza and Lee, 2021] which shows an $Ω(n)$ lower bound for zero-error randomized algorithms. %To our knowledge, it is the only regime of this problem where we have upper and lower bounds tight up to constants. These questions have been extensively studied in the past few years, especially due to the problem's connections to symmetric submodular function minimization. We also describe a simple polynomial time deterministic algorithm that makes $O(\frac{n\log n}{\log\log n})$ queries on undirected unweighted graphs and returns a maximal spanning forest, thereby (slightly) improving upon the state-of-the-art.

cs.DS↗

arXiv2022

Lattice-aligned gallium oxynitride nanolayer for GaN surface enhancement and function extension

Gallium nitride (GaN), as a promising alternative semiconductor to silicon, is of well-established use in photoelectronic and electronic technology. However, the vulnerable GaN surface has been a critical restriction that hinders the development of GaN-based devices, especially regarding device stability and reliability. Here, we overcome this challenge by converting the GaN surface into a gallium oxynitride (GaON) epitaxial nanolayer through an in-situ two-step "oxidation-reconfiguration" process. The oxygen plasma treatment overcomes the chemical inertness of the GaN surface, and the sequential thermal annealing manipulates the kinetic-thermodynamic reaction pathways to create a metastable GaON nanolayer with wurtzite lattice. This GaN-derived GaON nanolayer is a tailored structure for surface reinforcement and possesses several advantages, including wide bandgap, high thermodynamic stability, and large valence band offset with GaN substrate. These enhanced physical properties can be further leveraged to enable GaN-based applications in new scenarios, such as complementary logic integrated circuits, photoelectrochemical water splitting, and ultraviolet photoelectric conversion, making GaON a versatile functionality extender.

physics.app-ph↗