arXiv subjects

Weihao Zhu

Publications and source records attributed to Weihao Zhu.

9 recordsLinked to original sources

arXiv2026

Multiobjective Hypergraph Min-Cut in Quasi-Polynomial Time

We study the multiobjective hypergraph min-cut problem: Given a hypergraph $H=(V,E)$ and $k$ cost functions $c_1, c_2, \ldots, c_k:E\to\mathbb{Z}_{\ge 0}$, the goal is to find a non-empty proper subset $U\subsetneq V$ of vertices with minimum $\max_{i\in [k]} c_i(\delta(U))$. When $k$ is part of input, the problem is NP-hard (even in graphs). We focus on fixed-constant $k$ setting (e.g., $k=1, 2, 3, \ldots$). Single-objective hypergraph min-cut as well as multiobjective graph min-cut for a constant number of objectives admit polynomial-time algorithms. In contrast to these special cases, the complexity of multiobjective hypergraph min-cut remains open even for $k=2$. Known techniques fail to extend due to structural differences between graphs and hypergraphs. For $k$-objective hypergraph min-cut when $k$ is a fixed constant, we design a randomized PTAS, and two different randomized quasi-polynomial time algorithms. As an application of our $2$-objective hypergraph min-cut results, we obtain a quasi-polynomial time approximation scheme (QPTAS) for hypergraph connectivity interdiction. AI tools were used to iterate and refine the algorithmic ideas underlying this work.

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arXiv2026

A Polymatroidal Perspective on Random Contraction

Karger's elegant random contraction algorithm for finding a global mincut in a graph has been highly influential. More recent work has obtained several different (nonuniform) random contraction algorithms for mincut in hypergraphs and hedgegraphs. Motivated by the conceptual goal of understanding these algorithms in a unified fashion, we study random contraction algorithms for finding a minimum quotient of a polymatroid. We introduce the notion of quotient-bounded polymatroids and show that several existing results can be derived and understood under a common algorithmic framework for quotient-bounded polymatroids.

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arXiv2025

Stable-MoE: Lyapunov-based Token Routing for Distributed Mixture-of-Experts Training over Edge Networks

The sparse activation mechanism of mixture of experts (MoE) model empowers edge intelligence with enhanced training efficiency and reduced computational resource consumption. However, traditional token routing in distributed MoE training faces significant challenges in resource-constrained edge networks characterized by heterogeneous computing capabilities and stochastic token arrivals, which inevitably suffer from workload backlog, resource inefficiency, and performance degradation. To address this issue, we propose a novel Lyapunov-based token routing framework for distributed MoE training over resource-heterogeneous edge networks, termed Stable-MoE. Specifically, we formulate a stochastic optimization problem to maximize both system throughput and gating consistency via optimizing the token routing strategy and computational resource allocation, while ensuring long-term stability of both token and energy queues at the edge devices. Using the Lyapunov optimization, we transform the intractable long-term optimization problem into tractable per-slot subproblems by enabling online decision-making of token routing and computation frequency utilization without the knowledge of future system states. Experimental results on the SVHN and CIFAR-100 datasets demonstrate that Stable-MoE outperforms the baselines with at least 40% and 5% gains in system throughput and test accuracy, respectively.

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arXiv2025

Hedgegraph Polymatroids

Graphs and hypergraphs combine expressive modeling power with algorithmic efficiency for a wide range of applications. Hedgegraphs generalize hypergraphs further by grouping hyperedges under a color/hedge. This allows hedgegraphs to model dependencies between hyperedges and leads to several applications. However, it poses algorithmic challenges. In particular, the cut function is not submodular, which has been a barrier to algorithms for connectivity. In this work, we introduce two alternative partition-based measures of connectivity in hedgegraphs and study their structural and algorithmic aspects. Instead of the cut function, we investigate a polymatroid associated with hedgegraphs. The polymatroidal lens leads to new tractability results as well as insightful generalizations of classical results on graphs and hypergraphs.

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arXiv2025

When MoE Meets Blockchain: A Trustworthy Distributed Framework of Large Models

As an enabling architecture of Large Models (LMs), Mixture of Experts (MoE) has become prevalent thanks to its sparsely-gated mechanism, which lowers computational overhead while maintaining learning performance comparable to dense LMs. The essence of MoE lies in utilizing a group of neural networks (called experts) with each specializing in different types of tasks, along with a trainable gating network that selectively activates a subset of these experts to handle specific tasks. Traditional cloud-based MoE encounters challenges such as prolonged response latency, high bandwidth consumption, and data privacy leakage. To address these issues, researchers have proposed to deploy MoE over distributed edge networks. However, a key concern of distributed MoE frameworks is the lack of trust in data interactions among distributed experts without the surveillance of any trusted authority, and thereby prone to potential attacks such as data manipulation. In response to the security issues of traditional distributed MoE, we propose a blockchain-aided trustworthy MoE (B-MoE) framework that consists of three layers: the edge layer, the blockchain layer, and the storage layer. In this framework, the edge layer employs the activated experts downloaded from the storage layer to process the learning tasks, while the blockchain layer functions as a decentralized trustworthy network to trace, verify, and record the computational results of the experts from the edge layer. The experimental results demonstrate that B-MoE is more robust to data manipulation attacks than traditional distributed MoE during both the training and inference processes.

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arXiv2025

Online Disjoint Spanning Trees and Polymatroid Bases

Finding the maximum number of disjoint spanning trees in a given graph is a well-studied problem with several applications and connections. The Tutte-Nash-Williams theorem provides a min-max relation for this problem which also extends to disjoint bases in a matroid and leads to efficient algorithms. Several other packing problems such as element disjoint Steiner trees, disjoint set covers, and disjoint dominating sets are NP-Hard but admit an $O(\log n)$-approximation. C\u{a}linescu, Chekuri, and Vondr\'ak viewed all these packing problems as packing bases of a polymatroid and provided a unified perspective. Motivated by applications in wireless networks, recent works have studied the problem of packing set covers in the online model. The online model poses new challenges for packing problems. In particular, it is not clear how to pack a maximum number of disjoint spanning trees in a graph when edges arrive online. Motivated by these applications and theoretical considerations, we formulate an online model for packing bases of a polymatroid, and describe a randomized algorithm with a polylogarithmic competitive ratio. Our algorithm is based on interesting connections to the notion of quotients of a polymatroid that has recently seen applications in polymatroid sparsification. We generalize the previously known result for the online disjoint set cover problem and also address several other packing problems in a unified fashion. For the special case of packing disjoint spanning trees in a graph (or a hypergraph) whose edges arrive online, we provide an alternative to our general algorithm that is simpler and faster while achieving the same poly-logarithmic competitive ratio.

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arXiv2024

Solution for Temporal Sound Localisation Task of ECCV Second Perception Test Challenge 2024

This report proposes an improved method for the Temporal Sound Localisation (TSL) task, which localizes and classifies the sound events occurring in the video according to a predefined set of sound classes. The champion solution from last year's first competition has explored the TSL by fusing audio and video modalities with the same weight. Considering the TSL task aims to localize sound events, we conduct relevant experiments that demonstrated the superiority of sound features (Section 3). Based on our findings, to enhance audio modality features, we employ various models to extract audio features, such as InterVideo, CaVMAE, and VideoMAE models. Our approach ranks first in the final test with a score of 0.4925.

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arXiv2024

From Directed Steiner Tree to Directed Polymatroid Steiner Tree in Planar Graphs

In the Directed Steiner Tree (DST) problem the input is a directed edge-weighted graph $G=(V,E)$, a root vertex $r$ and a set $S \subseteq V$ of $k$ terminals. The goal is to find a min-cost subgraph that connects $r$ to each of the terminals. DST admits an $O(\log^2 k/\log \log k)$-approximation in quasi-polynomial time, and an $O(k^{\epsilon})$-approximation for any fixed $\epsilon > 0$ in polynomial-time. Resolving the existence of a polynomial-time poly-logarithmic approximation is a major open problem in approximation algorithms. In a recent work, Friggstad and Mousavi [ICALP 2023] obtained a simple and elegant polynomial-time $O(\log k)$-approximation for DST in planar digraphs via Thorup's shortest path separator theorem. We build on their work and obtain several new results on DST and related problems. - We develop a tree embedding technique for rooted problems in planar digraphs via an interpretation of the recursion in Friggstad and Mousavi [ICALP 2023]. Using this we obtain polynomial-time poly-logarithmic approximations for Group Steiner Tree, Covering Steiner Tree, and the Polymatroid Steiner Tree problems in planar digraphs. All these problems are hard to approximate to within a factor of $\Omega(\log^2 n/\log \log n)$ even in trees. - We prove that the natural cut-based LP relaxation for DST has an integrality gap of $O(\log^2 k)$ in planar graphs. This is in contrast to general graphs where the integrality gap of this LP is known to be $\Omega(k)$ and $\Omega(n^{\delta})$ for some fixed $\delta > 0$. - We combine the preceding results with density based arguments to obtain poly-logarithmic approximations for the multi-rooted versions of the problems in planar digraphs. For DST our result improves the $O(R + \log k)$ approximation of Friggstad and Mousavi [ICALP 2023] when $R= \omega(\log^2 k)$.

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arXiv2022

Time-Space Tradeoffs for Element Distinctness and Set Intersection via Pseudorandomness

In the Element Distinctness problem, one is given an array $a_1,\dots, a_n$ of integers from $[poly(n)]$ and is tasked to decide if $\{a_i\}$ are mutually distinct. Beame, Clifford and Machmouchi (FOCS 2013) gave a low-space algorithm for this problem running in space $S(n)$ and time $T(n)$ where $T(n) \le \widetilde{O}(n^{3/2}/S(n)^{1/2})$, assuming a random oracle (i.e., random access to polynomially many random bits). A recent breakthrough by Chen, Jin, Williams and Wu (SODA 2022) showed how to remove the random oracle assumption in the regime $S(n) = polylog(n)$ and $T(n) = \widetilde{O}(n^{3/2})$. They designed the first truly $polylog(n)$-space, $\widetilde{O}(n^{3/2})$-time algorithm by constructing a small family of hash functions $\mathcal{H} \subseteq \{h | h:[poly(n)]\to [n]\}$ with a certain pseudorandom property. In this paper, we give a significantly simplified analysis of the pseudorandom hash family by Chen et al. Our analysis clearly identifies the key pseudorandom property required to fool the BCM algorithm, allowing us to explore the full potential of this construction. As our main result, we show a time-space tradeoff for Element Distinctness without random oracle. Namely, for every $S(n),T(n)$ such that $T\approx \widetilde{O}(n^{3/2}/S(n)^{1/2})$, our algorithm can solve the problem in space $S(n)$ and time $T(n)$. Our algorithm also works for a related problem Set Intersection, for which this tradeoff is tight due to a matching lower bound by Dinur (Eurocrypt 2020). As two additional contributions, we show a more general pseudorandom property of the hash family, and slightly improve the seed length to sample the pseudorandom hash function.

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