arXiv subjects

Longkun Guo

Publications and source records attributed to Longkun Guo.

17 recordsLinked to original sources

arXiv2026

Parameterized and Streaming Algorithms for Euclidean Fair $k$-Center Clustering

Motivated by the growing importance of fairness in machine learning, fair $k$-center clustering has attracted considerable research attention as a fundamental problem. In this problem, a dataset is partitioned into $m$ disjoint groups, and the objective is to select $k$ data points as centers, subject to upper bounds on the number of centers chosen from each group, aiming to minimize the maximum distance between any data point and its assigned center. Focusing on Euclidean spaces, which are ubiquitous in machine learning applications, we first develop a parameterized approximation algorithm for Euclidean fair $k$-center with an approximation ratio of $2.732$. By incorporating this algorithm as a post-processing stage into a one-pass streaming framework for large-scale data, we obtain an approximation ratio of $4.464$. These ratios can be further respectively improved to $2.414$ and $3.828$ with a runtime exponential on $k$. To ensure polynomial-time complexity, we further design a one-pass streaming algorithm with an approximation ratio of $4.732$, which can be further improved to $4.42$, outperforming the state-of-the-art ratio. Finally, extensive experiments show that our methods significantly outperform state-of-the-art approaches in terms of clustering accuracy.

cs.LG↗

arXiv2026

Toward Trustworthy AI: Multi-Target Adversarial Attacks and Robust Defenses for Continuous Data Summarization

Trustworthy AI requires reliable data-processing pipelines, not only robust downstream predictive models. As an upstream component, data summarization determines which information is retained and passed to subsequent learning or decision modules. Therefore, adversarial perturbations to the summarization process can compromise trustworthy AI in an upstream manner: they may alter the selected summary, reduce its representativeness, and further degrade the utility of subsequent learning tasks. In this paper, we study adversarial attacks on continuous data summarization under similarity-level perturbations through DR-submodular optimization. We show that a class of multi-resolution image summarization objectives can be formulated as multilinear extensions of non-negative submodular set functions and satisfy DR-submodularity with $m$-weak monotonicity. We then formulate multi-target attack generation as a min-max problem, where one admissible perturbation of the similarity structure is optimized to degrade multiple target summarization models. To mitigate such perturbations, we formulate robust defense against mixed attack types as a regularized max-min problem. For both problems, we develop approximation algorithms with theoretical guarantees. Experiments on real-data and controlled clustered benchmarks show that the proposed attack is effective in representative low-to-moderate budget regimes and can induce downstream task-performance loss. The proposed defense improves the robustness--mitigation trade-off in structured settings, while also revealing the parameter sensitivity of robust protection on real data.

cs.AI↗

arXiv2026

Approximation Algorithm for Constrained $k$-Center Clustering: A Local Search Approach

Clustering is a long-standing research problem and a fundamental tool in AI and data analysis. The traditional k-center problem, a fundamental theoretical challenge in clustering, has a best possible approximation ratio of 2, and any improvement to a ratio of 2 - {\epsilon} would imply P = NP. In this work, we study the constrained k-center clustering problem, where instance-level cannot-link (CL) and must-link (ML) constraints are incorporated as background knowledge. Although general CL constraints significantly increase the hardness of approximation, previous work has shown that disjoint CL sets permit constant-factor approximations. However, whether local search can achieve such a guarantee in this setting remains an open question. To this end, we propose a novel local search framework based on a transformation to a dominating matching set problem, achieving the best possible approximation ratio of 2. The experimental results on both real-world and synthetic datasets demonstrate that our algorithm outperforms baselines in solution quality.

cs.LG↗

arXiv2026

Optimized Algorithms for Text Clustering with LLM-Generated Constraints

Clustering is a fundamental tool that has garnered significant interest across a wide range of applications including text analysis. To improve clustering accuracy, many researchers have incorporated background knowledge, typically in the form of must-link and cannot-link constraints, to guide the clustering process. With the recent advent of large language models (LLMs), there is growing interest in improving clustering quality through LLM-based automatic constraint generation. In this paper, we propose a novel constraint-generation approach that reduces resource consumption by generating constraint sets rather than using traditional pairwise constraints. This approach improves both query efficiency and constraint accuracy compared to state-of-the-art methods. We further introduce a constrained clustering algorithm tailored to the characteristics of LLM-generated constraints. Our method incorporates a confidence threshold and a penalty mechanism to address potentially inaccurate constraints. We evaluate our approach on five text datasets, considering both the cost of constraint generation and the overall clustering performance. The results show that our method achieves clustering accuracy comparable to the state-of-the-art algorithms while reducing the number of LLM queries by more than 20 times.

cs.LG↗

arXiv2025

Improved Streaming Algorithm for Fair $k$-Center Clustering

Many real-world applications pose challenges in incorporating fairness constraints into the $k$-center clustering problem, where the dataset consists of $m$ demographic groups, each with a specified upper bound on the number of centers to ensure fairness. Focusing on big data scenarios, this paper addresses the problem in a streaming setting, where data points arrive one by one sequentially in a continuous stream. Leveraging a structure called the $\lambda$-independent center set, we propose a one-pass streaming algorithm that first computes a reserved set of points during the streaming process. Then, for the post-streaming process, we propose an approach for selecting centers from the reserved point set by analyzing all three possible cases, transforming the most complicated one into a specially constrained vertex cover problem in an auxiliary graph. Our algorithm achieves a tight approximation ratio of 5 while consuming $O(k\log n)$ memory. It can also be readily adapted to solve the offline fair $k$-center problem, achieving a 3-approximation ratio that matches the current state of the art. Furthermore, we extend our approach to a semi-structured data stream, where data points from each group arrive in batches. In this setting, we present a 3-approximation algorithm for $m = 2$ and a 4-approximation algorithm for general $m$. Lastly, we conduct extensive experiments to evaluate the performance of our approaches, demonstrating that they outperform existing baselines in both clustering cost and runtime efficiency.

cs.DS↗

arXiv2024

Algorithmics and Complexity of Cost-Driven Task Offloading with Submodular Optimization in Edge-Cloud Environments

Emerging applications such as autonomous driving pose the challenge of efficient cost-driven offloading in edge-cloud environments. This involves assigning tasks to edge and cloud servers for separate execution, with the goal of minimizing the total service cost including communication and computation costs. In this paper, observing that the intra-cloud communication costs are relatively low and can often be neglected in many real-world applications, we consequently introduce the so-called communication assumption which posits that the intra-cloud communication costs are not higher than the inter-partition communication cost between cloud and edge servers, nor the cost among edge servers. As a preliminary analysis, we first prove that the offloading problem without the communication assumption is NP-hard, using a reduction from MAX-CUT. Then, we show that the offloading problem can be modeled as a submodular minimization problem, making it polynomially solvable. Moreover, this polynomial solvability remains even when additional constraints are imposed, such as when certain tasks must be executed on edge servers due to latency constraints. By combining both algorithmics and computational complexity results, we demonstrate that the difficulty of the offloading problem largely depends on whether the communication assumption is satisfied. Lastly, extensive experiments are conducted to evaluate the practical performance of the proposed algorithm, demonstrating its significant advantages over the state-of-the-art methods in terms of efficiency and cost-effectiveness.

cs.DM↗

arXiv2024

Obstacle-Aware Length-Matching Routing for Any-Direction Traces in Printed Circuit Board

Emerging applications in Printed Circuit Board (PCB) routing impose new challenges on automatic length matching, including adaptability for any-direction traces with their original routing preserved for interactiveness. The challenges can be addressed through two orthogonal stages: assign non-overlapping routing regions to each trace and meander the traces within their regions to reach the target length. In this paper, mainly focusing on the meandering stage, we propose an obstacle-aware detailed routing approach to optimize the utilization of available space and achieve length matching while maintaining the original routing of traces. Furthermore, our approach incorporating the proposed Multi-Scale Dynamic Time Warping (MSDTW) method can also handle differential pairs against common decoupled problems. Experimental results demonstrate that our approach has effective length-matching routing ability and compares favorably to previous approaches under more complicated constraints.

cs.AR↗

arXiv2024

Near-Optimal Algorithms for Constrained k-Center Clustering with Instance-level Background Knowledge

Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work, we build on widely adopted $k$-center clustering and model its input background knowledge as must-link (ML) and cannot-link (CL) constraint sets. However, most clustering problems including $k$-center are inherently $\mathcal{NP}$-hard, while the more complex constrained variants are known to suffer severer approximation and computation barriers that significantly limit their applicability. By employing a suite of techniques including reverse dominating sets, linear programming (LP) integral polyhedron, and LP duality, we arrive at the first efficient approximation algorithm for constrained $k$-center with the best possible ratio of 2. We also construct competitive baseline algorithms and empirically evaluate our approximation algorithm against them on a variety of real datasets. The results validate our theoretical findings and demonstrate the great advantages of our algorithm in terms of clustering cost, clustering quality, and running time.

cs.LG↗

arXiv2023

Curriculum-Enhanced Residual Soft An-Isotropic Normalization for Over-smoothness in Deep GNNs

Despite Graph neural networks' significant performance gain over many classic techniques in various graph-related downstream tasks, their successes are restricted in shallow models due to over-smoothness and the difficulties of optimizations among many other issues. In this paper, to alleviate the over-smoothing issue, we propose a soft graph normalization method to preserve the diversities of node embeddings and prevent indiscrimination due to possible over-closeness. Combined with residual connections, we analyze the reason why the method can effectively capture the knowledge in both input graph structures and node features even with deep networks. Additionally, inspired by Curriculum Learning that learns easy examples before the hard ones, we propose a novel label-smoothing-based learning framework to enhance the optimization of deep GNNs, which iteratively smooths labels in an auxiliary graph and constructs many gradual non-smooth tasks for extracting increasingly complex knowledge and gradually discriminating nodes from coarse to fine. The method arguably reduces the risk of overfitting and generalizes better results. Finally, extensive experiments are carried out to demonstrate the effectiveness and potential of the proposed model and learning framework through comparison with twelve existing baselines including the state-of-the-art methods on twelve real-world node classification benchmarks.

cs.LG↗

arXiv2023

Acceleration for Timing-Aware Gate-Level Logic Simulation with One-Pass GPU Parallelism

Witnessing the advancing scale and complexity of chip design and benefiting from high-performance computation technologies, the simulation of Very Large Scale Integration (VLSI) Circuits imposes an increasing requirement for acceleration through parallel computing with GPU devices. However, the conventional parallel strategies do not fully align with modern GPU abilities, leading to new challenges in the parallelism of VLSI simulation when using GPU, despite some previous successful demonstrations of significant acceleration. In this paper, we propose a novel approach to accelerate 4-value logic timing-aware gate-level logic simulation using waveform-based GPU parallelism. Our approach utilizes a new strategy that can effectively handle the dependency between tasks during the parallelism, reducing the synchronization requirement between CPU and GPU when parallelizing the simulation on combinational circuits. This approach requires only one round of data transfer and hence achieves one-pass parallelism. Moreover, to overcome the difficulty within the adoption of our strategy in GPU devices, we design a series of data structures and tune them to dynamically allocate and store new-generated output with uncertain scale. Finally, experiments are carried out on industrial-scale open-source benchmarks to demonstrate the performance gain of our approach compared to several state-of-the-art baselines.

cs.DS↗

arXiv2017

Approximation Algorithms for Minimizing Maximum Sensor Movement for Line Barrier Coverage in the Plane

Given a line barrier and a set of mobile sensors distributed in the plane, the Minimizing Maximum Sensor Movement problem (MMSM) for \textcolor{black}{line barrier coverage} is to compute relocation positions for the sensors in the plane such that the barrier is entirely covered by the monitoring area of the sensors while the maximum relocation movement (distance) is minimized. Its weaker version, decision MMSM is to determine whether the barrier can be covered by the sensors within a given relocation distance bound $D\in\mathbb{Z}^{+}$. This paper presents three approximation algorithms for decision MMSM. The first is a simple greedy approach, which runs in time $O(n\log n)$ and achieves a maximum movement $D^{*}+2r_{max}$, where $n$ is the number of the sensors, $D^{*}$ is the maximum movement of an optimal solution and $r_{max}$ is the maximum radii of the sensors. The second and the third algorithms improve the maximum movement to $D^{*}+r_{max}$ , running in time $O(n^{7}L)$ and $O(R^{2}\sqrt{\frac{M}{\log R}})$ by applying linear programming (LP) rounding and maximal matching tchniques respecitvely, where $R=\sum2r_{i}$, which is $O(n)$ in practical scenarios of uniform sensing radius for all sensors, and $M\leq n\max r_{i}$. Applying the above algorithms for $O(\log(d_{max}))$ time in binary search immediately yields solutions to MMSM with the same performance guarantee. In addition, we also give a factor-2 approximation algorithm which can be used to improve the performance of the first three algorithms when $r_{max}>D^{*}$. As shown in \cite{dobrev2015complexity}, the 2-D MMSM problem admits no FPTAS as it is strongly NP-complete, so our algorithms arguably achieve the best possible ratio.

cs.DS↗

arXiv2017

Efficient Approximation Algorithms for Multi-Antennae Largest Weight Data Retrieval

In a mobile network, wireless data broadcast over $m$ channels (frequencies) is a powerful means for distributed dissemination of data to clients who access the channels through multi-antennae equipped on their mobile devices. The $δ$-antennae largest weight data retrieval ($δ$ALWDR) problem is to compute a schedule for downloading a subset of data items that has a maximum total weight using $δ$ antennae in a given time interval. In this paper, we propose a ratio $1-\frac{1}{e}-ε$ approximation algorithm for the $δ$-antennae largest weight data retrieval ($δ$ALWDR) problem that has the same ratio as the known result but a significantly improved time complexity of $O(2^{\frac{1}ε}\frac{1}εm^{7}T^{3.5}L)$ from $O(ε^{3.5}m^{\frac{3.5}ε}T^{3.5}L)$ when $δ=1$ \cite{lu2014data}. To our knowledge, our algorithm represents the first ratio $1-\frac{1}{e}-ε$ approximation solution to $δ$ALWDR for the general case of arbitrary $δ$. To achieve this, we first give a ratio $1-\frac{1}{e}$ algorithm for the $γ$-separated $δ$ALWDR ($δ$A$γ$LWDR) with runtime $O(m^{7}T^{3.5}L)$, under the assumption that every data item appears at most once in each segment of $δ$A$γ$LWDR, for any input of maximum length $L$ on $m$ channels in $T$ time slots. Then, we show that we can retain the same ratio for $δ$A$γ$LWDR without this assumption at the cost of increased time complexity to $O(2^γm^{7}T^{3.5}L)$. This result immediately yields an approximation solution of same ratio and time complexity for $δ$ALWDR, presenting a significant improvement of the known time complexity of ratio $1-\frac{1}{e}-ε$ approximation to the problem.

cs.DS↗

arXiv2017

On the Complexity of Detecting Constrained Negative Cost Cycles

Given a positive integer $k$ and a directed graph with a cost on each edge, the $k$-length negative cost cycle ($k$\emph{LNCC}) problem is to determine whether there exists a negative cost cycle with at least $k$ edges, and the fixed-point \emph{$k$-}length negative cost cycle \emph{trail (FP$k$LNCCT)} problem is to determine whether there exists a negative trail enrouting a given vertex (as the fixed point) and containing only cycles with at least $k$ edges. The $k$\emph{LNCC} problem first emerged in deadlock avoidance in synchronized streaming computing network \cite{spaa10}, generalizing two famous problems: negative cycle detection and the $k$-cycle problem. As a warmup by-production, the paper first shows that \emph{FP$k$LNCCT is }${\cal NP}$-complete in multigraph\emph{ }even for\emph{ $k=3$} by reducing from the \emph{3SAT} problem. Then as the main result, we prove the ${\cal NP}$-completeness of $k$\emph{LNCC} by giving a sophisticated reduction from the 3 Occurrence 3-Satisfiability (\emph{3O3SAT}) problem, a known ${\cal NP}$-complete special case of 3SAT in which a variable occurs at most three times. The complexity result is interesting, since polynomial time algorithms are known for both $2$\emph{LNCC} (essentially no restriction on the value of $k$) and the $k$-cycle problem of fixed $k$. This paper closes the open problem proposed by Li et al. in \cite{spaa10} whether $k$\emph{LNCC} admits polynomial-time algorithms.

cs.CC↗

arXiv2015

Efficient Approximation Algorithms for Computing \emph{k} Disjoint Restricted Shortest Paths

Network applications, such as multimedia streaming and video conferencing, impose growing requirements over Quality of Service (QoS), including bandwidth, delay, jitter, etc. Meanwhile, networks are expected to be load-balanced, energy-efficient, and resilient to some degree of failures. It is observed that the above requirements could be better met with multiple disjoint QoS paths than a single one. Let $G=(V,\, E)$ be a digraph with nonnegative integral cost and delay on every edge, $s,\, t\in V$ be two specified vertices, and $D\in\mathbb{Z}_{0}^{+}$ be a delay bound (or some other constraint), the \emph{$k$ Disjoint Restricted Shortest Path} ($k$\emph{RSP})\emph{ Problem} is computing $k$ disjoint paths between $s$ and $t$ with total cost minimized and total delay bounded by $D$. Few efficient algorithms have been developed because of the hardness of the problem. In this paper, we propose efficient algorithms with provable performance guarantees for the $k$RSP problem. We first present a pseudo-polynomial-time approximation algorithm with a bifactor approximation ratio of $(1,\,2)$, then improve the algorithm to polynomial time with a bifactor ratio of $(1+ε,\,2+ε)$ for any fixed $ε>0$, which is better than the current best approximation ratio $(O(1+γ),\, O(1+\frac{1}γ)\})$ for any fixed $γ>0$ \cite{orda2004efficient}. To the best of our knowledge, this is the first constant-factor algorithm that almost strictly obeys the constraint for the $k$RSP problem.

cs.DM↗

arXiv2013

A Parameterized Approximation Algorithm for The Shallow-Light Steiner Tree Problem

For a given graph $G=(V,\, E)$ with a terminal set $S$ and a selected root $r\in S$, a positive integer cost and a delay on every edge and a delay constraint $D\in Z^{+}$, the shallow-light Steiner tree (\emph{SLST}) problem is to compute a minimum cost tree spanning the terminals of $S$, in which the delay between root and every vertex is restrained by $D$. This problem is NP-hard and very hard to approximate. According to known inapproximability results, this problem admits no approximation with ratio better than factor $(1,\, O(\log^{2}n))$ unless $NP\subseteq DTIME(n^{\log\log n})$ \cite{khandekar2013some}, while it admits no approximation ratio better than $(1,\, O(\log|V|))$ for D=4 unless $NP\subseteq DTIME(n^{\log\log n})$ \cite{bar2001generalized}. Hence, the paper focus on parameterized algorithm for \emph{SLST}. We firstly present an exact algorithm for \emph{SLST} with time complexity $O(3^{|S|}|V|D+2^{|S|}|V|^{2}D^{2}+|V|^{3}D^{3})$, where $|S|$ and $|V|$ are the number of terminals and vertices respectively. This is a pseudo polynomial time parameterized algorithm with respect to the parameterization: "number of terminals". Later, we improve this algorithm such that it runs in polynomial time $O(\frac{|V|^{2}}ε3^{|S|}+\frac{|V|^{4}}ε2^{|S|}+\frac{|V|^{6}}ε)$, and computes a Steiner tree with delay bounded by $(1+ε)D$ and cost bounded by the cost of an optimum solution, where $ε>0$ is any small real number. To the best of our knowledge, this is the first parameterized approximation algorithm for the \emph{SLST} problem.

cs.DS↗

arXiv2013

Constrained Fault-Tolerant Resource Allocation

In the Constrained Fault-Tolerant Resource Allocation (FTRA) problem, we are given a set of sites containing facilities as resources, and a set of clients accessing these resources. Specifically, each site i is allowed to open at most R_i facilities with cost f_i for each opened facility. Each client j requires an allocation of r_j open facilities and connecting j to any facility at site i incurs a connection cost c_ij. The goal is to minimize the total cost of this resource allocation scenario. FTRA generalizes the Unconstrained Fault-Tolerant Resource Allocation (FTRA_{\infty}) [18] and the classical Fault-Tolerant Facility Location (FTFL) [13] problems: for every site i, FTRA_{\infty} does not have the constraint R_i, whereas FTFL sets R_i=1. These problems are said to be uniform if all r_j's are the same, and general otherwise. For the general metric FTRA, we first give an LP-rounding algorithm achieving the approximation ratio of 4. Then we show the problem reduces to FTFL, implying the ratio of 1.7245 from [3]. For the uniform FTRA, we provide a 1.52-approximation primal-dual algorithm in O(n^4) time, where n is the total number of sites and clients. We also consider the Constrained Fault-Tolerant k-Resource Allocation (k-FTRA) problem where additionally the total number of facilities can be opened across all sites is bounded by k. For the uniform k-FTRA, we give the first constant-factor approximation algorithm with a factor of 4. Note that the above results carry over to FTRA_{\infty} and k-FTRA_{\infty}.

cs.DS↗

arXiv2013

Improved Approximation Algorithms for Computing k Disjoint Paths Subject to Two Constraints

For a given graph $G$ with positive integral cost and delay on edges, distinct vertices $s$ and $t$, cost bound $C\in Z^{+}$ and delay bound $D\in Z^{+}$, the $k$ bi-constraint path ($k$BCP) problem is to compute $k$ disjoint $st$-paths subject to $C$ and $D$. This problem is known NP-hard, even when $k=1$ \cite{garey1979computers}. This paper first gives a simple approximation algorithm with factor-$(2,2)$, i.e. the algorithm computes a solution with delay and cost bounded by $2*D$ and $2*C$ respectively. Later, a novel improved approximation algorithm with ratio $(1+β,\,\max\{2,\,1+\ln\frac{1}β\})$ is developed by constructing interesting auxiliary graphs and employing the cycle cancellation method. As a consequence, we can obtain a factor-$(1.369,\,2)$ approximation algorithm by setting $1+\ln\frac{1}β=2$ and a factor-$(1.567,\,1.567)$ algorithm by setting $1+β=1+\ln\frac{1}β$. Besides, by setting $β=0$, an approximation algorithm with ratio $(1,\, O(\ln n))$, i.e. an algorithm with only a single factor ratio $O(\ln n)$ on cost, can be immediately obtained. To the best of our knowledge, this is the first non-trivial approximation algorithm for the $k$BCP problem that strictly obeys the delay constraint.

cs.DS↗