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Junhao Gan

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AAMAS Conference 2026 Conference Paper

A Radius-Sensitive Approximation Algorithm for Connected Submodular Maximization

Philip Cervenjak
Junhao Gan
Naonori Kakimura
Seeun William Umboh
Anthony Wirth

Connected Submodular Maximization (CSM) is a graph problem with important applications to wireless network deployment, path planning, epidemic outbreaks, and cancer genome studies. In CSM, we are given a graph 𝐺, a non-negative monotone submodular function 𝑓 on subsets of the vertex set of 𝐺, and an integer 𝑘. The goal is to select a tree in 𝐺, with 𝑘 edges, whose vertex set maximizes 𝑓. We also study the more general Directed and Directed Rooted variants of CSM (DCSM and DRCSM respectively). In both variants, 𝐺 is directed and the solution must be an out-tree in 𝐺, with 𝑘 edges, whose vertex set maximizes 𝑓; DRCSM further specifies a vertex to be the root of the selected out-tree. For CSM, several previous works have proposed polynomial time approximation algorithms; the state-of-the-art polynomial time algorithm achieves a Ω( 1 √ 𝑘 )-approximation. We can also parameterize the approximation factor by the radius of the optimal solution, denoted by 𝑟; the state-of-the-art polynomial time algorithm achieves a Ω(1 𝑟 )-approximation. In this paper, we improve on the state-of-the-art approximation factor for CSM with respect to 𝑟 as well as 𝑘, noting that 𝑟 ≤ 𝑘. We propose a polynomial time framework that, for (Directed) CSM, achieves a Ω(𝜀3 𝑟𝜀 )-approximation for every constant 𝜀 ∈ (0, 1]. For DRCSM, our framework achieves a Ω(𝛿𝜀3 𝑟𝜀 )-approximation that violates the size constraint by at most a factor of 1 + 𝛿 for every 𝛿 ∈ [1 𝑘, 1]. A key component of our framework is GreedyRadius, an algorithm for DRCSM that outputs a bicriteria approximation, i. e. , an approximate solution that violates the size constraint by at most some factor. GreedyRadius takes an algorithm with a bicriteria approximation factor in terms of𝑘 and outputs a solution This work is licensed under a Creative Commons Attribution International 4. 0 License. Proc. of the 25th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2026), C. Amato, L. Dennis, V. Mascardi, J. Thangarajah (eds.), May 25 – 29, 2026, Paphos, Cyprus. © 2026 International Foundation for Autonomous Agents and Multiagent Systems (www. ifaamas. org). https: //doi. org/10. 65109/IPZQ7320 with the same bicriteria approximation factor (up to constants) in termsof𝑟. Moreover, touseasasubroutineforDRCSM, wepropose the algorithm RecApprox-𝑑, which achieves a 1 𝑑+1-approximation that violates the size constraint by at most a factor of (𝑑 + 1)2𝑘 1 𝑑. RecApprox-𝑑 uses a recursive greedy strategy, with𝑑 denoting the number of levels of recursion used. This enables the dependence on 𝜀 in the approximation factors of our overall framework.

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AAAI Conference 2026 Conference Paper

Towards Synthesizing High-Dimensional Tabular Data with Limited Samples

Zuqing Li
Junhao Gan
Jianzhong Qi

Diffusion-based tabular data synthesis models have yielded promising results. However, we observe that when the data dimensionality increases, existing models tend to degenerate and may perform even worse than simpler, non-diffusion-based models. This is because limited training samples in high-dimensional space often hinder generative models from capturing the distribution accurately. To mitigate the insufficient learning signals and to stabilize training under such conditions, we propose CtrTab, a condition-controlled diffusion model that injects perturbed ground-truth samples as auxiliary inputs during training. This design introduces an implicit $L_2$ regularization on the model’s sensitivity to the control signal, improving robustness and stability in high-dimensional, low-data scenarios. Experimental results across multiple datasets show that CtrTab outperforms state-of-the-art models, with a performance gap in accuracy over 90% on average.

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AAAI Conference 2025 Conference Paper

Accurate and Regret-Aware Numerical Problem Solver for Tabular Question Answering

Yuxiang Wang
Jianzhong Qi
Junhao Gan

Question answering on free-form tables (a.k.a. TableQA) is a challenging task because of the flexible structure and complex schema of tables. Recent studies use Large Language Models (LLMs) for this task, exploiting their capability in understanding the questions and tabular data, which are typically given in natural language and contain many textual fields, respectively. While this approach has shown promising results, it overlooks the challenges brought by numerical values which are common in tabular data, and LLMs are known to struggle with such values. We aim to address this issue, and we propose a model named TabLaP that uses LLMs as a planner rather than an answer generator. This approach exploits LLMs' capability in multi-step reasoning while leaving the actual numerical calculations to a Python interpreter for accurate calculation. Recognizing the inaccurate nature of LLMs, we further make a first attempt to quantify the trustworthiness of the answers produced by TabLaP, such that users can use TabLaP in a regret-aware manner. Experimental results on two benchmark datasets show that TabLaP is substantially more accurate than the state-of-the-art models, improving the answer accuracy by 5.7% and 5.8% on the two datasets, respectively.

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MFCS Conference 2020 Conference Paper

Graph Clustering in All Parameter Regimes

Junhao Gan
David F. Gleich
Nate Veldt
Anthony Wirth
Xin Zhang 0094

Resolution parameters in graph clustering control the size and structure of clusters formed by solving a parametric objective function. Typically there is more than one meaningful way to cluster a graph, and solving the same objective function for different resolution parameters produces clusterings at different levels of granularity, each of which can be meaningful depending on the application. In this paper, we address the task of efficiently solving a parameterized graph clustering objective for all values of a resolution parameter. Specifically, we consider a new analysis-friendly objective we call LambdaPrime, involving a parameter λ ∈ (0, 1). LambdaPrime is an adaptation of LambdaCC, a significant family of instances of the Correlation Clustering (minimization) problem. Indeed, LambdaPrime and LambdaCC are closely related to other parameterized clustering problems, such as parametric generalizations of modularity. They capture a number of specific clustering problems as special cases, including sparsest cut and cluster deletion. While previous work provides approximation results for a single value of the resolution parameter, we seek a set of approximately optimal clusterings for all values of λ in polynomial time. More specifically, we show that when a graph has m edges and n nodes, there exists a set of at most m clusterings such that, for every λ ∈ (0, 1), the family contains an optimal solution to the LambdaPrime objective. This bound is tight on star graphs. We obtain a family of O(log n) clusterings by solving the parametric linear programming (LP) relaxation of LambdaPrime at O(log n) λ values, and rounding each LP solution using existing approximation algorithms. We prove that this is asymptotically tight: for a certain class of ring graphs, for all values of λ, Ω(log n) feasible solutions are required to provide a constant-factor approximation for the LambdaPrime LP relaxation. To minimize the size of the clustering family, we further propose an algorithm that yields a family of solutions of a size no more than twice of the minimum LP-approximating family.

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