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This repository contains supplementary materials for our published survey paper:
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<ahref="https://[example.com](https://hosseinfani.github.io/res/papers/2025_CSUR_A_Survey_of_Subgraph_Optimization_for_Expert_Team_Formation.pdf)"><strong>A Survey of Subgraph Optimization for Expert Team Formation</strong></a>
> **[Notification of Acceptance:](https://hosseinfani.github.io/res/papers/2025_CSUR_R3_A_Survey_of_Subgraph_Optimization_for_Expert_Team_Formation.txt)**
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May 8, 2025
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**Ranking:** 1st out of 143 journals in Computer Science – Theory & Methods
Expert Team Formation is the search for gathering a team of experts who are expected to collaboratively work towards accomplishing a given project, a problem that has historically been solved in a variety of ways, including manually in a time-consuming and bias-filled manner, and algorithmically within disciplines like social sciences and management. In the present effort, while providing a taxonomy to distinguish between search-based versus learning-based approaches, we survey graph-based studies from the search-based category, motivated as they comprise the mainstream. We present a unifying and vetted overview of the various definitions in this realm, scrutinize assumptions, and identify shortfalls. We start by reviewing initial approaches to the Expert Team Formation problem to lay the conceptual foundations and set forth the necessary notions for a more grounded view of this realm. Next, we provide a detailed view of graph-based Expert Team Formation approaches based on the objective functions they optimize. We lay out who builds on whom and how algorithms have evolved to solve the drawbacks of previous works. Further, we categorize evaluation schemas and elaborate on metrics and insights that can be drawn from each. Referring to the evaluation schemas and metrics, we compare works and propose future directions.
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Within the search-based category, operations research, by and large, optimizes the mutually independent selection of experts, overlooking the organizational and collaborative ties among individuals [^1][^4][^5][^6]. However, graph-based methods rely on the premise that a team is inherently relational and is a property of the interaction among the experts and how effectively they can collaborate. Moreover,
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learning-based methods have been proposed to bring efficiency while enhancing efficacy due to their iterative and online learning procedure [^7][^8]. As seen in Figure 1, there is an overlap between team formation approaches. As an instance, graph-based and operations research-based methods, where optimization functions have been defined based on linear or nonlinear equation of Boolean variables
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representing edges on the expert graph [^9]. Additionally, learning-based methods utilize the expert graph to learn vector representations of skills using graph neural networks (GNNs), which helps reduce the complexity of neural models at the input layer [^12]. Specifically, graph neural networks [^10][^11] provide an effective and efficient general framework for solving graph analytics problems by converting
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a graph into a low-dimensional vector space while preserving its graph-structured information. Having demonstrated strong performances across a wide range of problems, including natural language processing [^13], knowledge graphs [^14] and recommender systems [^15], graph neural networks are gradually finding their application in Expert Team Formation [^12].
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Team formation involves selecting experts with certain skills to form a successful task-oriented team. Team formation approaches can be distinguished based on the way optimizations are performed: i) search-based, where the search for an *almost surely* successful team (optimum team) is carried out over the subgraphs of an expert graph using subgraph optimization methods, or it is performed on subsets of experts as variants of the set cover problem [^1][^2][^3] using operations research (OR) techniques including integer linear/nonlinear programming, and ii) learning-based, where machine learning approaches are used to learn the distributions of experts and skills in the context of previous (un)successful teams in order to draw
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future successful teams.
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<divalign="center">
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<imgsrc="figures/figs_draft/methods-survey.png"alt="Figure1: A taxonomy of the computational Expert Team Formation methods."width="800" >
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<palign="center"><em>Figure1: A taxonomy of the computational Expert Team Formation methods.</em></p>
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</div>
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Within the search-based category, operations research, by and large, optimizes the mutually independent selection of experts, overlooking the organizational and collaborative ties among individuals [^1][^4][^5][^6]. However, graph-based methods rely on the premise that a team is inherently relational and is a property of the interaction among the experts and how effectively they can collaborate. Moreover, learning-based methods have been proposed to bring efficiency while enhancing efficacy due to their iterative and online learning procedure [^7][^8]. As seen in Figure 1, there is an overlap between team formation approaches. As an instance, graph-based and operations research-based methods, where optimization functions have been defined based on linear or nonlinear equation of Boolean variables representing edges on the expert graph [^9].
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From Figure 2, recently, a paradigm shift to machine learning-based methods, including artificial neural networks and graph neural networks [^12][^16][^17][^18][^19], has been observed due to advanced hardware computing power, especially graphic processing units (GPUs) and tensor processing units (TPUs), that reduced elapsed time from months to days and/or hours opening doors to the analysis of massive collections of candidates coming from different fields. These methods are different from search-based solutions in that they *learn* the inherent structure of the ties among candidates and their skills. Wherein, all past successful and *un*successful team compositions are considered as training samples to predict future teams and the team's performance. Learning-based methods bring efficiency while enhancing efficacy due to the inherently *iterative* and *online* learning procedure, and can address the limitations of search-based solutions with respect to scalability. This line of research started with Sapienza et al. [^20] who employed a non-variational autoencoder neural network architecture and is being followed by researchers through other neural-based architectures such as variational Bayesian neural network [^8][^7][^21][^22][^23].
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Although learning-based literature is novel, it is still in its early stages. We chose to survey the graph-based approaches as they comprise the mainstream and a relatively larger body of research to be investigated in a survey such as the present one. Further, this body of work serves as a prelude to the learning-based works, especially the ones based on graph neural network in terms of the Expert Team Formation problem definition as well as experimental and evaluation settings. We are however tracing the learning-based paradigm's literature and its progress for a future potential survey.
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<palign="center">
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<imgsrc="figures/figs_draft/venn.png"alt="Figure1: Overlapping Team Formation Approaches">
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<imgsrc="figures/figs_draft/alluvial_new.png"alt="Figure2: Expert Team Formation methods in time;.">
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<palign="center"><em>Figure2: Expert Team Formation methods in time;.</em></p>
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</p>
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This survey pertains to the graph-based Expert Team Formation algorithms, that is, those that employ graphs to model the experts’ collaboration ties followed by subgraph optimization algorithms, as they comprise the mainstream body of research. While some OR-based works model the dataset as a graph structure, they opt for linear/non-linear integer/real programming methods as opposed to subgraph optimization. In this survey, we include works that not only model the data as graphs but also apply subgraph optimization methods. We exclude works that are based on operations research and learning-based methods, as they differ fundamentally from subgraph optimization algorithms. We recognize the importance of these areas and the wealth of work they include, but a thorough analysis of them is beyond the scope of this work and merits separate surveys.
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<palign="center">
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<imgsrc="figures/figs_draft/venn.png"alt="Figure3: Overlapping Team Formation Approaches.">
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<palign="center"><em>Figure3: Overlapping Team Formation Approaches.</em></p>
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</p>
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After screening 126 papers addressing Team Formation problems using computational and non-computational models, we present a comprehensive overview of 17 seminal graph-based research papers on the Expert Team Formation problem within the scope of our survey, including 18 unique objectives, to be optimized via 63 subgraph optimization algorithms considering variations of their exact algorithms and the heuristics they used to address the efficiency of their algorithms. Our survey brings forth a unifying and vetted methodology to review the various definitions of the notions, criticizes assumptions and comparative benchmarks, and points out shortfalls to smooth the path for future research directions. It targets the information retrieval (IR) and recommender systems (RecSys) research communities to propose new Expert Team Formation solutions and evaluate their effectiveness compared to existing methods and on datasets from various domains. Further, having regard to the unified comparative analysis, organizations and practitioners can compare different models and readily pick the most suitable one for their application to form teams of experts whose success is almost surely guaranteed.
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We present a comprehensive overview of 18 seminal graph-based solutions to the Team Formation problem,
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including 13 proposed optimization objectives, after screening 63 algorithms from 126 papers.
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The examined papers in this survey can be categorized as follows:
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[^1]: M. Muniz et al. A column generation approach for the team formation problem. https://www.sciencedirect.com/science/article/pii/S0305054823002708.
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[^13]: L. Wu et al. Graph Neural Networks for Natural Language Processing: A Survey. https://www.nowpublishers.com/article/Details/MAL-096.
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[^14]: Z. Ye et al. A Comprehensive Survey of Graph Neural Networks for Knowledge Graphs. https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=9831453.
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[^15]: S. Wu et al. Graph Neural Networks in Recommender Systems: A Survey. https://dl.acm.org/doi/pdf/10.1145/3535101.
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[^16]: M. J. Ahmed et al. Vector Representation Learning of Skills for Collaborative Team Recommendation. https://link.springer.com/chapter/10.1007/978-981-96-0567-5_15.
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[^17]: H. Fani et al. A Streaming Approach to Neural Team Formation Training. https://link.springer.com/chapter/10.1007/978-3-031-56027-9_20.
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[^18]: R. Barzegar et al. Adaptive Loss-based Curricula for Neural Team Recommendation. https://dl.acm.org/doi/pdf/10.1145/3701551.3703574.
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[^19]: K. Thang et al. Translative Neural Team Recommendation: From Multilabel Classification to Sequence Prediction.https://hosseinfani.github.io/res/papers/2025_SIGIR_Translative_Neural_Team_Recommendation_From_Multilabel_Classification_to_Sequence_Prediction.pdf.
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[^20]: A. Sapienza et al. {Deep Neural Networks for Optimal Team Composition.https://www.frontiersin.org/journals/big-data/articles/10.3389/fdata.2019.00014/full.
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[^21]: R. Hamidi Rad et al. Learning to Form Skill-based Teams of Experts. https://dl.acm.org/doi/pdf/10.1145/3340531.3412140.
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[^22]: R. Hamidi Rad et al. A Variational Neural Architecture for Skill-based Team Formation. https://dl.acm.org/doi/pdf/10.1145/3589762.
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[^23]: B. Liu et al. Coach-Player Multi-agent Reinforcement Learning for Dynamic Team Composition. https://proceedings.mlr.press/v139/liu21m/liu21m.pdf.
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