Forming Coordinated Teams that Balance Task Coverage and Expert Workload

TL;DR

The paper introduces Balanced-Coverage (Bal-anc-ed-Cov-er-age) and its networked variant (Net-work-Bal-anc-ed-Cov-er-age) to form teams that maximize partial task skill coverage while minimizing the maximum workload on experts, formalized as $F(A)=\lambda C(A)-L_{\max}(A)$. It provides a polynomial-time Threshold-Greedy algorithm with a provable guarantee $F(A)\ge (1-1/e)\lambda C(OPT)-L_{\max}(OPT)$ for Bal-anc-ed-Cov-er-age, and develops speedups (lazy evaluation, unimodality-based pruning) and a practical, scalable approach. For the network variant, it offers a heuristic NThreshold approach that leverages candidate teams, assignment strategies, and pruning under a radius constraint, with empirical evidence of strong performance on real datasets. The authors also develop an efficient tuning framework for balancing coverage and workload via the parameter $\lambda$, and demonstrate scalability and practical effectiveness through extensive experiments across multiple real-world datasets. Overall, the work advances team-formation by enabling flexible trade-offs between task coverage and expert workload, accommodating coordination costs, and scaling to large, real-world datasets.

Abstract

We study a new formulation of the team-formation problem, where the goal is to form teams to work on a given set of tasks requiring different skills. Deviating from the classic problem setting where one is asking to cover all skills of each given task, we aim to cover as many skills as possible while also trying to minimize the maximum workload among the experts. We do this by combining penalization terms for the coverage and load constraints into one objective. We call the corresponding assignment problem $\texttt{Balanced-Coverage}$, and show that it is NP-hard. We also consider a variant of this problem, where the experts are organized into a graph, which encodes how well they work together. Utilizing such a coordination graph, we aim to find teams to assign to tasks such that each team's radius does not exceed a given threshold. We refer to this problem as $\texttt{Network-Balanced-Coverage}$. We develop a generic template algorithm for approximating both problems in polynomial time, and we show that our template algorithm for $\texttt{Balanced-Coverage}$ has provable guarantees. We describe a set of computational speedups that we can apply to our algorithms and make them scale for reasonably large datasets. From the practical point of view, we demonstrate how to efficiently tune the two parts of the objective and tailor their importance to a particular application. Our experiments with a variety of real-world datasets demonstrate the utility of our problem formulation as well as the efficiency of our algorithms in practice.

Figures (6)

• Figure 1: Motivating example with 4 experts and 3 tasks.
• Figure 2: The best-greedy workload $L_{\max}\xspace(A\xspace)$ value and the coverage $C\xspace(A\xspace)$ corresponding to the best-greedy objective $F\xspace^{\lambda}(A\xspace)$ computed by Thres-hold-Greedy. Each subplot shows a range of values of the balancing coefficient $\lambda$ for each dataset.
• Figure 3: Running time (in seconds) of Thres-hold-Greedy and baseline algorithms, in logarithmic scale.
• Figure 4: The best-greedy workload $L_{\max}\xspace(A\xspace)$ value and the coverage $C\xspace(A\xspace)$ corresponding to the best-greedy objective $F\xspace^{\lambda}(A\xspace)$ computed by NThreshold-R-LP for $r = 0.3$. Each subplot shows a range of values of the balancing coefficient $\lambda$ for each dataset.
• Figure 5: The best-greedy workload $L_{\max}\xspace(A\xspace)$ value and the coverage $C\xspace(A\xspace)$ corresponding to the best-greedy objective $F\xspace^{\lambda}(A\xspace)$ computed by NThreshold-R-LP for $r = 0.7$. Each subplot shows a range of values of the balancing coefficient $\lambda$ for each dataset.

Theorems & Definitions (17)

• Proposition 1
• Theorem 2
• proof
• Theorem 3
• Lemma 1
• Theorem 4
• proof
• Theorem 5
• Proposition 6
• Proposition 7