Team Formation amidst Conflicts

TL;DR

The goal is to assign individuals to tasks, with given capacities, taking into account individuals' task preferences and the conflicts between them, taking into account individuals' task preferences and the conflicts between them.

Abstract

In this work, we formulate the problem of team formation amidst conflicts. The goal is to assign individuals to tasks, with given capacities, taking into account individuals' task preferences and the conflicts between them. Using dependent rounding schemes as our main toolbox, we provide efficient approximation algorithms. Our framework is extremely versatile and can model many different real-world scenarios as they arise in educational settings and human-resource management. We test and deploy our algorithms on real-world datasets and we show that our algorithms find assignments that are better than those found by natural baselines. In the educational setting we also show how our assignments are far better than those done manually by human experts. In the human resource management application we show how our assignments increase the diversity of teams. Finally, using a synthetic dataset we demonstrate that our algorithms scale very well in practice.

Figures (13)

• Figure 1: Education data; approximation ratio of the different algorithms. For all datasets we used the Inverse project-preference function and $\alpha =10$.
• Figure 2: Employee data; approximation ratio of the different algorithms for $\alpha = 1, 2, 3, 4$.
• Figure 3: Employee data; Diversity per department before (1$^{\text{st}}$ row) and after (2$^{\text{nd}}$ row) we run the Quadratic algorithm ($\alpha = 2$). $8\%$ of the employees changed department. The average male-female percentage gap decreased from $35\%$ to $26\%$.
• Figure 4: Synth-TF dataset; approximation ratios of the speedups; We used $\alpha = 10$.
• Figure 5: Friend graph for dataset Class-B. On top of nodes are the anonymized student ids.

Theorems & Definitions (20)

• Lemma 1
• Proposition 1: ageev2004pipage
• Theorem 1: ageev2004pipage
• Proposition 2
• Lemma 2: chekuri2010dependent
• Proposition 3
• Theorem 2
• Theorem 3
• Lemma 3
• proof