DeepAI

# A Computational Approach to Organizational Structure

An organizational structure defines how an organization arranges and manages its individuals. Because individuals in an organization take time to both perform tasks and communicate, organizational structure must take both computation and communication into account. Sociologists have studied organizational structure from an empirical perspective for decades, but their work has been limited by small sample sizes. By contrast, we study organizational structure from a computational and theoretical perspective. Specifically, we introduce a model of organizations that involves both computation and communication, and captures the spirit of past sociology experiments. In our model, each node in a graph starts with a token, and at any time can either perform computation to merge two tokens in t_c time, or perform communication by sending a token to a neighbor in t_m time. We study how to schedule computations and communications so as to merge all tokens as quickly as possible. As our first result, we give a polynomial-time algorithm that optimally solves this problem on a complete graph. This result characterizes the optimal graph structure---the edges used for communication in the optimal schedule---and therefore informs the optimal design of large-scale organizations. Moreover, since pre-existing organizations may want to optimize their workflow, we also study this problem on arbitrary graphs. We demonstrate that our problem on arbitrary graphs is not only NP-hard but also hard to approximate within a multiplicative 1.5 factor. Finally, we give an O( n ·OPT/t_m)-approximation algorithm for our problem on arbitrary graphs.

• 39 publications
• 17 publications
• 4 publications
• 29 publications
12/13/2018

### Shortest Reconfiguration of Matchings

Imagine that unlabelled tokens are placed on the edges of a graph, such ...
10/06/2022

### Sequentially Swapping Tokens: Further on Graph Classes

We study the following variant of the 15 puzzle. Given a graph and two t...
03/11/2021

### Hardness of Token Swapping on Trees

Given a graph where every vertex has exactly one labeled token, how can ...
04/30/2020

### Learning Bayesian Networks Under Sparsity Constraints: A Parameterized Complexity Analysis

We study the problem of learning the structure of an optimal Bayesian ne...
05/30/2022

### A principled framework for the design and analysis of token algorithms

We consider a decentralized optimization problem, in which n nodes colla...
06/25/2018

### Maximum Rooted Connected Expansion

Prefetching constitutes a valuable tool toward efficient Web surfing. As...
01/28/2022

### Placing Green Bridges Optimally, with Habitats Inducing Cycles

Choosing the placement of wildlife crossings (i.e., green bridges) to re...