Control in Stable Marriage and Stable Roommates: Complexity and Algorithms

TL;DR

This paper explores how a central authority can manipulate matching problems like Stable Marriage and Stable Roommates to achieve specific goals, analyzing the computational complexity and providing algorithms and intractability results.

Contribution

It introduces the complexity analysis of control problems in matching, offering new algorithms and proving intractability in certain cases.

Findings

Identifies computational complexity of control in matching problems

Provides efficient algorithms for some control scenarios

Establishes intractability results for other cases

Abstract

We study control problems in the context of matching under preferences: We examine how a central authority, called the controller, can manipulate an instance of the Stable Marriage or Stable Roommates problems in order to achieve certain goals. We investigate the computational complexity of the emerging problems, and provide both efficient algorithms and intractability results.