Extending Robinson Spaces: Complexity and Algorithmic Solutions for Non-Symmetric Dissimilarity Spaces

TL;DR

This paper generalizes Robinson spaces to asymmetric dissimilarities, introduces related complex problems, and explores their computational complexity and tractable cases.

Contribution

It extends Robinson spaces to asymmetric cases and analyzes the complexity of new seriation problems within this framework.

Findings

Problems are NP-hard and NP-complete.

Certain instances are solvable in polynomial time.

Provides insights into problem tractability.

Abstract

In this work, we extend the concept of Robinson spaces to asymmetric dissimilarities, enhancing their applicability in representing and analyzing complex data. Within this generalized framework, we introduce two different problems that extend the classical seriation problem: an optimization problem and a decision problem. We establish that these problems are NP-hard and NP-complete, respectively. Despite this complexity results, we identify several non-trivial instances where these problems can be solved in polynomial time, providing valuable insights into their tractability.