Cross-identification of stellar catalogs with multiple stars: Complexity and Resolution

TL;DR

This paper formulates the complex problem of cross-identifying stars in multiple catalogs as an optimization challenge, modeling it as a Maximum Weighted Stable Set Problem, analyzing its computational hardness, and applying it to real data.

Contribution

It introduces a novel modeling approach for multi-star catalog matching as a Maximum Weighted Stable Set Problem and characterizes its computational complexity.

Findings

The problem is NP-Hard.

A reduction to a stable set problem is demonstrated.

Partial characterization of forbidden subgraphs is provided.

Abstract

In this work, I present an optimization problem which consists of assigning entries of a stellar catalog to multiple entries of another stellar catalog such that the probability of such assignment is maximum. I show a way of modeling it as a Maximum Weighted Stable Set Problem which is further used to solve a real astronomical instance and I partially characterize the forbidden subgraphs of the resulting family of graphs given by that reduction. Finally, I prove that the problem is NP-Hard.