A tight analysis of Kierstead-Trotter algorithm for online unit interval coloring

TL;DR

This paper provides a precise analysis of the Kierstead-Trotter online interval coloring algorithm, establishing tight bounds on its performance for unit intervals and confirming its optimality.

Contribution

The paper proves that the Kierstead-Trotter algorithm uses at most 3 times the maximum clique size minus 3 colors for online unit interval coloring, and shows this bound is tight.

Findings

The number of colors used is at most 3ω(G) - 3.

The bound is proven to be the best possible.

The analysis confirms the algorithm's optimality for the problem.

Abstract

Kierstead and Trotter (Congressus Numerantium 33, 1981) proved that their algorithm is an optimal online algorithm for the online interval coloring problem. In this paper, for online unit interval coloring, we show that the number of colors used by the Kierstead-Trotter algorithm is at most $3 \omega(G) - 3$, where $\omega(G)$ is the size of the maximum clique in a given graph $G$, and it is the best possible.