摘要：We study the online graph coloring problem restricted to the intersection graphs of intervals with lengths in [1,Ïf]. For Ïf = 1 it is the class of unit interval graphs, and for Ïf = â^Z the class of all interval graphs. Our focus is on intermediary classes. We present a (1+Ïf)-competitive algorithm, which beats the state of the art for 1 < Ïf < 2, and proves that the problem we study can be strictly easier than online coloring of general interval graphs. On the lower bound side, we prove that no algorithm is better than 5/3-competitive for any Ïf > 1, nor better than 7/4-competitive for any Ïf > 2, and that no algorithm beats the 5/2 asymptotic competitive ratio for all, arbitrarily large, values of Ïf. That last result shows that the problem we study can be strictly harder than unit interval coloring. Our main technical contribution is a recursive composition of strategies, which seems essential to prove any lower bound higher than 2.
