A New Lower Bound for Deterministic Truthful Scheduling

We study the problem of truthfully scheduling m tasks to n selfish unrelated machines, under objective makespan minimization, as was introduced in seminal work Nisan and Ronen (in: The 31st Annual ACM symposium on Theory Computing (STOC), 1999). Closing current gap [2.618, n] approximation ratio deterministic truthful mechanisms is a notorious open field algorithmic mechanism design. provide first such improvement more than decade, since lower bounds 2.414 (for $$n=3$$ ) 2.618 $$n\rightarrow \infty$$ by Christodoulou et al. Proceedings 18th ACM-SIAM Symposium Discrete Algorithms (SODA), 2007) Koutsoupias Vidali Mathematical Foundations Computer Science (MFCS), 2007), respectively. More specifically, we show that currently best bound can be achieved even for just $$n=4$$ machines; $$n=5$$ already get improvement, namely 2.711; allowing number machines grow arbitrarily large 2.755.