How to Balance the Load Online When Jobs and Machines Are Both Selfish?
Wenqian Wang, Chenyang Xu, Yuhao Zhang
TL;DR
The paper tackles online load balancing with both selfish jobs and selfish machines, formalizing a two-sided truthful mechanism design problem for minimizing the makespan and the $\ell_q$ norm. It introduces a novel level-based, two-sided monotone online allocation framework that first computes a speed-size-feasible fractional solution and then rounds independently to an integral schedule, preserving truthfulness in expectation. Key innovations include the allocate-before-doubling and double-without-the-last techniques to maintain $\Lambda$-stability and monotonicity, enabling machine-side implementability and job-side implementability simultaneously. The main results deliver a randomized polynomial-time mechanism achieving an $O(\log m)$ competitive ratio for makespan and a $\tilde{O}(m^{\frac{1}{q}(1-\frac{1}{q})})$ competitive ratio for general $\ell_q$ norms, advancing the state of two-sided truthful online scheduling and opening avenues for tighter bounds and broader objective classes.
Abstract
In this paper, we study the classic optimization problem of Related Machine Online Load Balancing under the conditions of selfish machines and selfish jobs. We have $m$ related machines with varying speeds and $n$ jobs arriving online with different sizes. Our objective is to design an online truthful algorithm that minimizes the makespan while ensuring that jobs and machines report their true sizes and speeds. Previous studies in the online scenario have primarily focused on selfish jobs, beginning with the work of Aspnes et al. (JACM 1997). An $O(1)$-competitive online mechanism for selfish jobs was discovered by Feldman, Fiat, and Roytman (EC 2017). For selfish machines, truthful mechanisms have only been explored in offline settings, starting with Archer and Tardos (FOCS 2001). The best-known results are two PTAS mechanisms by Christodoulou and Kovács (SICOMP 2013) and Epstein et al. (MOR 2016). We design an online mechanism that is truthful for both machines and jobs, achieving a competitive ratio of $O(\log m)$. This is the first non-trivial two-sided truthful mechanism for online load balancing and also the first non-trivial machine-side truthful mechanism. Furthermore, we extend our mechanism to the $\ell_q$ norm variant of load balancing, maintaining two-sided truthfulness with a competitive ratio of $\tilde{O}(m^{\frac{1}{q}(1-\frac{1}{q})})$.