Optimal Lower Bounds for Anonymous Scheduling Mechanisms

Optimal Lower Bounds for Anonymous Scheduling Mechanisms

We consider the problem of designing truthful mechanisms on m unrelated machines, to minimize some optimization goal. Nisan and Ronen (1999) consider the specific goal of makespan minimization, and show a lower bound of 2, and an upper bound of m. This large gap inspired many attempts that yielded positive results for several special cases, but very partial success for the general case: the low...

An Optimal Lower Bound for Anonymous Scheduling Mechanism

We consider the problem of designing truthful mechanisms to minimize the makespan onm unrelated machines. In their seminal paper, Nisan and Ronen [14] showed a lower bound of 2, and an upper bound of m, thus leaving a large gap. They conjectured that their upper bound is tight, but were unable to prove it. Despite many attempts that yield positive results for several special cases, the conjectu...

Optimal Mechanisms for Scheduling

We study the design of optimal mechanisms in a setting where a service provider needs to schedule a set of non-preemptive jobs, one job at a time. Jobs need to be compensated for waiting, and waiting cost is private information. In this setting, an optimal mechanism is one that induces jobs to report truthfully their waiting cost, while minimizing the total expected compensation cost of the ser...

Some Lower Bounds for Estrada Index

Message Complexity Lower Bounds for Decentralized Anonymous Wave Algorithms

We prove an (DjEj) lower bound on the message complexity of decentralized anonymous wave algorithms for the unidirectional ring, the hypercube and the clique. Here D is the diameter and E the number of edges of the network. This proves that the Phase algorithm is optimal for them, and suggests that it is an optimal decentralized anonymous wave algorithm over arbitrary networks.