Invited Talk: Distributed Computational Complexities (Are You Volvo-Adicted or NASCAR-Obsessed?)

Roughly speaking, and if one ignores important research topics driven by modern applications of distributed computing (like, e.g., P2P systems and multi-core technology), the PODC community can be viewed as the union of two non-necessarily disjoint sub-communities. One is mostly focussing on the combined impact of asynchronism and faults on distributed computation, while the other is mostly focussing on the impact of network structural properties on distributed computation. Both communities address various forms of distributed computational complexities, through the analysis of different concepts. This includes, e.g., failure detectors and wait-free hierarchy for the former community, and compact labeling schemes and computing with advice for the latter community. This talk will describe examples taken from these latter frameworks aiming at demonstrating that many important notions of Distributed Computing seem to fit well with standard computational complexity, although they are not expressed using the traditional computational complexity format, i.e., complexity classes. The thesis that will be defended in the talk is that the traditional computational complexity format might well apply to Distributed Computing, and that our community may in fact take benefit from expressing its main challenges in this standard framework for making them accessible to a wider audience.