Towards a complexity theory for the congested clique
| Autor: | Jukka Suomela, Janne H. Korhonen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Polynomial hierarchy
Discrete mathematics ta113 FOS: Computer and information sciences TheoryofComputation_COMPUTATIONBYABSTRACTDEVICES Computer science 010102 general mathematics 0102 computer and information sciences Decision problem Computational Complexity (cs.CC) 01 natural sciences Nondeterministic algorithm Computer Science - Computational Complexity Canonical problem Computer Science - Distributed Parallel and Cluster Computing 010201 computation theory & mathematics Decision hierarchy Time hierarchy theorem Distributed Parallel and Cluster Computing (cs.DC) 0101 mathematics |
| Zdroj: | SPAA |
| Popis: | The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of lower bounds for the congested clique; indeed, it is now known that proving explicit congested clique lower bounds is as difficult as proving circuit lower bounds. In this work, we use various more traditional complexity theory tools to build a clearer picture of the complexity landscape of the congested clique: \beginitemize item Nondeterminism and beyond: We introduce the nondeterministic congested clique model (analogous to NP) and show that there is a natural canonical problem family that captures all problems solvable in constant time with nondeterministic algorithms. We further generalise these notions by introducing the constant-round decision hierarchy (analogous to the polynomial hierarchy). item Non-constructive lower bounds: We lift the prior non-uniform counting arguments to a general technique for proving non-constructive uniform lower bounds for the congested clique. In particular, we prove a time hierarchy theorem for the congested clique, showing that there are decision problems of essentially all complexities, both in the deterministic and nondeterministic settings. item Fine-grained complexity: We map out relationships between various natural problems in the congested clique model, arguing that a reduction-based complexity theory currently gives us a fairly good picture of the complexity landscape of the congested clique. \enditemize |
| Databáze: | OpenAIRE |
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