文章基本信息
- 标题：Hardness of FO Model-Checking on Random Graphs
- 本地全文：下载
- 作者：Jan Dreier ; Peter Rossmanith
- 期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
- 电子版ISSN：1868-8969
- 出版年度：2019
- 卷号：148
- 页码：1-15
- DOI：10.4230/LIPIcs.IPEC.2019.11
- 出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
- 摘要：It is known that FO model-checking is fixed-parameter tractable on Erdös - Rényi graphs G(n,p(n)) if the edge-probability p(n) is sufficiently small [Grohe, 2001] (p(n)=O(n^epsilon/n) for every epsilon>0). A natural question to ask is whether this result can be extended to bigger probabilities. We show that for Erdös - Rényi graphs with vertex colors the above stated upper bound by Grohe is the best possible. More specifically, we show that there is no FO model-checking algorithm with average FPT run time on vertex-colored Erdös - Rényi graphs G(n,n^delta/n) (0 < delta < 1) unless AW[*]subseteq FPT/poly. This might be the first result where parameterized average-case intractability of a natural problem with a natural probability distribution is linked to worst-case complexity assumptions. We further provide hardness results for FO model-checking on other random graph models, including G(n,1/2) and Chung-Lu graphs, where our intractability results tightly match known tractability results [E. D. Demaine et al., 2014]. We also provide lower bounds on the size of shallow clique minors in certain Erdös - Rényi and Chung - Lu graphs.
- 关键词：random graphs; FO model-checking
