On the Average-case Complexity of Parameterized Clique [article]

Nikolaos Fountoulakis, Tobias Friedrich, Danny Hermelin
2014 arXiv   pre-print
The k-Clique problem is a fundamental combinatorial problem that plays a prominent role in classical as well as in parameterized complexity theory. It is among the most well-known NP-complete and W[1]-complete problems. Moreover, its average-case complexity analysis has created a long thread of research already since the 1970s. Here, we continue this line of research by studying the dependence of the average-case complexity of the k-Clique problem on the parameter k. To this end, we define two
more » ... atural parameterized analogs of efficient average-case algorithms. We then show that k-Clique admits both analogues for Erdős-Rényi random graphs of arbitrary density. We also show that k-Clique is unlikely to admit neither of these analogs for some specific computable input distribution.
arXiv:1410.6400v1 fatcat:zp5kw6bbujewxdgsppg77evpny