On the average-case complexity of parameterized clique

Nikolaos Fountoulakis, Tobias Friedrich, Danny Hermelin

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6 Citations (Scopus)
179 Downloads (Pure)


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 natural 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 either of these analogs for some specific computable input distribution.
Original languageEnglish
JournalTheoretical Computer Science
Early online date19 Feb 2015
Publication statusE-pub ahead of print - 19 Feb 2015


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