57 research outputs found
Analysis of an exhaustive search algorithm in random graphs and the n^{c\log n} -asymptotics
We analyze the cost used by a naive exhaustive search algorithm for finding a
maximum independent set in random graphs under the usual G_{n,p} -model where
each possible edge appears independently with the same probability p. The
expected cost turns out to be of the less common asymptotic order n^{c\log n},
which we explore from several different perspectives. Also we collect many
instances where such an order appears, from algorithmics to analysis, from
probability to algebra. The limiting distribution of the cost required by the
algorithm under a purely idealized random model is proved to be normal. The
approach we develop is of some generality and is amenable for other graph
algorithms.Comment: 35 page
Computer Aided Verification
This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book
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