This note studies the average-case comparison-complexity of sorting n elements when there is a known distribution on inputs and the goal is to minimize
the expected number of comparisons. We generalize Fredman's algorithm which
is a variant of insertion sort and provide a basically tight upper bound: If \mu is
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Finding cliques in random graphs and the closely related ``planted'' clique variant, where a clique of size t is planted in a random G(n,1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for t = ... more >>>

Consider a systematic linear code where some (local) parity symbols depend on few prescribed symbols, while other (heavy) parity symbols may depend on all data symbols. Local parities allow to quickly recover any single symbol when it is erased, while heavy parities provide tolerance to a large number of simultaneous ... more >>>