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This article gives an efficient algorithm for obtaining K shortest simple paths between two specified nodes in an undirected graph G with non-negative edge lengths. Letting n be the number of nodes and m be the number of edges in G, its running time is

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We consider a class of n-job one-machine scheduling problems with ready time r(i), processing time p(i), and due time d(i) for each job i. Preemption is not allowed, and precedence constraints among jobs are not assumed. For this problem we show that there is a 0(n2)-time algorithm to find a schedule that minimizes the number of tardy jobs, under the assumption that r(i) < r(j) implies d(i) ≤ d(j).