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The classic Earliest Deadline First (EDF) algorithm is widely studied and used due to its simplicity and strong theoretical performance, but has not been rigorously analyzed for systems where jobs may execute critical sections protected by shared locks. Analyzing such systems is often challenging due to unpredictable delays caused by contention. In this paper, we propose a straightforward generalization of EDF, called EDF-Block. In this generalization, the critical sections are executed non-preemptively, but scheduling and lock acquisition priorities are based on EDF. We establish lower bounds on the speed augmentation required for any non-clairvoyant scheduler (EDF-Block is an example of non-clairvoyant schedulers) and for EDF-Block, showing that EDF-Block requires at least 4.11× speed augmentation for jobs and 4× for tasks. We then provide an upper bound analysis, demonstrating that EDF-Block requires speedup of at most 6 to schedule all feasible job and task sets. 

This article presents I/O-efficient algorithms for topologically sorting a directed acyclic graph and for the more general problem identifying and topologically sorting the strongly connected components of a directed graph G = ( V, E ). Both algorithms are randomized and have I/O-costs O ( sort ( E ) · poly(log V)), with high probability, where sort ( E ) = O( E / B log M / B ( E/B )) is the I/O cost of sorting an | E |-element array on a machine with size- B blocks and size- M cache/internal memory. These are the first algorithms for these problems that do not incur at least one I/O per vertex, and as such these are the first I/O-efficient algorithms for sparse graphs. By applying the technique of time-forward processing, these algorithms also imply I/O-efficient algorithms for most problems on directed acyclic graphs, such as shortest paths, as well as the single-source reachability problem on arbitrary directed graphs.