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We present new θ(n) time algorithms for testing pattern involvement for all length 4 permutations. For most of these permutations the previous best algorithms require O(n log n) time.

In a complete directed weighted graph there are jobs located at nodes of the graph. Job i has an associated processing time or handling time h i , and the job must start within a prespecified time window r i ; d i. A vehicle can move on the arcs of the graph, at unit speed, and that has to execute the jobs within their respective time windows. We consider… (More)

—We present new parallel algorithms for testing pattern involvement for all length 4 permutations. Our algorithms have the complexity of O(log n) time with n/ log n processors on the CREW PRAM model, O(log log log n) time with n/ log log log n processors or constant time and n log 3 n processors on a CRCW PRAM model. Parallel algorithms were not designed… (More)