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Titlebook: Algorithms and Complexity; 10th International C Dimitris Fotakis,Aris Pagourtzis,Vangelis Th. Pasc Conference proceedings 2017 Springer Int

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Tracking Pathsfollowing related problem: Given a graph ., two vertices . and ., and a set of forbidden vertices ., find a minimum-cardinality set of trackers ., such that a shortest path . from . to . passes through a forbidden vertex if and only if it passes through a vertex of .. We present a polynomial-time (exact) algorithm for this problem.
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Almost Optimal Cover-Free Families lower order multiplicative terms, . . . .. In fact, our construction time is almost linear in the size of the family. Before our work, such a result existed only for ., and ...As a sample application, we improve the running times of parameterized algorithms from the recent work of Gabizon, Lokshtanov and Pilipczuk [.].
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Scheduling Maintenance Jobs in Networks solutions..Interestingly, the preemptive and the non-preemptive problem can be solved efficiently on paths, whereas we show that mixing both leads to a weakly NP-hard problem that allows for a simple 2-approximation.
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