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The speed-robust scheduling problem is a two-stage problem where, given m machines, jobs must be grouped into at most m bags while the processing speeds of the machines are unknown. After the speeds are revealed, the grouped jobs must be assigned to the machines without being separated. To evaluate the performance of algorithms, we determine upper bounds on the worst-case ratio of the algorithm's makespan and the optimal makespan given full information. We refer to this ratio as the robustness factor. We give an algorithm with a robustness factor 2 - 1 m for the most general setting and improve this to 1.8 for equal-size jobs. For the special case of infinitesimal jobs, we give an algorithm with an optimal robustness factor equal to e e - 1 ≈ 1.58 . The particular machine environment in which all machines have either speed 0 or 1 was studied before by Stein and Zhong (ACM Trans Algorithms 16(1):1-20, 2020. https://doi.org/10.1145/3340320). For this setting, we provide an algorithm for scheduling infinitesimal jobs with an optimal robustness factor of 1 + 2 2 ≈ 1.207 . It lays the foundation for an algorithm matching the lower bound of 4 3 for equal-size jobs. [ABSTRACT FROM AUTHOR]

Tousled-like kinases (TLKs) are nuclear serine-threonine kinases essential for genome maintenance and proper cell division in animals and plants. A major function of TLKs is to phosphorylate the histone chaperone proteins ASF1a and ASF1b to facilitate DNA replication-coupled nucleosome assembly, but how TLKs selectively target these critical substrates is unknown. Here, we show that TLK2 selectivity towards ASF1 substrates is achieved in two ways. First, the TLK2 catalytic domain recognizes consensus phosphorylation site motifs in the ASF1 C-terminal tail. Second, a short sequence at the TLK2 N-terminus docks onto the ASF1a globular N-terminal domain in a manner that mimics its histone H3 client. Disrupting either catalytic or non-catalytic interactions through mutagenesis hampers ASF1 phosphorylation by TLK2 and cell growth. Our results suggest that the stringent selectivity of TLKs for ASF1 is enforced by an unusual interaction mode involving mutual recognition of a short sequence motifs by both kinase and substrate. Tousled-like kinase 2 (TLK2) phosphorylates ASF1 histone chaperones to promote nucleosome assembly in S phase. Here, the authors show that TLK2 targets ASF1 by simulating its client protein histone H3, exploiting a primordial protein interaction surface for regulatory control. [ABSTRACT FROM AUTHOR]