O(1/ε)O(1/\varepsilon) is the answer in online weighted throughput maximization

We study a fundamental online scheduling problem where jobs with processing times, weights, and deadlines arrive online over time at their release dates. The task is to preemptively schedule these jobs on a single or multiple (possibly unrelated) machines with the objective to maximize the weighted throughput, the total weight of jobs that complete before their deadline. To overcome known lower bounds for the competitive analysis, we assume that each job arrives with some slack $\varepsilon > 0$; that is, the time window for processing job $j$ on any machine $i$ on which it can be executed has length at least $(1+\varepsilon)$ times $j$'s processing time on machine $i$. Our contribution is a best possible online algorithm for weighted throughput maximization on unrelated machines: Our algorithm is $O\big(\frac1\varepsilon\big)$-competitive, which matches the lower bound for unweighted throughput maximization on a single machine. Even for a single machine, it was not known whether the problem with weighted jobs is "harder" than the problem with unweighted jobs. Thus, we answer this question and close weighted throughput maximization on a single machine with a best possible competitive ratio $\Theta\big(\frac1\varepsilon\big)$. While we focus on non-migratory schedules, our algorithm achieves the same (up to constants) performance guarantee when compared to an optimal migratory schedule

Online load balancing with general reassignment cost

We investigate a semi-online variant of load balancing with restricted assignment. In this problem, we are given n jobs, which need to be processed by m machines with the goal to minimize the maximum machine load. Since strong lower bounds rule out any competitive ratio of o(log⁡n), we may reassign jobs at a certain job-individual cost. We generalize a result by Gupta, Kumar, and Stein (SODA 2014) by giving a O(log⁡log⁡mn)-competitive algorithm with constant amortized reassignment cost

“E-Day” in Bern: promoting e-resources through an all-day event

For the first time a joint event between the library, the Medical Faculty and external partners was held at the medical library of Bern University. With a combination of promotional and social activities and information skills taster sessions the library tried to raise awareness of e-resources and increase their use

Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time

Knapsack problems are among the most fundamental problems in optimization. In the Multiple Knapsack problem, we are given multiple knapsacks with different capacities and items with values and sizes. The task is to find a subset of items of maximum total value that can be packed into the knapsacks without exceeding the capacities. We investigate this problem and special cases thereof in the context of dynamic algorithms and design data structures that efficiently maintain near-optimal knapsack solutions for dynamically changing input. More precisely, we handle the arrival and departure of individual items or knapsacks during the execution of the algorithm with worst-case update time polylogarithmic in the number of items. As the optimal and any approximate solution may change drastically, we maintain implicit solutions and support polylogarithmic time query operations that can return the computed solution value and the packing of any given item. While dynamic algorithms are well-studied in the context of graph problems, there is hardly any work on packing problems (and generally much less on non-graph problems). Motivated by the theoretical interest in knapsack problems and their practical relevance, our work bridges this gap

Speed-Robust Scheduling

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 given $m$ 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 $e/(e-1) \approx 1.58$. The particular machine environment in which all machines have either speed $0$ or $1$ was studied before by Stein and Zhong (SODA 2019). For this setting, we provide an algorithm for scheduling infinitesimal jobs with an optimal robustness factor of $(1+\sqrt{2})/2 \approx 1.207$. It lays the foundation for an algorithm matching the lower bound of $4/3$ for equal-size jobs

Speed-Robust Scheduling

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 given $m$ 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 $e/(e-1) \approx 1.58$. The particular machine environment in which all machines have either speed $0$ or $1$ was studied before by Stein and Zhong (SODA 2019). For this setting, we provide an algorithm for scheduling infinitesimal jobs with an optimal robustness factor of $(1+\sqrt{2})/2 \approx 1.207$. It lays the foundation for an algorithm matching the lower bound of $4/3$ for equal-size jobs

Accelerating Matroid Optimization through Fast Imprecise Oracles

Querying complex models for precise information (e.g. traffic models, database systems, large ML models) often entails intense computations and results in long response times. Thus, weaker models which give imprecise results quickly can be advantageous, provided inaccuracies can be resolved using few queries to a stronger model. In the fundamental problem of computing a maximum-weight basis of a matroid, a well-known generalization of many combinatorial optimization problems, algorithms have access to a clean oracle to query matroid information. We additionally equip algorithms with a fast but dirty oracle modelling an unknown, potentially different matroid. We design and analyze practical algorithms which only use few clean queries w.r.t. the quality of the dirty oracle, while maintaining robustness against arbitrarily poor dirty matroids, approaching the performance of classic algorithms for the given problem. Notably, we prove that our algorithms are, in many respects, best-possible. Further, we outline extensions to other matroid oracle types, non-free dirty oracles and other matroid problems

Silencing of Mcl-1 overcomes resistance of melanoma cells against TRAIL-armed oncolytic adenovirus by enhancement of apoptosis

Arming of oncolytic viruses with tumor necrosis factor-related apoptosis-inducing ligand (TRAIL) has been shown as a viable approach to increase the antitumor efficacy in melanoma. However, melanoma cells may be partially or completely resistant to TRAIL or develop TRAIL resistance, thus counteracting the antitumor efficiency of TRAIL-armed oncolytic viruses. Recently, we found that TRAIL resistance in melanoma cells can be overcome by inhibition of antiapoptotic Bcl-2 protein myeloid cell leukemia 1 (Mcl-1). Here, we investigated whether the cytotoxicity of AdV-TRAIL, an oncolytic adenovirus, which expresses TRAIL after induction by doxycycline (Dox), can be improved in melanoma cells by silencing of Mcl-1. Two melanoma cell lines, the TRAIL-resistant MeWo and the TRAIL-sensitive Mel-HO were investigated. Treatment of both cell lines with AdV-TRAIL resulted in a decrease of cell viability, which was caused by an increase of apoptosis and necrosis. The proapoptotic effects were dependent on induction of TRAIL by Dox and were more pronounced in Mel-HO than in MeWo cells. SiRNA-mediated silencing of Mcl-1 resulted in a further significant decrease of cell viability and a further increase of apoptosis and necrosis in AdV-TRAIL-infected MeWo and Mel-HO cells. However, while in absolute terms, the effects were more pronounced in Mel-HO cells, in relative terms, they were stronger in MeWo cells. These results show that silencing of Mcl-1 represents a suitable approach to increase the cytotoxicity of a TRAIL-armed oncolytic adenovirus in melanoma cells.TU Berlin, Open-Access-Mittel – 202