Asymptotically Optimal Approximation Algorithms for Coflow Scheduling

Many modern datacenter applications involve large-scale computations composed of multiple data flows that need to be completed over a shared set of distributed resources. Such a computation completes when all of its flows complete. A useful abstraction for modeling such scenarios is a {\em coflow}, which is a collection of flows (e.g., tasks, packets, data transmissions) that all share the same performance goal. In this paper, we present the first approximation algorithms for scheduling coflows over general network topologies with the objective of minimizing total weighted completion time. We consider two different models for coflows based on the nature of individual flows: circuits, and packets. We design constant-factor polynomial-time approximation algorithms for scheduling packet-based coflows with or without given flow paths, and circuit-based coflows with given flow paths. Furthermore, we give an $O(\log n/\log \log n)$-approximation polynomial time algorithm for scheduling circuit-based coflows where flow paths are not given (here $n$ is the number of network edges). We obtain our results by developing a general framework for coflow schedules, based on interval-indexed linear programs, which may extend to other coflow models and objective functions and may also yield improved approximation bounds for specific network scenarios. We also present an experimental evaluation of our approach for circuit-based coflows that show a performance improvement of at least 22% on average over competing heuristics.Comment: Fixed minor typo

Scheduling Bidirectional Traffic on a Path

We study the fundamental problem of scheduling bidirectional traffic along a path composed of multiple segments. The main feature of the problem is that jobs traveling in the same direction can be scheduled in quick succession on a segment, while jobs in opposing directions cannot cross a segment at the same time. We show that this tradeoff makes the problem significantly harder than the related flow shop problem, by proving that it is NP-hard even for identical jobs. We complement this result with a PTAS for a single segment and non-identical jobs. If we allow some pairs of jobs traveling in different directions to cross a segment concurrently, the problem becomes APX-hard even on a single segment and with identical jobs. We give polynomial algorithms for the setting with restricted compatibilities between jobs on a single and any constant number of segments, respectively

Anomalous electron-phonon coupling in kagome ferromagnetic Weyl semimetal Co3_3Sn2_2S2_2

We present results of a Raman scattering study of the Kagome ferromagnet Co$_3$Sn$_2$S$_2$, with a focus on electronic and phononic excitations and their interplay. In addition, the electronic band structure is analyzed theoretically, enabling a semi-quantitative explanation of the spectra. A prominent feature in the electronic spectra is a redistribution of spectral weight from low to high energies starting at the Curie temperature Tc. The Raman intensity is suppressed below approximately 1000cm$^{-1}$ and increases above to a peak at 2000 cm$^{-1}$ in all symmetries. Two Raman active phonon modes are identified in A$_{1g}$ and E$_g$ symmetry. The A$_{1g}$ phonon couples strongly to the electronic continuum as indicated by the asymmetric Fano-type line shape. The asymmetry depends non-monotonically on temperature and is maximal close to the magnetic transition. In the limit $T\to 0$ the phonon is nearly symmetric. The evolution of the coupling strength and the electronic continuum as a function of temperature is attributed to a band splitting induced by the ferromagnetic phase transition which substantially reduces the DOS towards $T=0$. The $3d_{z^2}$ electrons of the Co atoms in the crystal field modulated by the A$_{1g}$ phonon are implied to be a critical component contributing to the strong electron-phonon coupling of that phonon. These results allow a comprehensive understanding of the bulk band structure evolution as a function of temperature in Co$_3$Sn$_2$S$_2$, offering key insights for further studies of the driving force behind the long-range magnetic order and novel topological states in this compound.Comment: 9 pages, 4 figure

Key Factors Associated With Pulmonary Sequelae in the Follow-Up of Critically Ill COVID-19 Patients

Introduction: Critical COVID-19 survivors have a high risk of respiratory sequelae. Therefore, we aimed to identify key factors associated with altered lung function and CT scan abnormalities at a follow-up visit in a cohort of critical COVID-19 survivors. Methods: Multicenter ambispective observational study in 52 Spanish intensive care units. Up to 1327 PCR-confirmed critical COVID-19 patients had sociodemographic, anthropometric, comorbidity and lifestyle characteristics collected at hospital admission; clinical and biological parameters throughout hospital stay; and, lung function and CT scan at a follow-up visit. Results: The median [p25–p75] time from discharge to follow-up was 3.57 [2.77–4.92] months. Median age was 60 [53–67] years, 27.8% women. The mean (SD) percentage of predicted diffusing lung capacity for carbon monoxide (DLCO) at follow-up was 72.02 (18.33)% predicted, with 66% of patients having DLCO < 80% and 24% having DLCO < 60%. CT scan showed persistent pulmonary infiltrates, fibrotic lesions, and emphysema in 33%, 25% and 6% of patients, respectively. Key variables associated with DLCO < 60% were chronic lung disease (CLD) (OR: 1.86 (1.18–2.92)), duration of invasive mechanical ventilation (IMV) (OR: 1.56 (1.37–1.77)), age (OR [per-1-SD] (95%CI): 1.39 (1.18–1.63)), urea (OR: 1.16 (0.97–1.39)) and estimated glomerular filtration rate at ICU admission (OR: 0.88 (0.73–1.06)). Bacterial pneumonia (1.62 (1.11–2.35)) and duration of ventilation (NIMV (1.23 (1.06–1.42), IMV (1.21 (1.01–1.45)) and prone positioning (1.17 (0.98–1.39)) were associated with fibrotic lesions. Conclusion: Age and CLD, reflecting patients’ baseline vulnerability, and markers of COVID-19 severity, such as duration of IMV and renal failure, were key factors associated with impaired DLCO and CT abnormalities

Resource competition on integral polymatroids

We study competitive resource allocation problems in which players distribute their demands integrally over a set of resources subject to player-specific submodular capacity constraints. Each player has to pay for each unit of demand a cost that is a non-decreasing and convex function of the total allocation of that resource. This general model of resource allocation generalizes both singleton congestion games with integer-splittable demands and matroid congestion games with player-specific costs. As our main result, we show that in such general resource allocation problems a pure Nash equilibrium is guaranteed to exist by giving a pseudo-polynomial algorithm computing a pure Nash equilibrium