scholarly journals Primal beats dual on online packing LPs in the random-order model

2014 ◽  
Author(s):  
Thomas Kesselheim ◽  
Andreas Tönnis ◽  
Klaus Radke ◽  
Berthold Vöcking
Keyword(s):  
Random Order ◽  
Order Model

scholarly journals Scheduling in the Random-Order Model

Algorithmica ◽  
2021 ◽  
Author(s):  
Susanne Albers ◽  
Maximilian Janke
Keyword(s):  
Competitive Ratio ◽  
High Probability ◽  
Online Algorithm ◽  
Fundamental Problem ◽  
Random Order ◽  
Random Permutation ◽  
Worst Case Analysis ◽  
Makespan Minimization ◽  
Order Model ◽  
Worst Case

AbstractMakespan minimization on identical machines is a fundamental problem in online scheduling. The goal is to assign a sequence of jobs to m identical parallel machines so as to minimize the maximum completion time of any job. Already in the 1960s, Graham showed that Greedy is $$(2-1/m)$$ ( 2 - 1 / m ) -competitive. The best deterministic online algorithm currently known achieves a competitive ratio of 1.9201. No deterministic online strategy can obtain a competitiveness smaller than 1.88. In this paper, we study online makespan minimization in the popular random-order model, where the jobs of a given input arrive as a random permutation. It is known that Greedy does not attain a competitive factor asymptotically smaller than 2 in this setting. We present the first improved performance guarantees. Specifically, we develop a deterministic online algorithm that achieves a competitive ratio of 1.8478. The result relies on a new analysis approach. We identify a set of properties that a random permutation of the input jobs satisfies with high probability. Then we conduct a worst-case analysis of our algorithm, for the respective class of permutations. The analysis implies that the stated competitiveness holds not only in expectation but with high probability. Moreover, it provides mathematical evidence that job sequences leading to higher performance ratios are extremely rare, pathological inputs. We complement the results by lower bounds, for the random-order model. We show that no deterministic online algorithm can achieve a competitive ratio smaller than 4/3. Moreover, no deterministic online algorithm can attain a competitiveness smaller than 3/2 with high probability.

scholarly journals Improved Online Algorithms for Knapsack and GAP in the Random Order Model

Algorithmica ◽  
2021 ◽  
Author(s):  
Susanne Albers ◽  
Arindam Khan ◽  
Leon Ladewig
Keyword(s):  
Knapsack Problem ◽  
Competitive Ratio ◽  
Randomized Algorithm ◽  
Input Sequence ◽  
Random Order ◽  
Random Permutation ◽  
Secretary Problem ◽  
Order Model ◽  
Sequential Approach ◽  
Online Setting

AbstractThe knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the online setting, items are revealed one by one and the decision, if the current item is packed or discarded forever, must be done immediately and irrevocably upon arrival. We study the online variant in the random order model where the input sequence is a uniform random permutation of the item set. We develop a randomized (1/6.65)-competitive algorithm for this problem, outperforming the current best algorithm of competitive ratio 1/8.06 (Kesselheim et al. in SIAM J Comput 47(5):1939–1964, 2018). Our algorithm is based on two new insights: We introduce a novel algorithmic approach that employs two given algorithms, optimized for restricted item classes, sequentially on the input sequence. In addition, we study and exploit the relationship of the knapsack problem to the 2-secretary problem. The generalized assignment problem (GAP) includes, besides the knapsack problem, several important problems related to scheduling and matching. We show that in the same online setting, applying the proposed sequential approach yields a (1/6.99)-competitive randomized algorithm for GAP. Again, our proposed algorithm outperforms the current best result of competitive ratio 1/8.06 (Kesselheim et al. in SIAM J Comput 47(5):1939–1964, 2018).

scholarly journals A steady-state random-order mechanism for the oxidative deamination of norvaline by glutamate dehydrogenase

1983 ◽  
Vol 211 (1) ◽  
pp. 99-107 ◽  
Author(s):  
C LiMuti ◽  
J E Bell
Keyword(s):  
Steady State ◽  
Glutamate Dehydrogenase ◽  
Dissociation Constants ◽  
Random Order ◽  
Kinetic Mechanism ◽  
Order Model ◽  
Oxidative Deamination ◽  
Steady State Kinetics ◽  
Rapid Equilibrium ◽  
Good Agreement

The kinetic mechanism of glutamate dehydrogenase with the monocarboxylic substrate norvaline was examined by using initial-rate steady-state kinetics and inhibition kinetics. To a first approximation the reaction mechanism can be described as a rapid-equilibrium random-order one. Binding synergism between the monocarboxylic substrate and coenzyme is not observed. Dissociation constants for NAD+ and 2-oxoglutarate calculated from the kinetic data assuming a rapid-equilibrium random-order model are in good agreement with independently obtained estimates. Lineweaver-Burk plots with varied norvaline concentration are not strictly linear, and it is concluded that a steady-state random-order model more accurately reflects the observed kinetics with norvaline as substrate.

scholarly journals Primal Beats Dual on Online Packing LPs in the Random-Order Model

2018 ◽  
Vol 47 (5) ◽  
pp. 1939-1964 ◽  
Author(s):  
Thomas Kesselheim ◽  
Klaus Radke ◽  
Andreas Tönnis ◽  
Berthold Vöcking
Keyword(s):  
Random Order ◽  
Order Model

scholarly journals Data Streams as Random Permutations: the Distinct Element Problem

2012 ◽  
Vol DMTCS Proceedings vol. AQ,... (Proceedings) ◽  
Author(s):  
Ahmed Helmi ◽  
Jérémie Lumbroso ◽  
Conrado Martínez ◽  
Alfredo Viola
Keyword(s):  
Random Sample ◽  
Data Streams ◽  
Distinct Element ◽  
Random Order ◽  
Estimation Algorithm ◽  
Random Permutations ◽  
Order Model ◽  
Simple Observation ◽  
International Audience ◽  
Minimal Effort

International audience In this paper, we show that data streams can sometimes usefully be studied as random permutations. This simple observation allows a wealth of classical and recent results from combinatorics to be recycled, with minimal effort, as estimators for various statistics over data streams. We illustrate this by introducing RECORDINALITY, an algorithm which estimates the number of distinct elements in a stream by counting the number of $k$-records occurring in it. The algorithm has a score of interesting properties, such as providing a random sample of the set underlying the stream. To the best of our knowledge, a modified version of RECORDINALITY is the first cardinality estimation algorithm which, in the random-order model, uses neither sampling nor hashing.

Automated software supported versus manual aorto-iliac diameter measurements in CT angiography of patients with abdominal aortic aneurysms: Assessment of inter- and intraobserver variation

VASA ◽  
2005 ◽  
Vol 34 (4) ◽  
pp. 255-261 ◽  
Author(s):  
Diehm ◽  
Baumgartner ◽  
Silvestro ◽  
Herrmann ◽  
Triller ◽  
...  
Keyword(s):  
Ct Angiography ◽  
Iliac Artery ◽  
Automatic Measurement ◽  
Random Order ◽  
Aortic Aneurysms ◽  
Intraobserver Variability ◽  
Automatic Method ◽  
Left Common Iliac Artery ◽  
Abdominal Aortic ◽  
Intraobserver Variation

Background: Open surgical or endovascular abdominal aortic aneurysm (AAA) relies on precise preprocedual imaging. Purpose of this study was to assess inter- and intraobserver variation of software-supported automated and manual multi row detector CT angiography (MDCTA) in aortoiliac diameter measurements before AAA repair. Patients and methods: Thirty original MDCTA data sets (4 times 2mm collimation) of patients scheduled for endovascular AAA repair were studied on a dedicated software capable of creating two-dimensional reformatted planes orthogonal to the aortoiliac center-line. Measurements were performed twice with a four-week interval between readings. Data were analysed by two blinded readers at random order. Two different measurement methods were performed: reader-assisted freehand wall-to-wall measurement and semi-automatic measurement. Results: Aortoiliac diameters were significantly underestimated by the semi-automatic method as compared to reader-assisted measurements (p < 0.0031). Intraobserver variability of AAA diameter calculation was not significant (p > 0.15) for reader-assisted measurements except for the diameter of the left common iliac artery in reader 2 (p = 0.0045) and it was not significant (p > 0.14) using the semi-automatic method. Interobserver variability was not significant for AAA diameter measurements using the reader-assisted method and for proximal neck analysis with the semi-automatic method (p > 0.27). Relevant interobserver variation was observed for semi-automatic measurement of maximum AAA (p = 0.0007) and iliac artery diameters (p = 0.024). Conclusions: Dedicated MDCTA software provides a useful tool to minimize aortoiliac diameter measurement variation and to improve imaging precision before AAA repair. For reliable AAA diameter analysis the reader-assisted freehand measurement method is recommended to be applied to a set of reformatted CT data as provided by the software used in this study.

A New Technique to Measure the Level of Interest Using Heartbeat-Evoked Brain Potential

2021 ◽  
Vol 35 (1) ◽  
pp. 15-22
Author(s):  
Kohei Fuseda ◽  
Jun’ichi Katayama
Keyword(s):  
Brain Activity ◽  
Random Order ◽  
Overt Response ◽  
Brain Potential ◽  
Probe Technique ◽  
Dynamic Stimuli ◽  
Attentional Resources ◽  
Opposite Sex ◽  
A New Technique ◽  
Task Irrelevant

Abstract. Interest is a positive emotion related to attention. The event-related brain potential (ERP) probe technique is a useful method to evaluate the level of interest in dynamic stimuli. However, even in the irrelevant probe technique, the probe is presented as a physical stimulus and steals the observer’s attentional resources, although no overt response is required. Therefore, the probe might become a problematic distractor, preventing deep immersion of participants. Heartbeat-evoked brain potential (HEP) is a brain activity, time-locked to a cardiac event. No probe is required to obtain HEP data. Thus, we aimed to investigate whether the HEP can be used to evaluate the level of interest. Twenty-four participants (12 males and 12 females) watched attractive and unattractive individuals of the opposite sex in interesting and uninteresting videos (7 min each), respectively. We performed two techniques each for both the interesting and the uninteresting videos: the ERP probe and the HEP techniques. In the former, somatosensory stimuli were presented as task-irrelevant probes while participants watched videos: frequent (80%) and infrequent (20%) stimuli were presented at each wrist in random order. In the latter, participants watched videos without the probe. The P2 amplitude in response to the somatosensory probe was smaller and the positive wave amplitudes of HEP were larger while watching the videos of attractive individuals than while watching the videos of unattractive ones. These results indicate that the HEP technique is a useful method to evaluate the level of interest without an external probe stimulus.

Testing a Higher-Order Model of Psychological Resilience in Recruits

2010 ◽  
Author(s):  
Donald R. McCreary ◽  
Jennifer E. C. Lee ◽  
Kerry A. Sudom
Keyword(s):  
Higher Order ◽  
Psychological Resilience ◽  
Order Model
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