Continuous Monitoring of Distributed Data Streams over a Time-based Sliding Window

The past decade has witnessed many interesting algorithms for maintaining statistics over a data stream. This paper initiates a theoretical study of algorithms for monitoring distributed data streams over a time-based sliding window (which contains a variable number of items and possibly out-of-order items). The concern is how to minimize the communication between individual streams and the root, while allowing the root, at any time, to be able to report the global statistics of all streams within a given error bound. This paper presents communication-efficient algorithms for three classical statistics, namely, basic counting, frequent items and quantiles. The worst-case communication cost over a window is $O(\frac{k} {\epsilon} \log \frac{\epsilon N}{k})$ bits for basic counting and $O(\frac{k}{\epsilon} \log \frac{N}{k})$ words for the remainings, where $k$ is the number of distributed data streams, $N$ is the total number of items in the streams that arrive or expire in the window, and $\epsilon < 1$ is the desired error bound. Matching and nearly matching lower bounds are also obtained.Comment: 12 pages, to appear in the 27th International Symposium on Theoretical Aspects of Computer Science (STACS), 201

Scheduling for weighted flow time and energy with rejection penalty

This paper revisits the online problem of flow-time scheduling on a single processor when jobs can be rejected at some penalty [4]. The user cost of a job is defined as the weighted flow time of the job plus the penalty if it is rejected before completion. For jobs with arbitrary weights and arbitrary penalties, Bansal et al. [4] gave an online algorithm that is O((log W + log C) 2)-competitive for minimizing the total user cost when using a slightly faster processor, where W and C are the max-min ratios of job weights and job penalties, respectively. In this paper we improve this result with a new algorithm that can achieve a constant competitive ratio independent of W and C when using a slightly faster processor. Note that the above results assume a processor running at a fixed speed. This paper shows more interesting results on extending the above study to the dynamic speed scaling model, where the processor can vary the speed dynamically and the rate of energy consumption is a cubic or any increasing function of speed. A scheduling algorithm has to control job admission and determine the order and speed of job execution. This paper studies the tradeoff between the above-mentioned user cost and energy, and it shows two O(1)-competitive algorithms and a lower bound result on minimizing the user cost plus energy. These algorithms can also be regarded as a generalization of the recent work on minimizing flow time plus energy when all jobs must be completed (see the survey paper [1])

Non-clairvoyant scheduling for weighted flow time and energy on speed bounded processors

Abstract. We consider the online scheduling problem of minimizing total weighted flow time plus energy in the dynamic speed scaling model, where a processor can scale its speed dynamically between 0 and some maximum speed T. In the past few years this problem has been studied extensively under the clairvoyant setting, which requires the size of a job to be known at release time [1, 5, 6, 9, 15, 18–20]. For the non-clairvoyant setting, despite its practical importance, the progress is relatively limited. Only recently an online algorithm LAPS is known to be O(1)-competitive for minimizing (unweighted) flow time plus energy in the infinite speed model (i.e., T = ∞) [11, 12]. This paper makes two contributions to the non-clairvoyant scheduling. First, we resolve the open problem that the unweighted result of LAPS can be extended to the more realistic model with bounded maximum speed. Second, we show that another non-clairvoyant algorithm WRR is O(1)-competitive when weighted flow time is concerned. Note that WRR is not as efficient as LAPS for scheduling unweighted jobs as WRR has a much bigger constant hidden in its competitive ratio. This is the corrected version of the paper with the same title in CATS 2010 [13]; in particular, Lemmas 2 and 4 of Section 3 and the ordering of jobs in the potential analysis of Section 4 were given incorrectly before and are fixed in this version. On the other hand, the conjecture, given in Section 5, about the generalization of LAPS to the weighted setting has recently been resolved [14]. T.W. Lam is partly supported by HKU Grant 7176104

Sleep management on multiple machines for energy and flow time

In large data centers, determining the right number of operating servers is often non-trivial, especially when the workload is unpredictable. Using too many machines would waste energy, while using too few would affect the performance. This paper extends the traditional study of online flow-time scheduling on multiple machines to take sleep management and energy into consideration. Specifically, we study online algorithms that can determine dynamically when to wake up (or turn off) some of the machines and how to dispatch and schedule the jobs. The objective is to minimize the sum of flow time and energy. This paper presents two O(1)competitive algorithms, one for the model where machines running at a fixed speed, and the other allows dynamic speed scaling in each machine to further optimize energy usage. Like the previous work on the tradeoff between flow time and energy, the analysis of our algorithms is based on potential functions. What is new here is that the online and offline algorithms would use different subsets of machines at different times, and we need a more general potential analysis that can consider different match-ups of machines

Energy efficient online deadline scheduling

Abstract. This paper extends the study of online algorithms for energy-efficient deadline scheduling to the overloaded setting. Specifically, we consider a processor that can vary its speed between 0 and a maximum speed T to minimize its energy usage (of which the rate is roughly a cubic function of the speed). As the speed is upper bounded, the system may be overloaded with jobs and no scheduling algorithms can meet the deadlines of all jobs. An optimal schedule is expected to maximize the throughput, and furthermore, its energy usage should be the smallest among all schedules that achieve the maximum throughput. In designing a scheduling algorithm, one has to face the dilemma of selecting more jobs and being conservative in energy usage. Even if we ignore energy usage, the best possible online algorithm is 4-competitive on throughput [12]. On the other hand, existing work on energy-efficient scheduling focuses on minimizing the energy to complete all jobs on a processor with unbounded speed, giving several O(1)-competitive algorithms with respect to the energy usage [2,20]. This paper presents the first online algorithm for the more realistic setting where processor speed is bounded and the system may be overloaded; the algorithm is O(1)-competitive on both throughput and energy usage. If the maximum speed of the online scheduler is relaxed slightly to (1+ǫ)T for some ǫ&gt; 0, we can improve the competitive ratio on throughput to arbitrarily close to one, while maintaining O(1)-competitive on energy usage.

Pericyte derivation and transplantation for blood-CNS barrier reconstitution in CNS disorders

Disruption of the blood-central nervous system barrier (BCB) is increasingly recognized as a pathological factor in diseases and trauma of the central nervous system. Despite the neuropathological impact, current treatment modalities do not target the BCB; strategies to reconstitute the impaired BCB have been restricted to nutritional and dietary remedies. As an integral cell type in the neurovascular unit, pericytes are crucial to the development, maintenance, and repair of the BCB. As such, pericytes are well poised as cellular agents for reconstitution of the impaired BCB. Here, we summarize recent revelations regarding the role of BCB disruption in diseases and trauma of the central nervous system and highlight how pericytes are harnessed to provide targeted therapeutic effect in each case. This review will also address how recent advances in pericyte derivation strategies can serve to overcome practical hurdles in the clinical use of pericytes