Kirk Pruhs's research while affiliated with University of Pittsburgh and other places
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Publications (225)
This paper considers the basic problem of scheduling jobs online with preemption to maximize the number of jobs completed by their deadline on m identical machines. The main result is an O (1) competitive deterministic algorithm for any number of machines $$m >1$$ m > 1 .
Motivated by demand-responsive parking pricing systems, we consider posted-price algorithms for the online metric matching problem. We give an \(O(\log n)\)-competitive posted-price randomized algorithm in the case that the metric space is a line. In particular, in this setting we show how to implement the ubiquitous guess-and-double technique usin...
We consider the online transportation problem set in a metric space containing parking garages of various capacities. Cars arrive over time, and must be assigned to an unfull parking garage upon their arrival. The objective is to minimize the aggregate distance that cars have to travel to their assigned parking garage. We show that the natural gree...
We consider the online $k$-median clustering problem in which $n$ points arrive online and must be irrevocably assigned to a cluster on arrival. As there are lower bound instances that show that an online algorithm cannot achieve a competitive ratio that is a function of $n$ and $k$, we consider a beyond worst-case analysis model in which the algor...
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming technique, based on duality and projections, can be used to rederive some structural results that were previously est...
We show that there exist k-colorable matroids that are not (b,c)-decomposable when b and c are constants. A matroid is (b,c)-decomposable, if its ground set of elements can be partitioned into sets X1,X2,…,Xℓ with the following two properties. Each set Xi has size at most ck. Moreover, for all sets Y such that |Y∩Xi|≤1 it is the case that Y is b-co...
We show that there exist $k$-colorable matroids that are not $(b,c)$-decomposable when $b$ and $c$ are constants. A matroid is $(b,c)$-decomposable, if its ground set of elements can be partitioned into sets $X_1, X_2, \ldots, X_l$ with the following two properties. Each set $X_i$ has size at most $ck$. Moreover, for all sets $Y$ such that $|Y \cap...
This paper considers the basic problem of scheduling jobs online with preemption to maximize the number of jobs completed by their deadline on m identical machines. The main result is an O(1) competitive deterministic algorithm for any number of machines m>1.
This paper considers the basic problem of scheduling jobs online with preemption to maximize the number of jobs completed by their deadline on $m$ identical machines. The main result is an $O(1)$ competitive deterministic algorithm for any number of machines $m >1$.
Motivated by demand-responsive parking pricing systems we consider posted-price algorithms for the online metrical matching problem. Our main result is a polylog competitive posted-price algorithm in the case that the metric space is a spider.
Many tasks use data housed in relational databases to train boosted regression tree models. In this paper, we give a relational adaptation of the greedy algorithm for training boosted regression trees. For the subproblem of calculating the sum of squared residuals of the dataset, which dominates the runtime of the boosting algorithm, we provide a $...
Our main contribution is a polynomial-time algorithm to reduce a $k$-colorable gammoid to a $(2k-2)$-colorable partition matroid. It is known that there are gammoids that can not be reduced to any $(2k-3)$-colorable partition matroid, so this result is tight. We then discuss how such a reduction can be used to obtain polynomial-time algorithms with...
We consider the problem of efficiently estimating the size of the join of a collection of preprocessed relational tables from the perspective of instance optimality analysis. The running time of instance optimal algorithms is comparable to the minimum time needed to verify the correctness of a solution. Previously, instance optimal algorithms were...
We consider the matroid intersection cover problem. This is a special case of set cover where the sets are derived from the intersection of matroids. We introduce a technique for computing matroid intersection covers. We give polynomial-time algorithms to compute partition decompositions for matroids that commonly arise in combinatorial optimizatio...
We consider the problem of efficiently estimating the size of the inner join of a collection of preprocessed relational tables from the perspective of instance optimality analysis. The run time of instance optimal algorithms is comparable to the minimum time needed to verify the correctness of a solution. Previously instance optimal algorithms were...
Motivated by demand-responsive parking pricing systems we consider posted-price algorithms for the online metrical matching problem and the online metrical searching problem in a tree metric. Our main result is a poly-log competitive posted-price algorithm for online metrical searching.
The majority of learning tasks faced by data scientists involve relational data, yet most standard algorithms for standard learning problems are not designed to accept relational data as input. The standard practice to address this issue is to join the relational data to create the type of geometric input that standard learning algorithms expect. U...
Motivated by demand-responsive parking pricing systems we consider posted-price algorithms for the online metrical matching problem and the online metrical searching problem in a tree metric. Our main result is a poly-log competitive posted-price algorithm for online metrical searching.
In this paper, we consider the following dynamic fair allocation problem: Given a sequence of job arrivals and departures, the goal is to maintain an approximately fair allocation of the resource against a target fair allocation policy, while minimizing the total number of disruptions, which is the number of times the allocation of any job is chang...
In this paper, we consider the following dynamic fair allocation problem: Given a sequence of job arrivals and departures, the goal is to maintain an approximately fair allocation of the resource against a target fair allocation policy, while minimizing the total number of \em disruptions, which is the number of times the allocation of any job is c...
We consider gradient descent like algorithms for Support Vector Machine (SVM) training when the data is in relational form. The gradient of the SVM objective can not be efficiently computed by known techniques as it suffers from the ``subtraction problem''. We first show that the subtraction problem can not be surmounted by showing that computing a...
We consider the problem of evaluating an aggregation query, which is a sum-of-sum query or a sum-of-product query, subject to additive inequalities. Such aggregation queries, with a smallish number of additive inequalities, arise naturally/commonly in many applications, particularly in machine learning applications. We give a relatively complete ca...
In this paper, we consider the following dynamic fair allocation problem: Given a sequence of job arrivals and departures, the goal is to maintain an approximately fair allocation of the resource against a target fair allocation policy, while minimizing the total number of disruptions, which is the number of times the allocation of any job is chang...
We discuss what green computing algorithmics is, and what a theory of energy as a computational resource isn’t. We then present some open problems in this area, with enough background from the literature to put the open problems in context. This background should also be a reasonably representative sample of the green computing algorithmics literat...
We design and mathematically analyze sampling-based algorithms for regularized loss minimization problems that are implementable in popular computational models for large data, in which the access to the data is restricted in some way. Our main result is that if the regularizer's effect does not become negligible as the norm of the hypothesis scale...
Online matching on a line involves matching an online stream of requests to a given set of servers, all in the real line, with the objective of minimizing the sum of the distances between matched server-request pairs. The best previously known upper and lower bounds on the optimal deterministic competitive ratio are linear in the number of requests...
We introduce the itinerant list update problem (ILU), which is a relaxation of the classic list update problem in which the pointer no longer has to return to a home location after each request. The motivation to introduce ILU arises from the fact that it naturally models the problem of track memory management in Domain Wall Memory. Both online and...
We introduce the online Set Aggregation Problem, which is a natural generalization of the Multi-Level Aggregation Problem,
which in turn generalizes the TCP Acknowledgment Problem and the Joint Replenishment Problem.
We give a deterministic online algorithm, and show that its competitive ratio is logarithmic in the number of requests. We also give...
We study the Double Coverage (DC) algorithm for the k-server problem in tree metrics in the (h, k)-setting, i.e., when DC with k servers is compared against an offline optimum algorithm with h ≤ k servers. It is well-known that in such metric spaces DC is k-competitive (and thus optimal) for h = k. We prove that even if k > h the competitive ratio...
This paper considers the online machine minimization problem, a basic real time scheduling problem. The setting for this problem consists of n jobs that arrive over time, where each job has a deadline by which it must be completed. The goal is to design an online scheduler that feasibly schedules the jobs on a nearly minimal number of machines. An...
We show that one-dimensional Euclidean preference profiles can not be
characterized in terms of finitely many forbidden substructures. This result is
in strong contrast to the case of single-peaked and single-crossing preference
profiles, for which such finite characterizations have been derived in the
literature.
We consider the setting of a sensor that consists of a speed-scalable processor, a battery, and a solar cell that harvests energy from its environment at a time-invariant recharge rate. The processor must process a collection of jobs of various sizes. Jobs arrive at different times and have different deadlines. The objective is to minimize the *rec...
We give a polynomial time algorithm to compute an optimal energy and fractional weighted flow trade-off schedule for a speed-scalable processor with discrete speeds. Our algorithm uses a geometric approach that is based on structural properties obtained from a primal–dual formulation of the problem.
We introduce a scheduling algorithm Intermediate-SRPT, and show that it is O(logP)-competitive with respect to average flow time when scheduling jobs whose parallelizability is intermediate between being fully parallelizable and sequential. Here, the parameter P denotes the ratio between the maximum job size to the minimum. We also show a general m...
We consider three related online problems: Online Convex Optimization, Convex Body Chasing, and Lazy Convex Body Chasing. In Online Convex Optimization the input is an online sequence of convex functions over some Euclidean space. In response to a function, the online algorithm can move to any destination point in the Euclidean space. The cost is t...
One potential method to attain more energy-efficient circuits with the current technology is Near-Threshold Computing. However, this energy savings comes at a cost of increased functional failure, which necessitates that circuits must be more fault-tolerant, and thus contain more gates. Thus, achieving energy savings with Near-Threshold Computing i...
One potential method to attain more energy-efficient circuits with the current technology is Near-Threshold Computing, which means using less energy per gate by designing the supply voltages to be closer to the threshold voltage of transistors. However, this energy savings comes at a cost of a greater probability of gate failure, which necessitates...
The most commonly studied energy management technique is speed scaling, which involves operating the processor in a slow, energy-efficient mode at non-critical times, and in a fast, energy-inefficient mode at critical times. The natural resulting optimization problems involve scheduling jobs on a speed-scalable processor and have conflicting dual o...
IntroductionThe eleventh Workshop on Approximation and Online Algorithms (WAOA) was part of the federated ALGO conferences, and was held September 5 and 6, 2013, in Sophia Antipolis, France. The field of approximation algorithms studies how closely we can approximate optimal solutions to problems that are known to be computationally hard to solve e...
In the traditional approach to circuit design the supply voltages for each transistor/gate are set sufficiently high so that with sufficiently high probability no transistor fails. One potential method to attain more energy-efficient circuits is Near-Threshold Computing, which simply means that the supply voltages are designed to be closer to the t...
We study the Double Coverage (DC) algorithm for the k-server problem in the (h, k)-setting, i.e. when DC with k servers is compared against an offline optimum algorithm with \(h \le k\) servers. It is well-known that DC is k-competitive for \(h=k\). We prove that even if \(k>h\) the competitive ratio of DC does not improve; in fact, it increases up...
Online matching on a line involves matching an online stream of items of various sizes to stored items of various sizes, with the objective of minimizing the average discrepancy in size between matched items. The best previously known upper and lower bounds on the optimal deterministic competitive ratio are linear in the number of items, and consta...
We introduce a scheduling algorithm Intermediate-SRPT, and show that it is O(log P)-competitive with respect to average waiting time when scheduling jobs whose parallelizability is intermediate between being fully parallelizable and sequential. Here the parameter P denotes the ratio between the maximum job size to the minimum. We also show a genera...
We consider the classical problem of minimizing the total weighted flow-time
for unrelated machines in the online \emph{non-clairvoyant} setting. In this
problem, a set of jobs $J$ arrive over time to be scheduled on a set of $M$
machines. Each job $j$ has processing length $p_j$, weight $w_j$, and is
processed at a rate of $\ell_{ij}$ when schedul...
We initiate a competitive analysis of packet forwarding policies for maximum and average flow in a line network. We show that the policies Earliest Arrival and Furthest-To-Go are scalable, but not constant competitive, for maximum flow. We show that there is no constant competitive algorithm for average flow.KeywordsOptimal ScheduleCompetitive Rati...
We consider circuit routing with an objective of minimizing energy, in a
network of routers that are speed scalable and that may be shutdown when idle.
We consider both multicast routing and unicast routing. It is known that this
energy minimization problem can be reduced to a capacitated flow network design
problem, where vertices have a common ca...
We give a polynomial time algorithm to compute an optimal energy and fractional weighted flow trade-off schedule for a speed-scalable processor with discrete speeds. Our algorithm uses a geometric approach that is based on structural properties obtained from a primal-dual formulation of the problem. © Antonios Antoniadis, Neal Barcelo, Mario Consue...
We initiate the theoretical investigation of energy-efficient circuit design. We assume that the circuit design specifies the circuit layout as well as the supply voltages for the gates. To obtain maximum energy efficiency, the circuit design must balance the conflicting demands of minimizing the energy used per gate, and minimizing the number of g...
We consider virtual circuit routing protocols, with an objective of minimizing energy, in a network of components that are speed scalable, and that may be shutdown when idle. We assume that the speed s of a link is proportional to its load, and assume the standard model for component power, namely that the power is some constant static power σ plus...
We consider scheduling tasks that arrive over time on a speed scalable processor. At each time a schedule specifies a job to be run and the speed at which the processor is run. Processors are generally less energy efficient at higher speeds. We seek to understand the structure of schedules that optimally trade-off the energy used by the processor w...
We consider the first, and most well studied, speed scaling problem in the algorithmic literature: where the scheduling quality of service measure is a deadline feasibility constraint, and where the power ob-jective is to minimize the total energy used. Four online algorithms for this problem have been proposed in the algorithmic literature. Based...
We consider computing optimal k-norm preemptive schedules of jobs that arrive over time. In particular, we show that computing the optimal k-norm of flow schedule, 1 |r
j
, pmtn | ∑ j
(C
j
− r
j
)k
in standard 3-field scheduling notation, is strongly NP-hard for k ∈ (0, 1) and integers k ∈ (1, ∞ ). Further we show that computing the optimal k-norm...
We consider virtual circuit multicast routing in a network of links that are speed scalable. We assume that a link with load f uses power σ + f
α
, where σ is the static power, and α > 1 is some constant. We assume that a link may be shutdown if not in use. In response to the arrival of client i at vertex t
i
a routing path (the virtual circuit) P...
We give a randomized polynomial time algorithm with approximation ratio O(logφ(n)) for weighted set multi-cover instances with a shallow cell complexity of at most f(n,k) = n
φ(n) k
O(1). Up to constant factors, this matches a recent result of Könemann et al. for the set cover case, i.e. when all the covering requirements are 1. One consequence of...
We discuss the proportionally fair allocation of a set of indivisible items to k agents. We assume that each agent specifies only a ranking of the items from best to worst. Agents do not specify their valuations of the items. An allocation is proportionally fair if all agents believe that they have received their fair share of the value according t...
We consider speed scaling problems where the objective is to minimize a linear combination of arbitrary scheduling objective SS, and energy EE. A natural conjecture is that there is an O(1)O(1)-competitive algorithm for SS on a fixed speed processor if and only if there is an O(1)O(1)-competitive algorithm for S+ES+E on a processor with an arbitrar...
We use competitive analysis to study how best to use redundancy to achieve fault-tolerance in online real-time scheduling.
We show that the optimal way to use spatial redundancy depends on a complex interaction of the benefits, execution times,
release times, and latest start times of the jobs. We give a randomized online algorithm whose competitiv...
We consider a general online scheduling problem on a single machine with the objective of minimizing Σjwjg(Fj), where wj is the weight/importance of job Jj, Fj is the flow time of the job in the schedule, and g is an arbitrary non-decreasing cost function. Numerous natural scheduling objectives are special cases of this general objective. We show t...
We consider preemptive online scheduling algorithms to minimize the total weighted/unweighted flow time plus energy for speed-scalable heterogeneous multiprocessors. We show that the well-known priority scheduling algorithms Highest Density First, Weighted Shortest Elapsed Time First, and Weighted Late Arrival Processor Sharing, are not O(1)-speed...
We explore the revenue capabilities of truthful, monotone (“fair”) allocation and pricing functions for resource constrained auction mechanisms within a general framework that encompasses unlimited supply auctions, knapsack auctions, and auctions with general non-decreasing convex production cost functions. We study and compare the revenue obtainab...
We show that SETF, the idealized version of the uniprocessor scheduling algorithm used by Unix, is scalable for the objective of fractional flow on a homogeneous multiprocessor. We also give a potential function analysis for the objective of weighted fractional flow on a uniprocessor.KeywordsPotential FunctionSchedule AlgorithmCompetitive RatioOnli...
Phase-Change Memory (PCM) has the potential to replace DRAM as the primary memory technology due to its non-volatility, scalability, and high energy efficiency. However, the adoption of PCM will require technological solutions to surmount some deficiencies of PCM, such as writes requiring significantly more energy and time than reads. One way to li...
The converging trends of society's desire/need for more sustainable technologies, exponentially increasing power densities within computing devices, and exponentially more computing devices, have inevitably pushed power and energy management into the forefront of computing design and management for purely economic reasons. Thus we are in the midst...
We reinterpret some online greedy algorithms for a class of nonlinear
"load-balancing" problems as solving a mathematical program online. For
example, we consider the problem of assigning jobs to (unrelated) machines to
minimize the sum of the alpha^{th}-powers of the loads plus assignment costs
(the online Generalized Assignment Problem); or choos...
potential functions are used to show that a particular online algorithm is locally competitive in an amortized sense. Algorithm analyses using potential functions are sometimes criticized as seeming to be black magic
We show that a natural online algorithm for scheduling jobs on a
heterogeneous multiprocessor, with arbitrary power functions, is scalable for
the objective function of weighted flow plus energy.
We consider the speed scaling problem where the quality of service objective is deadline feasibility and the power objective
is temperature. In the case of batched jobs, we give a simple algorithm to compute the optimal schedule. For general instances,
we give a new online algorithm, and obtain an upper bound on the competitive ratio of this algori...
We consider the well-known cake cutting problem in which a protocol wants to divide a cake among n ≥ 2 players in such a way that each player believes that they got a fair share. The standard Robertson-Webb model allows the protocol to make two types of queries, Evaluation and Cut, to the players. A deterministic divide-and-conquer protocol with co...
“With multi-core it’s like we are throwing this Hail Mary pass down the field and now we have to run down there as fast as we can to see if we can catch it.” — David Patterson, UC Berkeley computer science professor We consider the setting of a multiprocessor where the speeds of the m processors can be individually scaled. Jobs arrive over time and...
A particularly important emergent technology is heterogeneous processors
(or cores), which many computer architects believe will be the dominant
architectural design in the future. The main advantage of a
heterogeneous architecture, relative to an architecture of identical
processors, is that it allows for the inclusion of processors whose
design i...
Speed scaling is a power management technique that involves dynamically changing the speed of a processor. This gives rise to dual-objective scheduling problems, where the operating system both wants to conserve energy and optimize some Quality of Service (QoS) measure of the resulting schedule. Yao, Demers, and Shenker [8] considered the problem w...
We state some of the most important open algorithmic problems in real-time scheduling, and survey progress made on these problems
since the 2009 Dagstuhl scheduling seminar.
We consider the problem of nonclairvoyantly scheduling jobs, which arrive over time and have varying sizes and degrees of
parallelizability, with the objective of minimizing the maximum flow. We give essentially tight bounds on the achievable competitiveness.
More specifically we show that the competitive ratio of every deterministic nonclairvoyant...
We consider the following general scheduling problem: The input consists of n jobs, each with an arbitrary release time, size, and a monotone function specifying the cost incurred when the job is completed at a particular time. The objective is to find a preemptive schedule of minimum aggregate cost. This problem formulation is general enough to in...
We consider a situation where jobs arrive over time at a data center, consisting of identical speed-scalable processors. For
each job, the scheduler knows how much income is lost as a function of how long the job is delayed. The scheduler also knows
the fixed cost of a unit of energy. The online scheduler determines which jobs to run on which proce...
We show that a natural nonclairvoyant online algorithm for scheduling jobs on a power-heterogeneous multiprocessor is bounded-speed bounded-competitive for the objective of flow plus energy.
We give a (2+ε)-speed O(1)-competitive algorithm for scheduling jobs with arbitrary speed-up curves for the l2 norm of flow. We give a similar result for the broadcast setting with varying page sizes.
We explore the revenue capabilities of truthful, monotone (“fair”) allocation and pricing functions for resource-constrained auction mechanisms within a general framework that encompasses unlimited supply auctions, knapsack auctions, and auctions with general non-decreasing convex production cost functions. We study and compare the revenue obtainab...
Amazon, Google, and IBM now sell cloud computing services.We consider the setting of a for-profit business selling data stream monitoring/management services and we investigate auction-based mechanisms for admission control of continuous queries. When submitting a query, each user also submits a bid of how much she is willing to pay for that query...
Often server systems do not implement the best known algorithms for optimizing average Quality of Service (QoS) out of concern of that these algorithms may be insuciently fair to individual jobs. The standard method for balancing average QoS and fairness is optimize the 'p metric, 1 < p < 1. Thus we consider server scheduling strategies to optimize...
Speed scaling is a power management technique that involves dynamically changing the speed of a processor. This gives rise to dual-objective scheduling problems, where the operating system both wants to conserve energy and optimize some Quality of Service (QoS) measure of the resulting schedule. In the most investigated speed scaling problem in the...
We give three results related to online nonclairvoyant speed scaling to minimize total flow time plus energy. We give a nonclairvoyant algorithm LAPS, and show that for every power function of the form P(s)=s
α
, LAPS is O(1)-competitive; more precisely, the competitive ratio is 8 for α=2, 13 for α=3, and \(\frac{2\alpha^{2}}{\ln\alpha}\) for α>3....
Citations
... Indeed, taking a complete graph on the elements of each partition class would result in a graph of at most 2·β(M ) 2 · r(M ) edges that covers every circuit of the matroid. The conjecture was disproved in [2] and independently in [31], and their proofs also show a lower bound of Θ β(M ) 2 · log β(M ) · r(M ) . ...
![[object Object]](https://i1.rgstatic.net/ii/profile.image/273670362890247-1442259507105_Q64/Benjamin-Moseley.jpg)
... The main algorithmic idea is that for each center c i we generate a collection of hyperspheres around c i containing geometrically increasing numbers of points. The space is then partitioned using these hyperspheres where each partition contains a portion of points in J. Using the algorithm from [3], we then sample a poly-log sized collection of points from each partition, and use this subsample to estimate the fraction of the points in this partition which are closer to c i than any other center. The estimated weight of c i is aggregated accordingly. ...
Reference: Relational Algorithms for k-means Clustering
... Matroids, versatile concepts with applications spanning optimization theory, combinatorial mathematics, topology, algebra, graph algorithms, game theory, geometry, and network theory, have garnered substantial interest. Numerous studies have delved into this subject matter (see, for example, [9][10][11][12][13][14][31][32][33]). Quasi-matroids, as defined in reference [7] (cf. ...
Reference: Quasi-Matroid on connectivity system
... The most common line of work in online fair allocation considers settings where agents are static and items arrive over time [16,47,24,9,6]; under stochastic arrivals, these tend to be easier as, intuitively, future allocations can be used to correct past imbalances. Closer to our setting are work on online cake cutting; this though is primarily under adversarial arrivals [46,26,42]. Finally, recent work considers upfront allocation of indivisible resources for stochastic demands [17,20]; these study similar tradeoffs between global objectives and individual guarantees as us, but are essentially static problems. ...
... Much of this prior work analyzes settings where the agents are static and the resources arrive over time, like we do (Benade et al. 2018;He et al. 2019). Another line of work studies the allocation of static resources among dynamically arriving and departing agents (Walsh 2011;Kash, Procaccia, and Shah 2014;Vardi 2015, 2017;Im et al. 2020). ...
... A major challenge in designing algorithms for such cost-functions is that one needs the balance two opposing goals (1) aggregating demands in the concave regime and (2) separating demands in the convex regime. Prior work [6,7,31] has mainly focused on the special case of uniform (or related) cost functions where the α e s and σ e ξ e s are uniform across all resources e. ...
... It is obvious that ICT should become sustainable in terms of energy [7][8][9]. There are at least three approaches that should be taken in parallel to achieve this goal. ...
... For doubling metrics, an O(log k)-competitive algorithm [7] is known. For OML, there have been many active studies [3,2,7,22,24,25] and the best upper bound on the competitive ratio [22,25] is O(log k), which is achieved by the deterministic algorithm called Robust-Matching [24]. ...
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... We present a deterministic O(log n log log n)-approximation algorithm for this problem, improving over a randomized O(log 2 n)-approximation by Olver et al. [22]. Our algorithm is based on first solving spreading-metric LP relaxation on a time-expanded graph, applying a tree decomposition on the basis of the LP solution, and finally converting the tree decomposition to a sequence of permutations. ...
... Other classical online problems have been also considered under such delay setting, such as the online service problem [5,14,8], the multi-level aggregation problem [10,15,16,8], facility location [11,8,9], bin packing [4,20], set cover [3,28] and others [25,22,9,28,17]. ...
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