Competitive Ratio Research Articles

Optimizing the planting time and stand density of sunn hemp intercropping for biomass productivity and competitiveness in a maize-based system

ContextOptimizing cover crop intercropping should aim to be sustainable, economically feasible and environmentally benign. Significant consideration must be given to cover crop plant timing and stand density adjustments to complement the resource demands of the dominant crop, while ensuring optimal biomass yields. ObjectiveThe study assessed a range of intercropping indices to evaluate the influence of different planting times and stand densities of sunn hemp (Crotalaria juncea L.) when intercropped with maize (Zea mays L.). The evaluation focused on interspecies interactions in relation to aboveground biomass production. MethodsA split-plot experiment was conducted using the in-field rainwater harvesting (IRWH) technique. The main plot factors included three intercropping times: simultaneous with maize planting, at the V15 and the R1 maize growth stages. The subplot factors consisted of three stand densities (16, 32 and 48 plants m−2), with three replicates for both the 2019/20 and 2020/21 seasons. Intercropping indices, including land equivalent ratio and coefficient, area time equivalent ratio, land use efficiency, system productivity index, percentage yield difference, relative crowding coefficient, aggressivity, competitive ratio and actual yield loss were employed to assess interspecific interactions and their impact on biomass productivity. ResultsResults show that intercropping sunn hemp at maize planting or the V15 maize growth stage can reduce stand density to 32 plants m−2 without reducing sunn hemp biomass yield. The land equivalent ratio was highest (2.20), with intercropping at the V15 maize growth stage and lowest (2.09) with simultaneous intercropping at maize planting. The relative crowding coefficient was highest (34.4) at the V15 maize growth stage at 32 plants m−2 stand density and lowest (−45.9) with simultaneous intercropping at planting at the same stand density. Intercropping during the R1 maize growth stage influenced competition on sunn hemp with the highest actual yield loss of − 0.07. Competitive ratios were significantly higher for maize (26.19) and sunn hemp (0.16) with R1 and V15 maize growth stage intercropping, respectively. However, sunn hemp's actual yield loss was higher (0.25) with intercropping during the V15 maize growth stage than in sole cropping. ConclusionsIntercropping sunn hemp both simultaneously with maize planting and during the V15 maize growth stage with a stand density of 32 plants m−2 demonstrated enhanced biomass productivity, thereby offering viable intensification choices. The utilization of multiple intercropping indices can contribute to a more comprehensive and precise evaluation of interspecies interactions, consequently leading to improved decision-making.

Online Partial Service Hosting at the Edge

We consider the problem of service hosting where an application provider can dynamically rent edge computing resources and serve user requests from the edge to deliver a better quality of service. A key novelty of this work is that we allow the service to be hosted partially at the edge that enables a fraction of the user query to be served by the edge. We model the total cost for (partially) hosting a service at the edge as a combination of the latency in serving requests, the bandwidth consumption, and the time-varying cost for renting edge resources. We propose an online policy called α-RetroRenting (α-RR) that dynamically determines the fraction of the service to be hosted at the edge in any time-slot, based on the history of the request arrivals and the rent cost sequence. As our main result, we derive an upper bound on α-RR’s competitive ratio with respect to the offline optimal policy that knows the entire request arrival and rent cost sequence in advance. In addition, we provide performance guarantees for our policy in the setting where the request arrival process is stochastic. We conduct extensive numerical evaluations to compare the performance of α-RR with various benchmarks for synthetic and trace-based request arrival and rent cost processes and find several parameter regimes where α-RR’s ability to store the service partially greatly improves cost-efficiency.

Online convex optimization with switching cost and delayed gradients

We consider the online convex optimization (OCO) problem with quadratic and linear switching cost in the limited information setting, where an online algorithm can choose its action using only gradient information about the previous objective function. For L-smooth and μ-strongly convex objective functions, we propose an online multiple gradient descent (OMGD) algorithm and show that its competitive ratio for the OCO problem with quadratic switching cost is at most 4(L+5)+16(L+5)μ. The competitive ratio upper bound for OMGD is also shown to be order-wise tight in terms of L,μ. In addition, we show that the competitive ratio of any online algorithm is max{Ω(L),Ω(Lμ)} in the limited information setting when the switching cost is quadratic. We also show that the OMGD algorithm achieves the optimal (order-wise) dynamic regret in the limited information setting. For the linear switching cost, the competitive ratio upper bound of the OMGD algorithm is shown to depend on both the path length and the squared path length of the problem instance, in addition to L,μ, and is shown to be order-wise, the best competitive ratio any online algorithm can achieve. Consequently, we conclude that the optimal competitive ratio for the quadratic and linear switching costs are fundamentally different in the limited information setting.

Online Bipartite Matching with Reusable Resources

We study the classic online bipartite matching problem with a twist: off-line vertices, called resources, are reusable. In particular, when a resource is matched to an online vertex, it is unavailable for a deterministic time duration d, after which it becomes available again for a rematch. Thus, a resource can be matched to many different online vertices over a period of time. Whereas recent work on the problem has resolved the asymptotic case in which we have large starting inventory (i.e., many copies) of every resource, we consider the (more general) case of unit inventory and give the first algorithms that are provably better than the naïve greedy approach, which has a competitive ratio of (exactly) 0.5. Our first algorithm, which achieves a competitive ratio of 0.589, generalizes the classic RANKING algorithm for online bipartite matching of nonreusable resources (Karp et al. 1990) by reranking resources independently over time. Whereas reranking resources frequently has the same worst case performance as greedy, we show that reranking intermittently on a periodic schedule succeeds in addressing reusability of resources and performs significantly better than greedy in the worst case. Our second algorithm, which achieves a competitive ratio of 0.505, is a primal-dual randomized algorithm that works by suggesting up to two resources as candidate matches for every online vertex and then breaking the tie to make the final matching selection in a randomized correlated fashion over time. As a key component of our algorithm, we suitably adapt and extend the powerful technique of online correlated selection (Fahrbach et al. 2020) to reusable resources in order to induce negative correlation in our tie-breaking step and beat the competitive ratio of 0.5. Both of our results also extend to the case in which off-line vertices have weights. Funding: R. Niazadeh’s research is supported by the Asness Junior Faculty Fellowship at The University of Chicago Booth School of Business.

Minimizing age of information under arbitrary arrival model with arbitrary packet size

We consider a single source–destination pair, where information updates (in short, updates) arrive at the source at arbitrary time instants. For each update, its size, i.e. the service time required for complete transmission to the destination, is also arbitrary. At any time, the source may choose which update to transmit, while incurring transmission cost that is proportional to the duration of transmission. We consider the age of information (AoI) metric that quantifies the staleness of the update (information) at the destination. At any time, AoI is equal to the difference between the current time, and the arrival time of the latest update (at the source) that has been completely transmitted (to the destination). The goal is to find a causal (i.e. online) scheduling policy that minimizes the sum of the AoI and the transmission cost, where the possible decisions at any time are (i) whether to preempt the update under transmission upon arrival of a new update, and (ii) if no update is under transmission, then choose which update to transmit (among the available updates). In this paper, we propose a causal policy called SRPT+ that at each time, (i) preempts the update under transmission if a new update arrives with a smaller size (compared to the remaining size of the update under transmission), and (ii) if no update is under transmission, then from the set of available updates with size less than a threshold (which is a function of the transmission cost and the current AoI), begins to transmit the update for which the ratio of the reduction in AoI upon complete transmission (if not preempted in future) and the remaining size, is maximum. We characterize the performance of SRPT+ using a metric called the competitive ratio, i.e. the ratio of the cost of causal policy and the cost of an optimal offline policy (that knows the entire input in advance), maximized over all possible inputs. We show that the competitive ratio of SRPT+ is at most 5. In the special case when there is no transmission cost, we further show that the competitive ratio of SRPT+ is at most 3.

Scheduling In-Band Network Telemetry With Convergence-Preserving Federated Learning

Conducting federated learning across distributed sites with In-Band Network Telemetry (INT) based data collection faces critical challenges, including control decisions of different frequencies, convergence of the models being trained, and resource provisioning coupled over time. To study this problem, we formulate a non-linear mixed-integer program to optimize the long-term INT overhead, resource cost, and federated learning cost. We then design polynomial-time online algorithms to solve this problem with only observable inputs on the fly, featuring laziness-aware resource adaption, online-learning-based INT flow selection and model aggregation control, as well as expectation-preserving randomized dependent rounding. We rigorously prove the parameterized-constant competitive ratio of our approach against the offline optimum, and the time-averaged constraint violation that vanishes in the long run. With extensive trace-driven evaluations, we confirm the superiority of our approach over other alternative approaches for reducing total cost and the efficacy of our trained models for solving real machine learning problems, reducing the real-time cost by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$34\%$</tex-math> </inline-formula> on average.

A bi-criteria algorithm for online non-monotone maximization problems: DR-submodular+concave

In this paper, we study a class of online non-monotone maximization problems under general constraint set. In each round, the function fed back by the environment is of composite structure: the sum of a DR-submodular function and a concave function. This setting covers a wide range of applications. We propose a Frank-Wolfe type online algorithm for solving the considered problem. In our algorithm, there is no need to have the ability to obtain exact gradients of the revealed functions. Adopting the Lyapunov function approach and variance reduction technique, the algorithm is shown to have the bi-criteria competitive ratio (1/4,3/8) with sub-linear regret under selecting suitable parameters.

Online search with a hint

We introduce the study of search problems, in a setting in which the searcher has some information, or hint concerning the hiding target. In particular, we focus on one of the fundamental problems in search theory, namely the linear search problem. Here, an immobile target is hidden at some unknown position on an unbounded line, and a mobile searcher, initially positioned at some specific point of the line called the root, must traverse the line so as to locate the target. The objective is to minimize the worst-case ratio of the distance traversed by the searcher to the distance of the target from the root, which is known as the competitive ratio of the search.We consider three settings in regards to the nature of the hint: i) the hint suggests the exact position of the target on the line; ii) the hint suggests the direction of the optimal search (i.e., to the left or the right of the root); and iii) the hint is a general k-bit string that encodes some information concerning the target. Our objective is to study the Pareto-efficiency of strategies in this model, with respect to the tradeoff between consistency and robustness. Namely, we seek optimal, or near-optimal tradeoffs between the searcher's performance if the hint is correct (i.e., provided by a trusted source) and if the hint is incorrect (i.e., provided by an adversary).We prove several results in each of these three settings. For positional hints, we show that the optimal consistency of r-robust strategies is (br+1)/(br−1), where br is defined to be equal to ρr+ρr2−4ρr2, and ρr=(r−1)/2, for all r≥9. For directional hints, we show that for every b≥1 and δ∈(0,1], there exists a strategy with consistency equal to c=1+2(b2b2−1+δb3b2−1) and robustness equal to 1+2(b2b2−1+1δb3b2−1); furthermore, we show again that this upper bound is tight. Last, for general k-bit hints, we show upper bounds for general k-bit hints, as well as lower bounds: specifically, we show that the consistency of any 9-robust strategy must be at least 5, and that the consistency of r-robust strategies is at least 1+2br/(br−1), in the case of a natural class of asymptotic strategies.

The Online Broadcast Range-Assignment Problem

Let P={p_0,ldots ,p_{n-1}} be a set of points in {mathbb R}^d, modeling devices in a wireless network. A range assignment assigns a range r(p_i) to each point p_iin P, thus inducing a directed communication graph mathcal {G}_r in which there is a directed edge (p_i,p_j) iff {{,textrm{dist},}}(p_i, p_j) leqslant r(p_i), where {{,textrm{dist},}}(p_i,p_j) denotes the distance between p_i and p_j. The range-assignment problem is to assign the transmission ranges such that mathcal {G}_r has a certain desirable property, while minimizing the cost of the assignment; here the cost is given by sum _{p_iin P} r(p_i)^{alpha }, for some constant alpha >1 called the distance-power gradient. We introduce the online version of the range-assignment problem, where the points p_j arrive one by one, and the range assignment has to be updated at each arrival. Following the standard in online algorithms, resources given out cannot be taken away—in our case this means that the transmission ranges will never decrease. The property we want to maintain is that mathcal {G}_r has a broadcast tree rooted at the first point p_0. Our results include the following.We prove that already in {mathbb R}^1, a 1-competitive algorithm does not exist. In particular, for distance-power gradient alpha =2 any online algorithm has competitive ratio at least 1.57.For points in {mathbb R}^1 and {mathbb R}^2, we analyze two natural strategies for updating the range assignment upon the arrival of a new point p_j. The strategies do not change the assignment if p_j is already within range of an existing point, otherwise they increase the range of a single point, as follows: Nearest-Neighbor (nn) increases the range of {{,textrm{nn},}}(p_j), the nearest neighbor of p_j, to {{,textrm{dist},}}(p_j, {{,textrm{nn},}}(p_j)), and Cheapest Increase (ci) increases the range of the point p_i for which the resulting cost increase to be able to reach the new point p_j is minimal. We give lower and upper bounds on the competitive ratio of these strategies as a function of the distance-power gradient alpha . We also analyze the following variant of nn in {mathbb R}^2 for alpha =2: 2-Nearest-Neighbor (2-nn) increases the range of {{,textrm{nn},}}(p_j) to 2cdot {{,textrm{dist},}}(p_j,{{,textrm{nn},}}(p_j)),We generalize the problem to points in arbitrary metric spaces, where we present an O(log n)-competitive algorithm.

Competitive Control

We consider control from the perspective of competitive analysis. Unlike much prior work on learning-based control, which focuses on minimizing regret against the best controller selected in hindsight from some specific class, we focus on designing an online controller which competes against a clairvoyant offline optimal controller. A natural performance metric in this setting is competitive ratio, which is the ratio between the cost incurred by the online controller and the cost incurred by the offline optimal controller. Using operator-theoretic techniques from robust control, we derive a computationally efficient state-space description of the the controller with optimal competitive ratio in both finite-horizon and infinite-horizon settings. We extend competitive control to nonlinear systems using Model Predictive Control (MPC) and present numerical experiments which show that our competitive controller can significantly outperform standard <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{2}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> controllers in the MPC setting.

An improved online replenishment policy and its competitive ratio analysis for a purchase-to-order seller

An improved online replenishment policy and its competitive ratio analysis for a purchase-to-order seller

Interspecific Competition as Affected by Nitrogen Application in Sweet Corn–Soybean Intercropping System

Corn (Zea mays L.)–soybean (Glycine max (L.) Merr.) intercropping is one of the main traditional intercropping systems used. We hypothesized that sweet corn–soybean intercropping with reduced nitrogen application could improve the crops’ fresh grain yield and nitrogen acquisition. We clarified whether sweet corn intercropped with soybean has the advantages of improved crop yield and carbon and nitrogen accumulation and assessed interspecific competition in the intercropping systems. A four-year (2017–2020) field experiment was conducted with three nitrogen application levels (0, 150, and 300 kg∙ha−1) and three planting patterns (monocropped sweet corn, monocropped soybean, sweet corn–soybean intercropping) at Jiangxi Agricultural University, Nanchang, China. The LER (land equivalent ratio), AG (aggressivity), and CR (competitive ratio) were calculated using the fresh grain yield and nitrogen and carbon accumulation of sweet corn and soybean. The LER values were greater than 1.0 in most of the intercropped patterns, except for the value based on the crops’ fresh grain yield without nitrogen application in 2020. Sweet corn had greater values of CR and AG than soybean in the intercropping system. Compared with common nitrogen application (300 kg∙ha−1), reduced nitrogen application (150 kg∙ha−1) did not significantly reduce the LER or the average CR and AG values. Under reduced nitrogen application, the values of LER, CR, and AG, based on the crops’ fresh grain yield and nitrogen acquisition, were not significantly different between the four years. In conclusion, based on the LER, CR, and AG, sweet corn–soybean intercropping had the advantage of crop yield and nitrogen acquisition, and sweet corn was the superior competitor. Sweet corn–soybean intercropping with nitrogen application (150 kg N ha−1) showed good inter-annual stability of crop productivity and competitiveness of the sweet corn.

Breaking the 2-competitiveness barrier for two servers in a tree

A randomized on-line algorithm is given for the 2-server problem on a tree, with competitiveness less than 1.94 against the oblivious adversary. This is the first algorithm for this problem with competitive ratio less than 2. The algorithm generalizes earlier work for the line using fractional analysis, and defines a potential in terms of isolation indices from T-theory.

Online cardinality constrained scheduling

In online load balancing problems, jobs arrive over a list. Upon arrival of a job, the algorithm is required to assign it immediately and irrevocably to a machine. We consider such a makespan minimization problem with an additional cardinality constraint, i.e., at most k jobs may be assigned to each machine, where k is a parameter of the problem. We present both upper and lower bounds on the competitive ratio of online algorithms for this problem with identical machines.

The Secretary Problem with Predictions

The value maximization version of the secretary problem is the problem of hiring a candidate with the largest value from a randomly ordered sequence of candidates. In this work, we consider a setting where predictions of candidate values are provided in advance. We propose an algorithm that achieves a nearly optimal value if the predictions are accurate and results in a constant-factor competitive ratio otherwise. We also show that the worst-case competitive ratio of an algorithm cannot be higher than some constant [Formula: see text], which is the best possible competitive ratio when we ignore predictions, if the algorithm performs nearly optimally when the predictions are accurate. Additionally, for the multiple-choice secretary problem, we propose an algorithm with a similar theoretical guarantee. We empirically illustrate that if the predictions are accurate, the proposed algorithms perform well; meanwhile, if the predictions are inaccurate, performance is comparable to existing algorithms that do not use predictions.

Optimized Controller Provisioning in Software-Defined LEO Satellite Networks

The controller provisioning, which adjusts the number, locations, and members of satellite controllers adaptive to the dynamic network load and topology, fundamentally impacts the performance of software-defined satellite networks (SDSNs). An ideal provisioning strategy should achieve a low total control overhead throughout the entire satellite operation period, which is extremely challenging since the network load can only be predicted in a short time scale. Existing methods can hardly achieve this goal for they greedily configure controllers in each time slot, where switches have to frequently migrate from one controller to another. In this paper, we focus on achieving globally optimized strategies with only current network load information. We firstly propose a comprehensive control overhead model and formulate the Controller Provisioning Problem (CPP) in SDSNs as a non-convex integer programming problem. To solve the problem, we propose an approximate algorithm named AROA by introducing a regularization framework and based on randomized rounding. We theoretically derive its competitive ratio. To produce strategies in time for future large satellite constellations, we further propose a more efficient heuristic algorithm HROA. Evaluations on our built simulation system show that our proposed methods significantly outperform related schemes in control overhead, latency, and scalability.

Efficient Distributed DNNs in the Mobile-Edge-Cloud Continuum

In the mobile-edge-cloud continuum, a plethora of heterogeneous data sources and computation-capable nodes are available. Such nodes can cooperate to perform a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">distributed</i> learning task, aided by a learning controller (often located at the network edge). The controller is required to make decisions concerning (i) data selection, i.e., which data sources to use; (ii) model selection, i.e., which machine learning model to adopt, and (iii) matching between the layers of the model and the available physical nodes. All these decisions influence each other, to a significant extent and often in counter-intuitive ways. In this paper, we formulate a problem addressing all of the above aspects and present a solution concept called RightTrain, aiming at making the aforementioned decisions in a joint manner, minimizing energy consumption subject to learning quality and latency constraints. RightTrain leverages an expanded-graph representation of the system and a delay-aware Steiner tree to obtain a provably near-optimal solution while keeping the time complexity low. Specifically, it runs in polynomial time and its decisions exhibit a competitive ratio of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2(1+\epsilon)$</tex-math> </inline-formula> , outperforming state-of-the-art solutions by over 50%. Our approach is also validated through a real-world implementation.

A good balance for an online scheduling problem considering both learning and deteriorating effects in the handicraft process

The paper considers an online scheduling problem with the effects of both learning and deterioration to minimize the total completion time. More specifically, we assume that the actual processing length of job Jj is p jr = p j r b + at , where pj is the initial processing time of Jj , t is the starting time of Jj , r is the seating arrangement position of Jj , b is the learning factor and a is the deterioration factor, respectively. For this problem, we show that the performance ratio of any deterministic online algorithm is not <2 and provide a best possible online algorithm DSBPT with a competitive ratio of 2. Furthermore, we also present a concise computational simulation study to verify the effectiveness and efficiency of the proposed algorithm DSBPT, as well as the management implications provided for decision-makers to production optimization.

Online scheduling with deterioration and unexpected processor breakdown

In this paper, we investigate a single processor scheduling problem where the breakdown interval emerges on the processor in an online way. In particular, in our setting, the relevant data of each job Jk, including the release date rk and the deteriorating rate bk, is known in advance. Furthermore, for each job Jk, its processing time pk is a simple linear function of its starting time Sk, i.e., pk=bkSk. We are interested in scheduling the jobs to minimize the makespan. In addition, we indicate that, there exists no online algorithm such that the competitive ratio is less than 1+bmin, where bmin=min1≤k≤n⁡bk. Moreover, we propose an online algorithm with a competitive ratio of 1+bmax, where bmax=max1≤k≤n⁡bk.

Augmenting productivity and profitability through Sesame–Legume intercropping

IntroductionIntercropping contributes a significant role in sustainable agricultural system as it improves soil conservation, productivity and stability of yield and makes better use of production elements. However, the economic advantages and dis advantages of sesame and legume intercropping is not quantified. MethodsField experiment, consisted of seven treatments, conducted in 2016 and 2017 cropping seasons using randomized complete block design with three replications. Land equivalent ratio, Competitive Ratio (CR), Relative crowding coefficient (K), Aggressivity (A), Sesame equivalent yield, Legume equivalent yield (LEY), Monetary Advantage Index, Area Time Equivalent Ratio (ATER), Land Saved and correlation of the indexes were competed. ResultsThe highest total LER (0.63) recorded from sesame intercropped with half as well as full seed rate of mungbean. Sesame intercropped with half seed rate of mungbean showed lower CR (1.57) and the total K of the system was greater than a unity in three of the treatments except in sesame + half seed rate of soybean with total K of 0.81. Sesame intercropped with half seed rate of soybean was dominant with aggressivity (0.13) while it was dominated in both of the other treatments with negative aggressivity. The highest MAI (1181.15 and 1239.1) was gained from sesame intercropped with mungbean at full and half seed rates respectively and the ATER value of sesame + half seed rate of soybean was greater than a unity while sesame + half seed rate of soybean scored lower than unity (0.94). Grain yield showed a positively strong correlation with LEY, SEY, and Ktot while it showed a negative correlation with CRs and As. Based on the PCA biplot the intercropping indexes grouped in to three clusters (I-III): cluster I, II and III consisted of 3, 1 and 9 intercropping indexes respectively. ConclusionLS, LER and MAI are the best indexes to compute the economic profitability of a mixed cropping. Generally, based on the LS, LER and MAI sesame-legume intercropping practice is economically profitable.