Standard Greedy Algorithm Research Articles

Large-W limit of the knapsack problem.

We formulate the knapsack problem (KP) as a statistical physics system and compute the corresponding partition function as an integral in the complex plane. The introduced formalism allows us to derive three statistical-physics-based algorithms for the KP: one based on the recursive definition of the exact partition function, another based on the large weight limit of that partition function, and a final one based on the zero-temperature limit of the second. Comparing the performances of the algorithms, we find that they do not consistently outperform (in terms of runtime and accuracy) dynamic programming, annealing, or standard greedy algorithms. However, the exact partition function is shown to reproduce the dynamic programming solution to the KP, and the zero-temperature algorithm is shown to produce a greedy solution. Therefore, although dynamic programming and greedy solutions to the KP are conceptually distinct, a statistical physics formalism introduced reveals that the large weight-constraint limit of the former leads to the latter. We conclude by discussing how to extend this formalism in order to obtain more accurate versions of the introduced algorithms and other similar combinatorial optimization problems.

Expanding Reverse Nearest Neighbors

In a graph, the reverse nearest neighbors (RNN) of vertex f refer to the set of vertices that consider f as their nearest neighbor. When f represents a facility like a subway station, its RNN comprises potential users who prefer the nearest facility. In practice, there may be underutilized facilities with small RNN sizes, and relocating these facilities to expand their service can be costly or infeasible. A more cost-effective approach involves selectively upgrading some edges (e.g., reducing their weights) to expand the RNN sizes of underutilized facilities. This motivates our research on the Expanding Reverse Nearest Neighbors (ERNN) problem, which aims to maximize the RNN size of a target facility by upgrading a limited number of edges. Solving the ERNN problem allows underutilized facilities to serve more users and alleviate the burden on other facilities. Despite numerous potential applications, ERNN is hard to solve: It can be proven to be NP-hard and APX-hard, and it exhibits non-monotonic and non-submodular properties. To overcome these challenges, we propose novel greedy algorithms that improve efficiency by minimizing the number of edges that need to be processed and the cost of processing each edge. Experimental results demonstrate that the proposed algorithms achieve orders of magnitude speedup compared to the standard greedy algorithm while greatly expanding the RNN.

On the spanning and routing ratios of the directed Θ6-graph

The family of Θk-graphs is an important class of sparse geometric spanners with a small spanning ratio. Although they are a well-studied class of geometric graphs, no bound is known on the spanning and routing ratios of the directed Θ6-graph. We show that the directed Θ6-graph of a point set P, denoted Θ→6(P), is a 7-spanner and there exist point sets where the spanning ratio is at least 4−ε, for any ε>0. It is known that the standard greedy Θ-routing algorithm may have an unbounded routing ratio on Θ→6(P). We design a simple, online, local, memoryless routing algorithm on Θ→6(P) whose routing ratio is at most 8 and show that no algorithm can have a routing ratio better than 6−ε.

The Network Visibility Problem

Social media is an attention economy where broadcasters are constantly competing for attention in their followers’ feeds. Broadcasters are likely to elicit greater attention from their followers if their posts remain visible at the top of their followers’ feeds for a longer period of time. However, this depends on the rate at which their followers receive information in their feeds, which in turn depends on the broadcasters they follow. Motivated by this observation and recent calls for fairness of exposure in social networks, in this article, we look at the task of recommending links from the perspective of visibility optimization. Given a set of candidate links provided by a link recommendation algorithm, our goal is to find a subset of those links that would provide the highest visibility to a set of broadcasters. To this end, we first show that this problem reduces to maximizing a nonsubmodular nondecreasing set function under matroid constraints. Then, we show that the set function satisfies a notion of approximate submodularity that allows the standard greedy algorithm to enjoy theoretical guarantees. Experiments on both synthetic and real data gathered from Twitter show that the greedy algorithm is able to consistently outperform several competitive baselines.

Universal quantum state preparation via revised greedy algorithm

Preparation of quantum state lies at the heart of quantum information processing. The greedy algorithm provides a potential method to effectively prepare quantum state. However, the standard greedy (SG) algorithm, in general, cannot take the global maxima and instead becomes stuck on a local maxima. Based on the SG algorithm, in this paper we propose a revised version to design dynamic pulses to realize universal quantum state preparation, i.e. preparing an arbitrary state from another arbitrary one. As applications, we implement this scheme to the universal preparation of single- and two-qubit state in the context of semiconductor quantum dots and superconducting circuits. Evaluation results show that our scheme outperforms the alternative numerical optimizations with higher preparation quality while possesses the comparable high efficiency. Compared with the emerging machine learning, it shows better accessibility and does not require any training. Moreover, the numerical results show that the pulse sequences generated by our scheme are robust against various errors and noises. Our scheme opens a new avenue of optimization in few-level system and limited action space quantum control problems.

The Machine-Part Cell Formation Problem with Non-Binary Values: A MILP Model and a Case of Study in the Accounting Profession

The traditional machine-part cell formation problem simultaneously clusters machines and parts in different production cells from a zero–one incidence matrix that describes the existing interactions between the elements. This manuscript explores a novel alternative for the well-known machine-part cell formation problem in which the incidence matrix is composed of non-binary values. The model is presented as multiple-ratio fractional programming with binary variables in quadratic terms. A simple reformulation is also implemented in the manuscript to express the model as a mixed-integer linear programming optimization problem. The performance of the proposed model is shown through two types of empirical experiments. In the first group of experiments, the model is tested with a set of randomized matrices, and its performance is compared to the one obtained with a standard greedy algorithm. These experiments showed that the proposed model achieves higher fitness values in all matrices considered than the greedy algorithm. In the second type of experiment, the optimization model is evaluated with a real-world problem belonging to Human Resource Management. The results obtained were in line with previous findings described in the literature about the case study.

An energy‐aware virtual machines consolidation method for cloud computing: Simulation and verification

AbstractCloud systems have become an essential part of our daily lives owing to various Internet‐based services. Consequently, their energy utilization has also become a necessary concern in cloud computing systems increasingly. Live migration, including several virtual machines (VMs) packed on in minimal physical machines (PMs) as virtual machines consolidation (VMC) technique, is an approach to optimize power consumption. In this article, we have proposed an energy‐aware method for the VMC problem, which is called energy‐aware virtual machines consolidation (EVMC), to optimize the energy consumption regarding the quality of service guarantee, which comprises: (1) the support vector machine classification method based on the utilization rate of all resource of PMs that is used for PM detection in terms of the amount' load; (2) the modified minimization of migration approach which is used for VM selection; (3) the modified particle swarm optimization which is implemented for VM placement. Also, the evaluation of the functional requirements of the method is presented by the formal method and the non‐functional requirements by simulation. Finally, in contrast to the standard greedy algorithms such as modified best fit decreasing, the EVMC decreases the active PMs and migration of VMs, respectively, 30%, 50% on average. Also, it is more efficient for the energy 30% on average, resources and the balance degree 15% on average in the cloud.

A Performance Study of Some Approximation Algorithms for Computing a Small Dominating Set in a Graph

We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent Linear programming (LP) rounding algorithms and a hybrid algorithm that we design by combining the greedy and LP rounding algorithms. Over the range of test data, all algorithms perform better than anticipated in theory, and have small performance ratios, measured as the size of output divided by the LP objective lower bound. However, each have advantages over the others. For instance, LP rounding algorithm normally outperforms the other algorithms on sparse real-world graphs. On a graph with 400,000+ vertices, LP rounding took less than 15 s of CPU time to generate a solution with performance ratio 1.011, while the greedy and hybrid algorithms generated solutions of performance ratio 1.12 in similar time. For synthetic graphs, the hybrid algorithm normally outperforms the others, whereas for hypercubes and k-Queens graphs, greedy outperforms the rest. Another advantage of the hybrid algorithm is to solve very large problems that are suitable for application of LP rounding (sparse graphs) but LP formulations become formidable in practice and LP solvers crash, as we observed on a real-world graph with 7.7 million+ vertices and a planar graph on 1,000,000 vertices.

Population Distribution of GvL and GvH Minor Histocompatibility Antigens

Background: Donor-derived T cells that target minor histocompatibility antigens (mHAs) in allogeneic hematopoietic cell transplant (HCT) mediate graft versus leukemia (GvL) and graft versus host (GvH) effects. Prediction of mHAs that drive GvL has garnered interest for targeted immunotherapy, but there have been few large-scale studies of population prevalence of predicted mHAs. Prioritization of mHAs that are shared among patients would allow for treatment of more individuals with mHA-targeting therapies. We report here population metrics of predicted mHAs in a dataset of over 3000 patients treated with HCT and reported to CIBMTR from 2000-2011. Our goal is to identify the most common mHAs within leukemia and Myelodysplastic Syndrome (MDS) patient populations to target with T cell immunotherapies or graft engineering techniques. Methods: Data is derived from two cohorts of donor recipient HCT pairs (DRPs) treated for Acute Myeloid Leukemia (AML), Acute Lymphocytic Leukemia (ALL), and MDS from the CIBMTR and previously analyzed in DISCOVeRY-BMT. Cohort 1 included 2609 10/10 HLA-matched DRPs treated from 2000-2008, and Cohort 2 included 572 10/10 HLA-matched DRPs treated from 2009-2011 plus 351 8/8 HLA-matched DRPs treated from 2000-2011 (Hahn et al. 2015, Biol Blood Marrow Transplant). Cohorts were combined for analyses. Approximately 20,000 missense SNPs were extracted from Illumina HumanOmni Express genotyping data. Computational mHA prediction was performed according to prior work from our lab (Lansford et al. 2018, Blood Adv.). Minor mismatches were predicted based on coding SNPs present in the recipient but not donor. mHAs were defined as mismatches that would lead to variant peptides predicted to bind at least 1 recipient HLA molecule and be expressed in leukemia cells (GvL mHA) and/or acute GvHD target organs (GvH mHA). GvL mHAs were categorized as "GvL,No_GvH" or "GvL" based on transcripts per million (TPM) corresponding to GvH organs, with "GvL" indicating between 5-50 TPM and "GvL,No_GvH" indicating <5 TPM. GvH mHAs were categorized similarly with respect to expression in leukemia cells. "GvL,GvH" indicated mHAs expressed highly in both leukemia and in GvHD target organs. Results: Patient demographics and number of total predicted mHAs from each ethnic group are shown in Table 1. Number of predicted mHAs per patient varied widely both within and between HLA types (Figure 1). Despite underrepresentation of some ethnic groups in our dataset, we identified thousands of potential mHAs in each group (Figure 2A). GvL mHA and GvH mHA proportions were similar across recipient ethnicities (Figure 2A-B). GvL mHA made up approximately half of predicted mHAs for each ethnic group (Figure 2B). Total numbers of mHAs per HCT recipient were significantly different between recipient ethnic groups within each cohort (Figure 2C). Although proportions of GvL vs GvH mHAs were stable across HLA alleles, there were substantial differences in number of predicted mHA by allele (Figure 3). Despite limited representation of some HLA types in our dataset, we were able to identify GvL mHAs for potential therapeutic targeting corresponding to 56 HLA alleles. We generated ranked lists of the most common shared mHA for each HLA allele, using an implementation of the standard greedy algorithm solution to the maximum set coverage problem. With this method, we identified the fewest number of mHA peptides needed to cover desired percentages of the recipient population with at least one mHA. For example, for HLA A*02:01, HLA*B07:02, and HLA*C07:01, engineering T cells to target the top nine to twelve peptides would allow for treatment of 80% of the patient population in our cohorts (Figure 4). These represent common HLA alleles in Caucasian, African American, Hispanic, and Asian populations, indicating that this technique can identify targets that could be therapeutically beneficial for a greater diversity of patients than standard treatments. mHA pools can also be filtered on peptide expression or HLA binding to ensure that the targeted peptides are highly expressed and presented. Conclusions: Despite differences in predicted number of mHA by ethnicity and HLA alleles, shared GvL mHA exist across common HLA. To the extent that these are targetable by adoptive cellular therapy, we can expand equal access to mHA targeted immunotherapies, improving upon traditional models where only the most prevalent HLA types are covered. Disclosures Armistead: Cell Microsystems: Patents & Royalties: Patent application U.S. 16/347,104 "Automated collection of a specified number of cells"; GeneCentric: Consultancy. Vincent:GeneCentric Therapeutics: Consultancy.

A Comprehensive Analysis of ACO for Wireless Sensor Network Routing

The proliferations of IoT technologies and applications have led to an increased interest in Wireless Sensor Networks (and in particular, multi-hop networks). Wireless sensor networks are composed of small mobile terminals which have limited system resources. Due to this, these networks are vulnerable to changes in network status arising from changes in the network parameters such as, position / layout of sensors, signal strength, environmental conditions, etc. In addition, the network nodes are also constrained in terms of energy provided by the battery. It is an significant consideration to be accounted so as to prolong their operational time, since this adds to the network lifetime. Lot of research has gone into routing and transmission technologies for wireless sensor networks. Conventional routing mechanisms for WSNs still suffer from energy-hole problem caused by difficulties in adaptive route management. Thus, it is imperative that efficient routing mechanisms be developed in order to conserve energy and improve network lifetime. One popular approach is to use meta-heuristic algorithms for optimal path selection in a WSN route management system. A very popular meta-heuristic algorithm used for this objective is the Ant Colony Optimization (ACO) algorithms. ACO has been used as a base for many routing management systems. In this paper an extensive analysis of the performance of ACO based route selection mechanism is reported and also reporting a comparative analysis of efficacy of the ACO routing algorithm over the standard Greedy algorithm in finding routes with different count of sensor nodes and different count of ants. Then find that the ACO routing algorithm outdoes the Greedy algorithm with respect to the number of routes identified.

The Approximability of Multiple Facility Location on Directed Networks with Random Arc Failures

We introduce and study the maximum reliability coverage problem, where multiple facilities are to be located on a network whose arcs are subject to random failures. Our model assumes that arcs fail independently with non-uniform probabilities, and the objective is to locate a given number of facilities, aiming to maximize the expected demand serviced. In this context, each demand point is said to be serviced (or covered) when it is reachable from at least one facility by an operational path. The main contribution of this paper is to establish tight bounds on the approximability of maximum reliability coverage on bidirected trees as well as on general networks. Quite surprisingly, we show that this problem is NP-hard on bidirected trees via a carefully-constructed reduction from the partition problem. On the positive side, we make use of approximate dynamic programming ideas to devise an FPTAS on bidirected trees. For general networks, while maximum reliability coverage is $$(1 - 1/e + \epsilon )$$ -inapproximable as an extension of the max k-cover problem, even estimating its objective value is #P-complete, due to generalizing certain network reliability problems. Nevertheless, we prove that by plugging-in a sampling-based additive estimator into the standard greedy algorithm, a matching approximation ratio of $$1 - 1/e - \epsilon $$ can be attained.

Systematic comparison between methods for the detection of influential spreaders in complex networks

Influence maximization is the problem of finding the set of nodes of a network that maximizes the size of the outbreak of a spreading process occurring on the network. Solutions to this problem are important for strategic decisions in marketing and political campaigns. The typical setting consists in the identification of small sets of initial spreaders in very large networks. This setting makes the optimization problem computationally infeasible for standard greedy optimization algorithms that account simultaneously for information about network topology and spreading dynamics, leaving space only to heuristic methods based on the drastic approximation of relying on the geometry of the network alone. The literature on the subject is plenty of purely topological methods for the identification of influential spreaders in networks. However, it is unclear how far these methods are from being optimal. Here, we perform a systematic test of the performance of a multitude of heuristic methods for the identification of influential spreaders. We quantify the performance of the various methods on a corpus of 100 real-world networks; the corpus consists of networks small enough for the application of greedy optimization so that results from this algorithm are used as the baseline needed for the analysis of the performance of the other methods on the same corpus of networks. We find that relatively simple network metrics, such as adaptive degree or closeness centralities, are able to achieve performances very close to the baseline value, thus providing good support for the use of these metrics in large-scale problem settings. Also, we show that a further 2–5% improvement towards the baseline performance is achievable by hybrid algorithms that combine two or more topological metrics together. This final result is validated on a small collection of large graphs where greedy optimization is not applicable.

2D Partial Unwinding-A Novel Non-Linear Phase Decomposition of Images.

This paper aims at proposing a novel 2D non-linear phase decomposition of images, which performs the image processing tasks better than the traditional Fourier transformation (linear phase decomposition), but further, it has additional mathematical properties allowing more effective image analysis, including adaptive decomposition components and positive instantaneous phase derivatives. 1D unwinding Blaschke decomposition has recently been proposed and studied. Through factorization it expresses arbitrary 1D signal into an infinite linear combination of Blaschke products. It offers fast converging positive frequency decomposition in the form of rational approximation. However, in the multi-dimensional cases, the usual factorization mechanism does not work. As a consequence, there is no genuine unwinding decomposition for multi-dimensions. In this paper, a 2D partial unwinding decomposition based on algebraic transforms reducing multi-dimensions to the 1D case is proposed and analyzed. The result shows that the fast convergence offers efficient image reconstruction. The tensor type decomposing terms are mutually orthogonal, giving rise to 2D positive frequency decomposition. The comparison results show that the proposed method outperforms the standard greedy algorithm and the most commonly used methods in the Fourier category. An application in watermarking is presented to demonstrate its potential in applications.

A Method for Optimized Deployment of Unmanned Aerial Vehicles for Maximum Coverage and Minimum Interference in Cellular Networks

We focus on the problem of deploying unmanned aerial vehicles to service mobile users in a cellular network, with the aim of maximizing coverage and reducing interference effects. An optimization model that is distributed in nature is proposed and a maximizing algorithm is developed to find a locally optimal solution. The performance of this distributed algorithm is shown to be superior in quality and solution time to a standard greedy algorithm. Testing on a simulation of a practical scenario is performed to demonstrate the application of the method to real scenarios as well as to illustrate the tradeoff between maximizing coverage and minimizing interference.

Matroidal Choice Functions

In some game-theoretic models, an agent is supposed to choose a subset of available items under a matroid constraint. If an agent always chooses a subset according to the standard greedy algorithm for matroids, then this choice rule fulfills the “substitutability," an essential property for the existence of equilibria in matching market models. In this paper, we introduce a notion of “matroidal choice functions" to capture the entire class of substitutable choice rules under a matroid constraint. For such functions, we provide two characterizations: one is by the behavior of an online greedy algorithm, and the other is by a local condition. We also show that matroidal choice functions extend choice rules defined by the maximization algorithm for valuated matroids and discrete concave functions.

An efficient ant colony optimization algorithm for the blocks relocation problem

In this paper we present an ant colony optimization (ACO) algorithm for the Blocks Relocation Problem (BRP). The method is applied to both versions of the problem most commonly considered in literature, i.e., the restricted (rBRP) and the unrestricted (uBRP) BRP with distinct due dates. In case of the uBRP a new heuristic is proposed and incorporated in a standard greedy algorithm. The performance of the basic greedy approach is enhanced by extending it to the ACO metaheuristic. In it, a novel approach for defining the pheromone matrix is proposed. More precisely, it only stores a small amount of information instead of the complete bay state. Further, we show that the proposed ACO method can easily be adapted for solving the BRP in which the objective function is related to the crane operation time. Our computational results show that the proposed approach manages to outperform existing methods for the BRP.

Exploring microservices for enhancing internet QoS

AbstractWith the enhancements in the field of software‐defined networking and virtualization technologies, novel networking paradigms such as network function virtualization and the Internet of Things are rapidly gaining ground. The development of Internet of Things and 5G networks and explosion in online services has resulted in an exponential growth of devices connected to the network. As a result, application service providers and Internet service providers are being confronted with the unprecedented challenge of accommodating increasing service and traffic demands from the geographically distributed users. To tackle this problem, many and ISPs, such as Netflix, Facebook, and AT&T, are increasingly adopting microservices application architecture. Despite the success of microservices in the industry, there is no specific standard or research work for service providers as guidelines, especially from the perspective of basic microservice operations. In this work, we aim to bridge this gap between the industry and the academia and discuss different microservice deployment, discovery, and communication options for service providers as a means to forming complete service chains. In addition, we address the problem of scheduling microservices across multiple clouds, including microclouds. We consider different user‐level service level agreements, such as latency and cost, while scheduling such services. We aim to reduce the overall turnaround time and costs for the deployment of complete end‐to‐end service. In this work, we present a novel affinity‐based fair weighted scheduling heuristic to solve this problem. We also compare the results of the proposed solution with standard greedy scheduling algorithms presented in the literature and observe significant improvements.

Improved Sufficient Conditions for Support Recovery of Sparse Signals Via Orthogonal Matching Pursuit

The orthogonal matching pursuit (OMP) algorithm is a standard greedy algorithm in the context of compressed sensing. Due to its high efficiency and effectiveness, OMP has drawn much attention in the recent decade. The goal of this paper is to study different conditions for stable recovery of sparse signals with OMP from a limited number of linear measurements for noisy signals. Specifically, two new sufficient conditions on the minimum magnitude of nonzero elements of sparse signals under which OMP can precisely recover the support of sparse signals are presented under the $\ell _{\infty }$ -Gaussian and bounded noise, respectively. Our conditions are much weaker when compared with the existing ones.

Utopia in the solution of the Bucket Order Problem

This paper deals with group decision making and, in particular, with rank aggregation, which is the problem of aggregating individual preferences (rankings) in order to obtain a consensus ranking. Although this consensus ranking is usually a permutation of all the ranked items, in this paper we tackle the situation in which some items can be tied, that is, the consensus shows that there is no preference among them. This problem has arisen recently and is known as the Optimal Bucket Order Problem (OBOP).In this paper we propose two improvements to the standard greedy algorithm usually considered to approach the bucket order problem: the Bucket Pivot Algorithm (BPA). The first improvement is based on the introduction of the Utopian Matrix, a matrix associated to a pair order matrix that represents the precedences in a collection of rankings. This idealization constitutes a superoptimal solution to the OBOP, which can be used as an extreme (sometimes feasible) best value. The second improvement is based on the use of several items as pivots to generate the bucket order, in contrast to BPA that only uses a single pivot. The set of items playing the role of decision-maker is dynamically created. We analyze separately the contribution of each improvement and also their joint effect. The statistical analysis of the experiments carried out shows that the combined use of both techniques is the best choice, showing a significant improvement in accuracy (17%) with respect to the original BPA and providing an important reduction in the variance of the output. Moreover, we provide decision rules to help the decision maker to select the right algorithm according to the problem instance.

Efficient influence spread estimation for influence maximization under the linear threshold model

This paper investigates the influence maximization (IM) problem in social networks under the linear threshold (LT) model. Kempe et al. (ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 137–146, 2003) showed that the standard greedy algorithm, which selects the node with the maximum marginal gain repeatedly, brings a -factor approximation solution to this problem. However, Chen et al. (International Conference on Data Mining, pp. 88–97, 2010) proved that the problem of computing the expected influence spread (EIS) of a node is #P-hard. Therefore, to compute the marginal gain exactly is computational intractable. We step-up on investigating efficient algorithm to compute EIS. We show that the EIS of a node can be computed by finding cycles through it, and we further develop an exact algorithm to compute EIS within a small number of hops and an approximation algorithm to estimate EIS without the hop constraint. Based on the proposed EIS algorithms, we finally develop an efficient greedy based algorithm for IM. We compare our algorithm with some well-known IM algorithms on four real-world social networks. The experimental results show that our algorithm is more accurate than others in finding the most influential nodes, and it is also better than or competitive with them in terms of running time. IM is a big topic in social network analysis. In this paper, we investigate efficient influence spread estimation for IM under the LT model. We develop two influence spread estimation algorithms and a new greedy based algorithm for IM under the LT model. The performance of the proposed algorithms are analyzed theoretically and evaluated through simulations.