Simple Optimal Algorithm Research Articles

A simple optimal algorithm for k-tuple dominating problem in interval graphs

A simple optimal algorithm for k-tuple dominating problem in interval graphs

Simple Optimal Sampling Algorithm to Strengthen Digital Soil Mapping Using the Spatial Distribution of Machine Learning Predictive Uncertainty: A Case Study for Field Capacity Prediction

Machine learning models are now capable of delivering coveted digital soil mapping (DSM) benefits (e.g., field capacity (FC) prediction); therefore, determining the optimal sample sites and sample size is essential to maximize the training efficacy. We solve this with a novel optimal sampling algorithm that allows the authentic augmentation of insufficient soil features using machine learning predictive uncertainty. Nine hundred and fifty-three forest soil samples and geographically referenced forest information were used to develop predictive models, and FCs in South Korea were estimated with six predictor set hierarchies. Random forest and gradient boosting models were used for estimation since tree-based models had better predictive performance than other machine learning algorithms. There was a significant relationship between model predictive uncertainties and training data distribution, where higher uncertainties were distributed in the data scarcity area. Further, we confirmed that the predictive uncertainties decreased when additional sample sites were added to the training data. Environmental covariate information of each grid cell in South Korea was then used to select the sampling sites. Optimal sites were coordinated at the cell having the highest predictive uncertainty, and the sample size was determined using the predictable rate. This intuitive method can be generalized to improve global DSM.

Optimal algorithms for scheduling under time-of-use tariffs

We consider a natural generalization of classical scheduling problems to a setting in which using a time unit for processing a job causes some time-dependent cost, the time-of-use tariff, which must be paid in addition to the standard scheduling cost. We focus on preemptive single-machine scheduling and two classical scheduling cost functions, the sum of (weighted) completion times and the maximum completion time, that is, the makespan. While these problems are easy to solve in the classical scheduling setting, they are considerably more complex when time-of-use tariffs must be considered. We contribute optimal polynomial-time algorithms and best possible approximation algorithms. For the problem of minimizing the total (weighted) completion time on a single machine, we present a polynomial-time algorithm that computes for any given sequence of jobs an optimal schedule, i.e., the optimal set of time slots to be used for preemptively scheduling jobs according to the given sequence. This result is based on dynamic programming using a subtle analysis of the structure of optimal solutions and a potential function argument. With this algorithm, we solve the unweighted problem optimally in polynomial time. For the more general problem, in which jobs may have individual weights, we develop a polynomial-time approximation scheme (PTAS) based on a dual scheduling approach introduced for scheduling on a machine of varying speed. As the weighted problem is strongly NP-hard, our PTAS is the best possible approximation we can hope for. For preemptive scheduling to minimize the makespan, we show that there is a comparably simple optimal algorithm with polynomial running time. This is true even in a certain generalized model with unrelated machines.

A general exact optimal sample allocation algorithm: With bounded cost and bounded sample sizes

With a bound on cost and bounds on stratum sample sizes, a cost weighted objective function is decomposed to reveal a general simple exact optimal sample allocation algorithm for minimizing sampling variances. Some known allocation methods are special cases.

Online Stochastic Matching: New Algorithms and Bounds

Online matching has received significant attention in recent years due to its close connection to Internet advertising. As the seminal work of Karp, Vazirani, and Vazirani has an optimal $$(1 - 1/{\mathbf {\mathsf{{e}}}})$$ competitive ratio in the standard adversarial online model, much effort has gone into developing useful online models that incorporate some stochasticity in the arrival process. One such popular model is the “known I.I.D. model” where different customer-types arrive online from a known distribution. We develop algorithms with improved competitive ratios for some basic variants of this model with integral arrival rates, including: (a) the case of general weighted edges, where we improve the best-known ratio of 0.667 due to Haeupler, Mirrokni and Zadimoghaddam (WINE, 2011) to 0.705; and (b) the vertex-weighted case, where we improve the 0.7250 ratio of Jaillet and Lu (Math Oper Res 39(3):624–646, 2013) to 0.7299. We also consider an extension of stochastic rewards, a variant where each edge has an independent probability of being present. For the setting of stochastic rewards with non-integral arrival rates, we present a simple optimal non-adaptive algorithm with a ratio of $$1-1/{\mathbf {\mathsf{{e}}}}$$ . For the special case where each edge is unweighted and has a uniform constant probability of being present, we improve upon $$1-1/{\mathbf {\mathsf{{e}}}}$$ by proposing a strengthened LP benchmark. One of the key ingredients of our improvement is the following (offline) approach to bipartite-matching polytopes with additional constraints. We first add several valid constraints in order to get a good fractional solution $$\mathbf {f}$$ ; however, these give us less control over the structure of $$\mathbf {f}$$ . We next remove all these additional constraints and randomly move from $$\mathbf{f }$$ to a feasible point on the matching polytope with all coordinates being from the set $$\{0, 1/k, 2/k, \ldots , 1\}$$ for a chosen integer k. The structure of this solution is inspired by Jaillet and Lu (2013) and is a tractable structure for algorithm design and analysis. The appropriate random move preserves many of the removed constraints (approximately with high probability and exactly in expectation). This underlies some of our improvements and could be of independent interest.

Task scheduling in distributed real-time systems

An approach to the flow shop scheduling of the computation process in distributed realtime systems is considered. This approach is based on the concept of a solvable class of systems for which simple optimal scheduling algorithms exist.

Joint Power Allocation and Subcarrier-Relay Assignment for OFDM-Based Decode-and-Forward Relay Networks

In this letter, the joint optimization problem of power allocation and subcarrier-relay assignment in orthogonal-frequency-division multiplexing-based decode-and-forward relaying network is addressed. The objective is to allocate the resources fairly to maximize the signal-to-noise ratio of the poorest channel. We propose a simple optimal algorithm with polynomial time complexity to solve this nonconvex optimization problem.

Energy-Efficient Transmission in Heterogeneous Wireless Networks: A Delay-Aware Approach

In this paper, we investigate the delay-aware energy-efficient transmission problem in dynamic heterogeneous wireless networks (HWNs) with time-variant channel conditions, random traffic loads, and user mobility. By jointly considering subcarrier assignment, power allocation, and time fraction determination, we formulate it as a stochastic optimization problem to maximize the system energy efficiency (EE) and to ensure network stability. By leveraging the fractional programming theory and the Lyapunov optimization technique, we first propose a general algorithm framework, referred to as the eTrans, to solve the formulation. Further, we exploit the special structure of the subproblem embedded in the eTrans to develop the extremely simple and low complexity but optimal algorithms for subcarrier assignment, power allocation, and time fraction determination. In particular, all of them have closed-form solutions, and no iteration is required, which paves the way for employing the eTrans to practical applications. The theoretical analysis and simulation results exhibit that eTrans can flexibly strike a balance between EE and average delay by simply tuning an introduced control parameter.

Decision-making without a brain: how an amoeboid organism solves the two-armed bandit.

Several recent studies hint at shared patterns in decision-making between taxonomically distant organisms, yet few studies demonstrate and dissect mechanisms of decision-making in simpler organisms. We examine decision-making in the unicellular slime mould Physarum polycephalum using a classical decision problem adapted from human and animal decision-making studies: the two-armed bandit problem. This problem has previously only been used to study organisms with brains, yet here we demonstrate that a brainless unicellular organism compares the relative qualities of multiple options, integrates over repeated samplings to perform well in random environments, and combines information on reward frequency and magnitude in order to make correct and adaptive decisions. We extend our inquiry by using Bayesian model selection to determine the most likely algorithm used by the cell when making decisions. We deduce that this algorithm centres around a tendency to exploit environments in proportion to their reward experienced through past sampling. The algorithm is intermediate in computational complexity between simple, reactionary heuristics and calculation-intensive optimal performance algorithms, yet it has very good relative performance. Our study provides insight into ancestral mechanisms of decision-making and suggests that fundamental principles of decision-making, information processing and even cognition are shared among diverse biological systems.

Using solvable classes in flowshop scheduling

A periodic processes scheduling problem appears for flexible manufacturing systems, computer systems, and other applications. The paper considers an approach to flow shop scheduling in terms of real-time distributed computing systems. The approach is based on the concept of solvable class of systems, for which simple optimal scheduling algorithms exist. The proposed approach belongs to the class of fast approximate algorithms; it slightly falls behind the known heuristic NEH algorithm regarding the optimality criterion, but it is much faster.

대용량 데이터 전송을 위한 다중 셀 MISO 하향 능동 안테나 시스템에서 3D 빔포밍 기법

본 논문은 다중 셀 다중입력 단일 출력 (MISO : multiple-input single-output) 하향링크 능동 안테나 시스템 (AAS : active antenna systems)에서 기지국의 수직 각도를 최적화하는 새로운 기법을 제시한다. 본 연구에서는 기존의 전역 탐색 방식 대신 간단하면서 최적의 값에 근사한 알고리듬들을 제안한다. 먼저, random matrix theory의 특성을 반영하여 평균 전송용량에 large system approximation이 적용된 수직적 빔포밍 알고리듬을 소개한다. 다음으로, signal-to-leakage-and-noise ratio (SLNR)을 기반으로 최적화 문제를 간단하게 만드는 수직적 빔포밍 알고리듬을 제안한다. 실험 결과를 통해 제안된 알고리듬들의 성능이 기존의 전역 탐색 알고리듬에 비해 복잡도가 매우 감소됨에도 불구하고 거의 비슷한 성능을 보임을 증명하였다. In this paper, we provide a new approach which optimizes the vertical tilting angle of the base station for multi-cell multiple-input single-output (MISO) downlink active antenna systems (AAS). Instead of the conventional optimal algorithm which requires an exhaustive search, we propose simple and near optimal algorithms. First, we represent a large system approximation based vertical beamforming algorithm which is applied to the average sum rate by using the random matrix theory. Next, we suggest a signal-to-leakage-and-noise ratio (SLNR) based vertical beamforming algorithm which simplifies the optimization problem considerably. In the simulation results, we demonstrate that the performance of the proposed algorithms is near close to the exhaustive search algorithm with substantially reduced complexity.

Flat-relative optimal extraction

Optimal extraction is a key step in processing the raw images of spectra as registered by two-dimensional detector arrays to a one-dimensional format. Previously reported algorithms reconstruct models for a mean one-dimensional spatial profile to assist a properly weighted extraction. We outline a simple optimal extraction algorithm including error propagation, which is very suitable for stabilised, fibre-fed spectrographs and does not model the spatial profile shape. A high signal-to-noise, master-flat image serves as reference image and is directly used as an extraction profile mask. Each extracted spectral value is the scaling factor relative to the cross-section of the unnormalised master-flat which contains all information about the spatial profile as well as pixel-to-pixel variations, fringing, and blaze. The extracted spectrum is measured relative to the flat spectrum. Using echelle spectra of the HARPS spectrograph we demonstrate a competitive extraction performance in terms of signal-to-noise and show that extracted spectra can be used for high precision radial velocity measurement. Pre- or post-flat-fielding of the data is not necessary, since all spectrograph inefficiencies inherent to the extraction mask are automatically accounted for. Also the reconstruction of the mean spatial profile by models is not needed, thereby reducing the number of operations to extract spectra. Flat-relative optimal extraction is a simple, efficient, and robust method that can be applied easily to stabilised, fibre-fed spectrographs.

Grouping Algorithm for Partner Selection in Cooperative Transmission

The partner selection problem for cooperative transmission is considered. Our objective is sum power minimization. We provide a simple optimal rate allocation algorithm for two cooperating node pairs and closed-form optimal rate allocations for some cases. With these results, we determine the partner for each node pair by Gabow's Algorithm. For a large number of nodes, we propose the grouping algorithm which is near-optimal but reduces the communication and computational overhead. We show the significant improvement of power consumption by our scheme and the fast convergence of the grouping algorithm through simulations.

Optimal Placement of PMUs by Integer Linear Programming

This letter presents a simple optimal placement algorithm of phasor measurement units (PMU) by using integer linear programming. Cases with and without conventional power flow and injection measurements are considered. The measurement placement problems under those cases are formulated as an integer linear programming which saves the CPU computation time greatly. Simulation results show that the proposed algorithm can be used in practice.

A simple optimal parallel algorithm for constructing a spanning tree of a trapezoid graph

Let G be a connected graph with n vertices. A spanning tree of G is an acyclic subgraph of G that has n vertices and n−1 edges. In this paper, we propose a simple optimal parallel algorithm for constructing a spanning tree of a trapezoid graph in O(log n) time with O(n/log n) processors on the EREW PRAM computational model.

A new compensation current real-time computing method for power active filter based on double linear construction algorithm

Considering the detection principle that “when load current is periodic current, the integral in a cycle for absolute value of load current subtracting fundamental active current is the least”, harmonic current real-time detection methods for power active filter are proposed based on direct computation, simple iterative algorithm and optimal iterative algorithm. According to the direct computation method, the amplitude of the fundamental active current can be accurately calculated when load current is placed in stable state. The simple iterative algorithm and the optimal iterative algorithm provide an idea about judging the state of load current. On the basis of the direct computation method, the simple iterative algorithm, the optimal iterative algorithm and precise definition of the basic concepts such as the true amplitude of the fundamental active current when load current is placed in varying state, etc., the double linear construction idea is proposed in which the amplitude of the fundamental active current at the moment of the sample is accurately calculated by using the first linear construction and the condition which disposes the next sample is created by using the second linear construction. On the basis of the double linear construction idea, a harmonic current real-time detection method for power active filter is proposed based on the double linear construction algorithm. This method has the characteristics of small computing quantity, fine real-time performance, being capable of accurately calculating the amplitude of the fundamental active current and so on.

Maximizing throughput in wireless networks via gossiping

A major challenge in the design of wireless networks is the need for distributed scheduling algorithms that will efficiently share the common spectrum. Recently, a few distributed algorithms for networks in which a node can converse with at most a single neighbor at a time have been presented. These algorithms guarantee 50% of the maximum possible throughput. We present the first distributed scheduling framework that guarantees maximum throughput . It is based on a combination of a distributed matching algorithm and an algorithm that compares and merges successive matching solutions. The comparison can be done by a deterministic algorithm or by randomized gossip algorithms. In the latter case, the comparison may be inaccurate. Yet, we show that if the matching and gossip algorithms satisfy simple conditions related to their performance and to the inaccuracy of the comparison (respectively), the framework attains the desired throughput.It is shown that the complexities of our algorithms, that achieve nearly 100% throughput, are comparable to those of the algorithms that achieve 50% throughput. Finally, we discuss extensions to general interference models. Even for such models, the framework provides a simple distributed throughput optimal algorithm.

Lowest common ancestors in trees and directed acyclic graphs

We study the problem of finding lowest common ancestors ( LCA) in trees and directed acyclic graphs ( DAGs). Specifically, we extend the LCA problem to DAGs and study the LCA variants that arise in this general setting. We begin with a clear exposition of Berkman and Vishkin's simple optimal algorithm for LCA in trees. Their ideas lay the foundation for our work on LCA problems in DAGs. We present an algorithm that finds all-pairs-representative LCA in DAGs in O ˜ ( n 2.688 ) operations, provide a transitive-closure lower bound for the all-pairs-representative-LCA problem, and develop an LCA-existence algorithm that preprocesses the DAG in transitive-closure time. We also present a suboptimal but practical O ( n 3 ) algorithm for all-pairs-representative LCA in DAGs that uses ideas from the optimal algorithms in trees and DAGs. Our results reveal a close relationship between the LCA, all-pairs-shortest-path, and transitive-closure problems. We conclude the paper with a short experimental study of LCA algorithms in trees and DAGs. Our experiments and source code demonstrate the elegance of the preprocessing-query algorithms for LCA in trees. We show that for most trees the suboptimal Θ ( n log n ) -preprocessing Θ ( 1 ) -query algorithm should be preferred, and demonstrate that our proposed O ( n 3 ) algorithm for all-pairs-representative LCA in DAGs performs well in both low and high density DAGs.

Scheduling in Switching Networks with Set-Up Delays

We consider the (preemptive bipartite scheduling problem PBS) (Crescenzi et al., “On approximating a scheduling problem,” Journal of Combinatorial Optimization, vol. 5, pp. 287–297, 2001) arising in switching communication systems, where each input and output port can be involved in at most one communication at the same time. Given a set of communication tasks to be communicated from the transmitters to the receivers of such a system, we aim to find a schedule minimizing the overall transmission time. To achieve this, we allow the preemption of communication tasks. However, in practice preemption comes with a cost, d, and this renders the problem NP-hard (Gopal et al., “An optimal switching algorithm for multibeam satellite systems with variable bandwidth beams,” IEEE Trans. Commun., vol.30, pp. 2475–2481, 1982). In this paper, we present a $$2 - \frac{1}{d+1}$$ approximation algorithm, which is the first one for the PBS problem with approximation ratio strictly less than two. Furthermore, we propose a simple optimal polynomial time algorithm for a subclass of instances of the PBS problem.

On the Strongly Connected and Biconnected Components of the Complement of Graphs

Abstract In this paper, we consider the problems of computing the strongly connected components and the biconnected components of the complement of a given graph. In particular, for a directed graph G on n vertices and m edges, we present a simple algorithm for computing the strongly connected components of G ¯ which runs in optimal O ( n + m ) time. The algorithm can be parallelized to yield an O ( log 2 n ) -time and O ( m 1.188 / log n ) -processor solution. As a byproduct, we obtain a very simple optimal parallel co-connectivity algorithm. Additionally, we establish properties which, for an undirected graph on n vertices and m edges, enable us to describe an O ( n + m ) -time algorithm for computing the biconnected components of G ¯ , which can be parallelized resulting in an algorithm that runs in O ( log n ) time using O ( ( n + m ) / log n ) processors.