Enumeration Algorithm Research Articles

Algorithms for Parallel Generic hp -Adaptive Finite Element Software

The hp -adaptive finite element method—where one independently chooses the mesh size ( h ) and polynomial degree ( p ) to be used on each cell—has long been known to have better theoretical convergence properties than either h - or p -adaptive methods alone. However, it is not widely used, owing at least in part to the difficulty of the underlying algorithms and the lack of widely usable implementations. This is particularly true when used with continuous finite elements. Herein, we discuss algorithms that are necessary for a comprehensive and generic implementation of hp -adaptive finite element methods on distributed-memory, parallel machines. In particular, we will present a multistage algorithm for the unique enumeration of degrees of freedom suitable for continuous finite element spaces, describe considerations for weighted load balancing, and discuss the transfer of variable size data between processes. We illustrate the performance of our algorithms with numerical examples and demonstrate that they scale reasonably up to at least 16,384 message passage interface processes. We provide a reference implementation of our algorithms as part of the open source library deal.II .

Competitive network restructuring with spatially loyal customers. A bilevel facility delocation problem

In this paper we address the problem faced by a company that needs to decide the number and location of facilities to close in order to reduce the size of their retail distribution network, whilst minimising the market share that is lost to their competitor, who is also engaged in a network reduction process. The problem is modelled as a bilevel competitive delocation model and is formulated as a variant of the well-known (r|p)-centroid problem. The formulation takes into account the existence of a certain level of customer loyalty, which implies that customers may decide to visit a more distant facility of their regular provider rather than rely on a closer competitor’s facility. A depth-first search implicit enumeration algorithm is proposed for solving a diverse set of instances of the problem. The analysis of an instance based on a real-life setting, and intensive numerical experimentation, provide evidence of the effectiveness of the algorithm for the solution of real-size problems, and confirm the practical validity of our modelling approach. Our results also highlight the importance of considering spatial loyalty in network restructuring scenarios.

Enumerating grammar-based extractions

We propose a new grammar-based language for defining information extractors from documents (text) that is built upon the well-studied framework of document spanners for extracting structured data from text. While previously studied formalisms for document spanners are mainly based on regular expressions, we use an extension of context-free grammars, called extraction grammars, to define the new class of context-free spanners. Extraction grammars are simply context-free grammars extended with variables that capture interval positions of the document, namely spans. While regular expressions are efficient for tokenizing and tagging, context-free grammars are also efficient for capturing structural properties. Indeed, we show that context-free spanners are strictly more expressive than their regular counterparts. We reason about the expressive power of our new class and present a pushdown-automata model that captures it. We show that extraction grammars can be evaluated with polynomial data complexity. Nevertheless, as the degree of the polynomial depends on the query, we present an enumeration algorithm for unambiguous extraction grammars that, after quintic preprocessing, outputs the results sequentially, without repetitions, with a constant delay between every two consecutive ones.

Enumerating Empty and Surrounding Polygons

We are given a set S of n points in the Euclidean plane. We assume that S is in general position. A simple polygon P is an empty polygon of S if each vertex of P is a point in S and every point in S is either outside P or a vertex of P. In this paper, we consider the problem of enumerating all the empty polygons of a given point set. To design an efficient enumeration algorithm, we use a reverse search by Avis and Fukuda with child lists. We propose an algorithm that enumerates all the empty polygons of S in O(n2 |ϵ(S) |)-time, where ϵ(S) is the set of empty polygons of S. Moreover, by applying the same idea to the problem of enumerating surrounding polygons of a given point set S, we propose an enumeration algorithm that enumerates them in O(n2)-delay, while the known algorithm enumerates in O(n2 log n)-delay, where a surrounding polygon of S is a polygon such that each vertex of the polygon is a point in S and every point in S is either inside the polygon or a vertex of the polygon.

Combination of Bases and an Evaluation of the Set of Extremal 3-Uniform Hypergraphs

The main problem with hypergraphs is their storage. If the hypergraph does not contain singularities, then sparse matrices are often used to describe it. Adjacency matrices are often used to work with k-uniform hypergraphs, but they take up a large amount of space in computer memory and, in general, storage of k-uniform arrays is not very convenient. Here we propose one solution for describing and storing extremal k-uniform hypergraphs. This base is a unique characteristic of an extremal hypergraph that uniquely describes it. In addition, bases can be used to search for the power of extremal k-uniform hypergraphs. We present base enumeration algorithms and present a hypothesis about the analytical form of formulas describing the cardinality of the set of extremal k-uniform hypergraphs. For this task, the base combination operation, also introduced here, is used.

Spatial focusing algorithm for source enumeration with rotating uniform circular sonar arrays

AbstractSource enumeration with large snapshots is feasible for a static uniform circular sonar array (UCSA). However, the dimension of the signal subspace in the array coordinate system exceeds the number of signal sources due to the rotation of the UCSA, which makes standard source enumeration ineffective. To address this issue, a spatial focusing approach for source enumeration with rotating UCSAs is presented. The approach is based on the concept of phase‐mode excitation and makes use of the UCSA heading information to achieve spatial focusing. The proposed algorithm provides reliable source enumeration with a high signal‐to‐noise ratio (SNR) when compared to the previous signal‐subspace transformation (SST) method. Simulations demonstrate that the proposed algorithm outperforms the other three methods in the conditions of a low SNR and a small angular separation.

Exact and heuristic algorithms for the domination problem

In a simple connected graph G=(V,E), a subset of vertices S⊆V is a dominating set if any vertex v∈V∖S is adjacent to some vertex x from this subset. A number of real-life problems can be modeled using this problem which is known to be among the difficult NP-hard problems in its class. We formulate the problem as an integer liner program (ILP) and compare the performance with the two earlier existing exact state-of-the-art algorithms and exact implicit enumeration and heuristic algorithms that we propose here. Our exact algorithm was able to find optimal solutions much faster than ILP and the above two exact algorithms for middle-dense instances. For graphs with a considerable size, our heuristic algorithm was much faster than both, ILP and our exact algorithm. It found an optimal solution for more than half of the tested instances, whereas it improved the earlier known state-of-the-art solutions for almost all the tested benchmark instances. Among the instances where the optimum was not found, it gave an average approximation error of 1.18.

Adjustable Robust Optimization with Discrete Uncertainty

In this paper, we study adjustable robust optimization (ARO) problems with discrete uncertainty. Under a very general modeling framework, we show that such two-stage robust problems can be exactly reformulated as ARO problems with objective uncertainty only. This reformulation is valid with and without the fixed recourse assumption and is not limited to continuous wait-and-see decision variables unlike most of the existing literature. Additionally, we extend an enumerative algorithm akin to a branch-and-cut scheme for which we study the asymptotic convergence. We discuss how to apply the reformulation on two variants of well-known optimization problems, a facility location problem in which uncertainty may affect the capacity values and a multiple knapsack problem with uncertain weights, and we report extensive computational results demonstrating the effectiveness of the approach. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This work was supported by the Air Force Office of Scientific Research [Grants FA8655-20-1-7012, FA8655-20-1-7019].

A Cooperative Hunting Method for Multi-USV Based on the A* Algorithm in an Environment with Obstacles.

A single unmanned surface combatant (USV) has poor mission execution capability, so the cooperation of multiple unmanned surface ships is widely used. Cooperative hunting is an important aspect of multi USV collaborative research. Therefore, this paper proposed a cooperative hunting method for multi-USV based on the A* algorithm in an environment with obstacles. First, based on the traditional A* algorithm, a path smoothing method based on USV minimum turning radius is proposed. At the same time, the post order traversal recursive algorithm in the binary tree method is used to replace the enumeration algorithm to obtain the optimal path, which improves the efficiency of the A* algorithm. Second, a biomimetic multi USV swarm collaborative hunting method is proposed. Multiple USV clusters simulate the hunting strategy of lions to pre-form on the target's path, so multiple USV clusters do not require manual formation. During the hunting process, the formation of multiple USV groups is adjusted to limit the movement and turning of the target, thereby reducing the range of activity of the target and improving the effectiveness of the algorithm. To verify the effectiveness of the algorithm, two sets of simulation experiments were conducted. The results show that the algorithm has good performance in path planning and target search.

Assessing edge-coupled interdependent network disintegration via rank aggregation and elite enumeration

The disintegration of networks is a widely researched topic with significant applications in fields such as counter-terrorism and infectious disease control. While the traditional approaches for achieving network disintegration involve identifying critical sets of nodes or edges, limited research has been carried out on edge-based disintegration strategies. We propose a novel algorithm, i.e., a rank aggregation elite enumeration algorithm based on edge-coupled networks (RAEEC), which aims to implement tiling for edge-coupled networks by finding important sets of edges in the network while balancing effectiveness and efficiency. Our algorithm is based on a two-layer edge-coupled network model with one-to-one links, and utilizes three advanced edge importance metrics to rank the edges separately. A comprehensive ranking of edges is obtained using a rank aggregation approach proposed in this study. The top few edges from the ranking set obtained by RAEEC are then used to generate an enumeration set, which is continuously iteratively updated to identify the set of elite attack edges. We conduct extensive experiments on synthetic networks to evaluate the performance of our proposed method, and the results indicate that RAEEC achieves a satisfactory balance between efficiency and effectiveness. Our approach represents a significant contribution to the field of network disintegration, particularly for edge-based strategies.

Solution techniques for Bi-level Knapsack Problems

Traditional funding mechanisms for healthcare projects involve ranking the projects and awarding funds based on their cost to benefit ratio. An alternative funding mechanism based on Bi-level programming was proposed in the literature. We refer to this as Donor-Recipient Bi-level Knapsack Problem (DR-BKP), which we explore further in this work. There are two participants, a leader (a donor agency) and a follower (recipient country) in this problem. Both the participants have their individual budgets. There is a set of projects, each having a certain cost and profit associated. The cost of projects are common to both the participants however the profits can be different for them. There is an external project that is of exclusive interest to the follower. The leader decides on cost subsidies to provide for the projects that is within her budget, while the follower solves a knapsack problem with the cost subsidised projects and the external project. Two enumerative algorithms were proposed in the literature for Bi-level problems with discrete upper level variables. We adapt them for DR-BKP that has continuous upper level variables having non-linear interaction with lower level variables. We first show the existence of a solution for DR-BKP and show the convergence of these algorithms. We provide evidence for Σ2P-hardness by showing that the problem is both NP-hard and Co-NP hard. Finally, we have implemented these two enumerative algorithms and shared the results and analyses of the computational experiments. A set of fifteen differing data sets each having randomly generated 10 instances have been solved to evaluate the performance of the proposed algorithms.

Heuristic algorithm for nested Markov decision process: Solution quality and computational complexity

A nested Markov decision process (NMDP) is a multi-level MDP consisting of an outer MDP and several inner MDPs. These MDPs are dependent on each other such that, each state of the outer MDP induces a unique inner MDP. We propose for the first time an algorithm to solve an infinite horizon nested Markov decision process under the average reward criterion (NMDP-HA). The algorithm incorporates the policy iteration method, which is composed of the value-determination operation and the policy improvement routine. To evaluate the solution quality and computational complexity of the NMDP-HA, we develop a specialized enumerative algorithm adapted from a completely observable MDP equivalent of the NMDP problem. The proposed NMDP-HA is illustrated with several numerical examples and our results for the problem instances evaluated indicate that the heuristic algorithm can find the same optimal solution in a fraction of the time the total enumeration algorithm uses to exhaustively search the entire solution space. For the cases, where the optimal solution is not found, the percentage deviation from the optimal solution is less than 5%.

Hereditary Cohesive Subgraphs Enumeration on Bipartite Graphs: The Power of Pivot-based Approaches

Finding cohesive subgraphs from a bipartite graph is a fundamental operator in bipartite graph analysis. In this paper, we focus on the problem of mining cohesive subgraphs from a bipartite graph that satisfy a hereditary property. Here a cohesive subgraph meets the hereditary property if all of its subgraphs satisfy the same property as itself. We show that several important cohesive subgraph models, such as maximal biclique and maximal k-biplex, satisfy the hereditary property. The problem of enumerating all maximal hereditary subgraphs was known to be NP-hard. To solve this problem, we first propose a novel and general pivot-based enumeration framework to efficiently enumerate all maximal hereditary subgraphs in a bipartite graph. Then, based on our general framework, we develop a new pivot-based algorithm with several pruning techniques to enumerate all maximal bicliques. We prove that the worst-case time complexity of our pivot-based maximal biclique enumeration algorithm is O(m x 2n/2 ) (or O(m\times 1.414^n)) which is near optimal since there exist up to O(2n/2 ) maximal bicliques in a bipartite graph with n vertices and m edges. Moreover, we also show that our algorithm can achieve polynomial-delay time complexity with a slight modification. Third, on the basis of our general framework, we also devise a novel pivot-based algorithm with several non-trivial pruning techniques to enumerate maximal k-biplexes in a bipartite graph. Finally, we conduct extensive experiments using 11 real-world bipartite graphs to evaluate the proposed algorithms. The results show that our pivot-based solutions can achieve one order of magnitude (three orders of magnitude) faster than the state-of-the-art maximal biclique enumeration algorithms (maximal k-biplex enumeration algorithms).

A TEDE Algorithm Studies the Effect of Dataset Grouping on Supervised Learning Accuracy

Datasets are the basis for research on deep learning methods in computer vision. The impact of the percentage of training sets in a dataset on the performance of neural network models needs to be further explored. In this paper, a twice equal difference enumeration (TEDE) algorithm is proposed to investigate the effect of different training set percentages in the dataset on the performance of the network model, and the optimal training set percentage is determined. By selecting the Pascal VOC dataset and dividing it into six different datasets from largest to smallest, and then dividing each dataset into the datasets to be analyzed according to five different training set percentages, the YOLOv5 convolutional neural network is used to train and test the 30 datasets to determine the optimal neural network model corresponding to the training set percentages. Finally, tests were conducted using the Udacity Self-Driving dataset with a self-made Tire Tread Defects (TTD) dataset. The results show that the network model performance is superior when the training set accounts for between 85% and 90% of the overall dataset. The results of dataset partitioning obtained by the TEDE algorithm can provide a reference for deep learning research.

Polynomial-delay enumeration algorithms in set systems

We consider a set system (V,C⊆2V) on a finite set V of elements, where we call a set C∈C a component. We assume that two oracles L1 and L2 are available, where given two non-empty subsets X⊆Y⊆V, L1(X,Y) returns a maximal component C∈C with X⊆C⊆Y; and given a set Y⊆V, L2(Y) returns all maximal components C∈C with C⊆Y. Given a system (V,C) along with a set I of items and a function σ:V→2I, a component C∈C is called a solution if the set of common items in C is inclusively maximal; i.e., ⋂v∈Cσ(v)⊋⋂v∈Xσ(v) for any component X∈C with C⊊X. We prove that there exists an algorithm of enumerating all solutions (or all components) in delay bounded by a polynomial with respect to the input size; an upper bound on the number of maximal components that is returned by L2; and the running times of the oracles.

A fuel-efficient reliable path finding algorithm in stochastic networks under spatial correlation

Transport activities are regarded as a major source of fuel consumption and CO2 emission production. To reduce the negative impact of traffic-related CO2 emission, this paper proposes a reliable path-finding algorithm for improving fuel efficiency in stochastic networks under the uncertainty of travel time and fuel consumption with the consideration of spatial correlation. A reliable constrained path-finding model is developed and formulated to minimize the fuel consumption budget while guaranteeing the specified on-time arrival probability. A heuristic label setting algorithm is developed to precisely solve the formulated problem. The proposed algorithm overcomes the time-consuming drawbacks of traditional path enumeration algorithms. The applicability and efficiency of the proposed algorithm are verified on real-world traffic data acquired from the Beijing and Xi‘an networks in China. The experiments demonstrate that our proposed algorithm can significantly reduce fuel consumption compared to existing studies. The experiment in Beijing shows that using the proposed algorithm can reduce 0.9 kg of CO2 emissions on average per trip compared to existing studies.

Efficient keyword search on graph data for finding diverse and relevant answers

PurposeThis paper studies a keyword search over graph-structured data used in various fields such as semantic web, linked open data and social networks. This study aims to propose an efficient keyword search algorithm on graph data to find top-k answers that are most relevant to the query and have diverse content nodes for the input keywords.Design/methodology/approachBased on an aggregative measure of diversity of an answer set, this study proposes an approach to searching the top-k diverse answers to a query on graph data, which finds a set of most relevant answer trees whose average dissimilarity should be no lower than a given threshold. This study defines a diversity constraint that must be satisfied for a subset of answer trees to be included in the solution. Then, an enumeration algorithm and a heuristic search algorithm are proposed to find an optimal solution efficiently based on the diversity constraint and an A* heuristic. This study also provides strategies for improving the performance of the heuristic search method.FindingsThe results of experiments using a real data set demonstrate that the proposed search algorithm can find top-k diverse and relevant answers to a query on large-scale graph data efficiently and outperforms the previous methods.Originality/valueThis study proposes a new keyword search method for graph data that finds an optimal solution with diverse and relevant answers to the query. It can provide users with query results that satisfy their various information needs on large graph data.

Routing battery-constrained delivery drones in a depot network: A business model and its optimization–simulation assessment

This paper proposes a novel business model for on-demand package shipment services using drones, and evaluates different modeling and solution approaches for the drone routing problem that underpins the service operation. In the proposed service, customers’ shipment orders of arbitrary origins and destinations, payload weights and bid values are collected every five minutes, and available drones from multiple depots are then dispatched to fulfill a subset of these orders in a way to maximize profit. A drone path starts from a depot, serves one or more customer orders in sequence, and ends at a depot for battery recharging, which incurs a fixed cost. Two mixed integer programming (MIP) formulations are presented to model the drone dispatch and routing problem. To improve solution efficiency, three computational approaches, including two column generation based algorithms and a brute-force path enumeration algorithm, are developed and compared. Computational experiments suggest, somewhat surprisingly, that the brute-force approach is the most effective and most scalable one, outperforming other alternatives by a substantial margin in both computing time and solution quality. Furthermore, an optimization–simulation framework is proposed to assess the system performance over a long horizon that spans multiple dispatch periods without complicating the optimization model. Using the simulation framework, useful managerial insights including the effects of battery capacity, wind condition and computing capability on the fleet dispatch operation, are generated, which will guide real-world implementations of the new business model.

Multi-objective holistic optimization method for CR SRPS based on cross-scale failure simulation of composite to improve oil recovery benefits

A carbon/glass hybrid fiber continuous sucker rod (CR) with lower specific gravity, better corrosion resistance and higher strength was developed to replace the steel rod in oil production. This paper proposes a multi-objective holistic optimization method of sucker rod pumping system (SRPS) using CR for improving oil recovery benefits. Firstly, based on the cross-scale failure criterion and finite element simulation, a judgment index for fatigue damage of CR and their joints under multiple loads, namely fatigue strength margin (FSM), is constructed, and used as a life characterization parameter of SRPS. After it is verified with liner correlation between the production cycle and FSM of realistic SRPS, FSM in addition to energy consumption and the production rate are included in the optimization objectives. Then, a multi-objective optimization model with the holistic parameters of CR SRPS as the decision variables is established. To improve the efficiency of solving the model, a hierarchical enumeration algorithm with the strategy of reducing the optimization space repeatedly by weakened constraints is presented. Finally, the proposed method was applied to the design of CR SRPS for realistic oil wells, its effectiveness and superiority are verified by the application effect and comparison results with current methods.

Enumeration of regular fractional factorial designs with four-level and two-level factors

Abstract Designs for screening experiments usually include factors with two levels only. Adding a few four-level factors allows for the inclusion of multi-level categorical factors or quantitative factors with possible quadratic or third-order effects. Three examples motivated us to generate a large catalogue of designs with two-level factors as well as four-level factors. To create the catalogue, we considered three methods. In the first method, we select designs using a search table, and in the second method, we use a procedure that selects candidate designs based on the properties of their projections into fewer factors. The third method is actually a benchmark method, in which we use a general orthogonal array enumeration algorithm. We compare the efficiencies of the new methods for generating complete sets of nonisomorphic designs. Finally, we use the most efficient method to generate a catalogue of designs with up to three four-level factors and up to 20 two-level factors for run sizes 16, 32, 64, and 128. In some cases, a complete enumeration was infeasible. For these cases, we used a bounded enumeration strategy instead. We demonstrate the usefulness of the catalogue by revisiting the motivating examples.