Fast Filtering of Search Results Sorted by Attribute

2022 ◽  
Vol 40 (2) ◽  
pp. 1-24
Franco Maria Nardini ◽  
Roberto Trani ◽  
Rossano Venturini

Modern search services often provide multiple options to rank the search results, e.g., sort “by relevance”, “by price” or “by discount” in e-commerce. While the traditional rank by relevance effectively places the relevant results in the top positions of the results list, the rank by attribute could place many marginally relevant results in the head of the results list leading to poor user experience. In the past, this issue has been addressed by investigating the relevance-aware filtering problem, which asks to select the subset of results maximizing the relevance of the attribute-sorted list. Recently, an exact algorithm has been proposed to solve this problem optimally. However, the high computational cost of the algorithm makes it impractical for the Web search scenario, which is characterized by huge lists of results and strict time constraints. For this reason, the problem is often solved using efficient yet inaccurate heuristic algorithms. In this article, we first prove the performance bounds of the existing heuristics. We then propose two efficient and effective algorithms to solve the relevance-aware filtering problem. First, we propose OPT-Filtering, a novel exact algorithm that is faster than the existing state-of-the-art optimal algorithm. Second, we propose an approximate and even more efficient algorithm, ϵ-Filtering, which, given an allowed approximation error ϵ, finds a (1-ϵ)–optimal filtering, i.e., the relevance of its solution is at least (1-ϵ) times the optimum. We conduct a comprehensive evaluation of the two proposed algorithms against state-of-the-art competitors on two real-world public datasets. Experimental results show that OPT-Filtering achieves a significant speedup of up to two orders of magnitude with respect to the existing optimal solution, while ϵ-Filtering further improves this result by trading effectiveness for efficiency. In particular, experiments show that ϵ-Filtering can achieve quasi-optimal solutions while being faster than all state-of-the-art competitors in most of the tested configurations.

2015 ◽  
Vol 07 (03) ◽  
pp. 1550032 ◽  
Abdullah N. Arslan ◽  
Betsy George ◽  
Kirsten Stor

The pattern matching with wildcards and length constraints problem is an interesting problem in the literature whose computational complexity is still open. There are polynomial time exact algorithms for its special cases. There are heuristic algorithms, and online algorithms that do not guarantee an optimal solution to the original problem. We consider two special cases of the problem for which we develop offline solutions. We give an algorithm for one case with provably better worst case time complexity compared to existing algorithms. We present the first exact algorithm for the second case. This algorithm uses integer linear programming (ILP) and it takes polynomial time under certain conditions.

Sensors ◽  
2019 ◽  
Vol 19 (2) ◽  
pp. 273 ◽  
Peihuang Huang ◽  
Wenxing Zhu ◽  
Longkun Guo

Given a set of sensors distributed on the plane and a set of Point of Interests (POIs) on a line segment, a primary task of the mobile wireless sensor network is to schedule covering the POIs by the sensors, such that each POI is monitored by at least one sensor. For balancing the energy consumption, we study the min-max line barrier target coverage (LBTC) problem which aims to minimize the maximum movement of the sensors from their original positions to their final positions at which the coverage is composed. We first proved that when the radius of the sensors are non-uniform integers, even 1-dimensional LBTC (1D-LBTC), a special case of LBTC in which the sensors are distributed on the line segment instead of the plane, is NP -hard. The hardness result is interesting, since the continuous version of LBTC to cover a given line segment instead of the POIs is known polynomial solvable. Then we present an exact algorithm for LBTC with uniform radius and sensors distributed on the plane, via solving the decision version of LBTC. We argue that our algorithm runs in time O ( n 2 log n ) and produces an optimal solution to LBTC. The time complexity compares favorably to the state-of-art runtime O ( n 3 log n ) of the continuous version which aims to cover a line barrier instead of the targets. Last but not the least, we carry out numerical experiments to evaluate the practical performance of the algorithms, which demonstrates a practical runtime gain comparing with an optimal algorithm based on integer linear programming.

2013 ◽  
Vol 4 (4) ◽  
pp. 23-45 ◽  
B. S. P. Mishra ◽  
S. Dehuri ◽  
G.-N. Wang

Nowadays computers are used to solve a variety and multitude of complex problems facing in every sphere of peoples’ life. However, many of the problems are intractable in nature exact algorithm might need centuries to manage with formidable challenges. In such cases heuristic or in a broader sense meta-heuristic algorithms that find an approximate solution but have acceptable time and space complexity play indispensable role. In this article, the authors present a state-of-the-art review on meta-heuristic algorithm popularly known as artificial bee colony (ABC) inspired by honey bees. Moreover, the ABC algorithm for solving single and multi-objective optimization problems have been studied. A few potential application areas of ABC are highlighted as an end note of this article.

2021 ◽  
Vol 72 ◽  
pp. 39-67
Shaowei Cai ◽  
Jinkun Lin ◽  
Yiyuan Wang ◽  
Darren Strash

This paper explores techniques to quickly solve the maximum weight clique problem (MWCP) in very large scale sparse graphs. Due to their size, and the hardness of MWCP, it is infeasible to solve many of these graphs with exact algorithms. Although recent heuristic algorithms make progress in solving MWCP in large graphs, they still need considerable time to get a high-quality solution. In this work, we focus on solving MWCP for large sparse graphs within a short time limit. We propose a new method for MWCP which interleaves clique finding with data reduction rules. We propose novel ideas to make this process efficient, and develop an algorithm called FastWClq. Experiments on a broad range of large sparse graphs show that FastWClq finds better solutions than state-of-the-art algorithms while the running time of FastWClq is much shorter than the competitors for most instances. Further, FastWClq proves the optimality of its solutions for roughly half of the graphs, all with at least 105 vertices, with an average time of 21 seconds.

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Fan Yuan ◽  
Dachuan Xu ◽  
Donglei Du ◽  
Min Li

<p style='text-indent:20px;'>We study stable instances of the <inline-formula><tex-math id="M2">\begin{document}$ k $\end{document}</tex-math></inline-formula>-means problem with penalties in fixed-dimensional Euclidean space. An instance of the problem is called <inline-formula><tex-math id="M3">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula>-stable if this instance exists a sole optimal solution and the solution keeps unchanged when distances and penalty costs are scaled by a factor of no more than <inline-formula><tex-math id="M4">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula>. Stable instances of clustering problem have been used to explain why certain heuristic algorithms with poor theoretical guarantees perform quite well in practical. For any fixed <inline-formula><tex-math id="M5">\begin{document}$ \epsilon &gt; 0 $\end{document}</tex-math></inline-formula>, we show that when using a common multi-swap local-search algorithm, a <inline-formula><tex-math id="M6">\begin{document}$ (1+\epsilon) $\end{document}</tex-math></inline-formula>-stable instance of the <inline-formula><tex-math id="M7">\begin{document}$ k $\end{document}</tex-math></inline-formula>-means problem with penalties in fixed-dimensional Euclidean space can be solved accurately in polynomial time.</p>

Tung T. Vu ◽  
Ha Hoang Kha

In this research work, we investigate precoder designs to maximize the energy efficiency (EE) of secure multiple-input multiple-output (MIMO) systems in the presence of an eavesdropper. In general, the secure energy efficiency maximization (SEEM) problem is highly nonlinear and nonconvex and hard to be solved directly. To overcome this difficulty, we employ a branch-and-reduce-and-bound (BRB) approach to obtain the globally optimal solution. Since it is observed that the BRB algorithm suffers from highly computational cost, its globally optimal solution is importantly served as a benchmark for the performance evaluation of the suboptimal algorithms. Additionally, we also develop a low-complexity approach using the well-known zero-forcing (ZF) technique to cancel the wiretapped signal, making the design problem more amenable. Using the ZF based method, we transform the SEEM problem to a concave-convex fractional one which can be solved by applying the combination of the Dinkelbach and bisection search algorithm. Simulation results show that the ZF-based method can converge fast and obtain a sub-optimal EE performance which is closed to the optimal EE performance of the BRB method. The ZF based scheme also shows its advantages in terms of the energy efficiency in comparison with the conventional secrecy rate maximization precoder design.

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 303
Nikolai Krivulin

We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings. We formulate the problem as a bi-objective optimization problem of constrained matrix approximation in the Chebyshev sense in logarithmic scale. The problem is to approximate the pairwise comparison matrices for each criterion simultaneously by a common consistent matrix of unit rank, which determines the vector of ratings. We represent and solve the optimization problem in the framework of tropical (idempotent) algebra, which deals with the theory and applications of idempotent semirings and semifields. The solution involves the introduction of two parameters that represent the minimum values of approximation error for each matrix and thereby describe the Pareto frontier for the bi-objective problem. The optimization problem then reduces to a parametrized vector inequality. The necessary and sufficient conditions for solutions of the inequality serve to derive the Pareto frontier for the problem. All solutions of the inequality, which correspond to the Pareto frontier, are taken as a complete Pareto-optimal solution to the problem. We apply these results to the decision problem of interest and present illustrative examples.

2021 ◽  
Vol 1 (2) ◽  
pp. 1-23
Arkadiy Dushatskiy ◽  
Tanja Alderliesten ◽  
Peter A. N. Bosman

Surrogate-assisted evolutionary algorithms have the potential to be of high value for real-world optimization problems when fitness evaluations are expensive, limiting the number of evaluations that can be performed. In this article, we consider the domain of pseudo-Boolean functions in a black-box setting. Moreover, instead of using a surrogate model as an approximation of a fitness function, we propose to precisely learn the coefficients of the Walsh decomposition of a fitness function and use the Walsh decomposition as a surrogate. If the coefficients are learned correctly, then the Walsh decomposition values perfectly match with the fitness function, and, thus, the optimal solution to the problem can be found by optimizing the surrogate without any additional evaluations of the original fitness function. It is known that the Walsh coefficients can be efficiently learned for pseudo-Boolean functions with k -bounded epistasis and known problem structure. We propose to learn dependencies between variables first and, therefore, substantially reduce the number of Walsh coefficients to be calculated. After the accurate Walsh decomposition is obtained, the surrogate model is optimized using GOMEA, which is considered to be a state-of-the-art binary optimization algorithm. We compare the proposed approach with standard GOMEA and two other Walsh decomposition-based algorithms. The benchmark functions in the experiments are well-known trap functions, NK-landscapes, MaxCut, and MAX3SAT problems. The experimental results demonstrate that the proposed approach is scalable at the supposed complexity of O (ℓ log ℓ) function evaluations when the number of subfunctions is O (ℓ) and all subfunctions are k -bounded, outperforming all considered algorithms.

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 511
Syed Mohammad Minhaz Hossain ◽  
Kaushik Deb ◽  
Pranab Kumar Dhar ◽  
Takeshi Koshiba

Proper plant leaf disease (PLD) detection is challenging in complex backgrounds and under different capture conditions. For this reason, initially, modified adaptive centroid-based segmentation (ACS) is used to trace the proper region of interest (ROI). Automatic initialization of the number of clusters (K) using modified ACS before recognition increases tracing ROI’s scalability even for symmetrical features in various plants. Besides, convolutional neural network (CNN)-based PLD recognition models achieve adequate accuracy to some extent. However, memory requirements (large-scaled parameters) and the high computational cost of CNN-based PLD models are burning issues for the memory restricted mobile and IoT-based devices. Therefore, after tracing ROIs, three proposed depth-wise separable convolutional PLD (DSCPLD) models, such as segmented modified DSCPLD (S-modified MobileNet), segmented reduced DSCPLD (S-reduced MobileNet), and segmented extended DSCPLD (S-extended MobileNet), are utilized to represent the constructive trade-off among accuracy, model size, and computational latency. Moreover, we have compared our proposed DSCPLD recognition models with state-of-the-art models, such as MobileNet, VGG16, VGG19, and AlexNet. Among segmented-based DSCPLD models, S-modified MobileNet achieves the best accuracy of 99.55% and F1-sore of 97.07%. Besides, we have simulated our DSCPLD models using both full plant leaf images and segmented plant leaf images and conclude that, after using modified ACS, all models increase their accuracy and F1-score. Furthermore, a new plant leaf dataset containing 6580 images of eight plants was used to experiment with several depth-wise separable convolution models.

2022 ◽  
Vol 24 (3) ◽  
pp. 0-0

This paper introduces a new approach of hybrid meta-heuristics based optimization technique for decreasing the computation time of the shortest paths algorithm. The problem of finding the shortest paths is a combinatorial optimization problem which has been well studied from various fields. The number of vehicles on the road has increased incredibly. Therefore, traffic management has become a major problem. We study the traffic network in large scale routing problems as a field of application. The meta-heuristic we propose introduces new hybrid genetic algorithm named IOGA. The problem consists of finding the k optimal paths that minimizes a metric such as distance, time, etc. Testing was performed using an exact algorithm and meta-heuristic algorithm on random generated network instances. Experimental analyses demonstrate the efficiency of our proposed approach in terms of runtime and quality of the result. Empirical results obtained show that the proposed algorithm outperforms some of the existing technique in term of the optimal solution in every generation.

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