Tax code prediction is a crucial yet underexplored task in automating invoicing and compliance management for large-scale e-commerce platforms. Each product must be accurately mapped to a node within a multi-level taxonomic hierarchy defined by national standards, where errors lead to financial inconsistencies and regulatory risks. This paper presents Taxon, a semantically aligned and expert-guided framework for hierarchical tax code prediction. Taxon integrates (i) a feature-gating mixture-of-experts architecture that adaptively routes multi-modal features across taxonomy levels, and (ii) a semantic consistency model distilled from large language models acting as domain experts to verify alignment between product titles and official tax definitions. To address noisy supervision in real business records, we design a multi-source training pipeline that combines curated tax databases, invoice validation logs, and merchant registration data to provide both structural and semantic supervision. Extensive experiments on the proprietary TaxCode dataset and public benchmarks demonstrate that Taxon achieves state-of-the-art performance, outperforming strong baselines. Further, an additional full hierarchical paths reconstruction procedure significantly improves structural consistency, yielding the highest overall F1 scores. Taxon has been deployed in production within Alibaba's tax service system, handling an average of over 500,000 tax code queries per day and reaching peak volumes above five million requests during business event with improved accuracy, interpretability, and robustness.

Feature engineering plays a critical role in machine learning (ML), but existing methods often struggle with high computational cost and limited scalability when applied to large-scale and sparse datasets. In this article, we propose EaSFE, an efficient and scalable feature engineering framework that unifies feature generation, filtering, and evaluation in an end-to-end manner. EaSFE is designed to efficiently construct and select informative features while explicitly considering computational and memory constraints. To achieve scalability, EaSFE incorporates parallel and distributed execution mechanisms, as well as a chunk-based data processing strategy that enables memory-efficient feature engineering on large datasets. In addition, EaSFE adopts tailored storage and execution strategies to handle high-dimensional sparse data effectively. Extensive experiments on multiple real-world datasets demonstrate that EaSFE consistently improves predictive performance (e.g., 5% accuracy improvement in poker ) while substantially enhancing efficiency (i.e., over 10x speedup) compared to existing feature engineering methods. In addition, EaSFE is demonstrated to scale to large and sparse datasets, successfully handling datasets with over 119 million training instances and 54 million features.

Parameter-efficient fine-tuning (PEFT) of pre-trained language models (PLMs) has shown promising results by updating significantly fewer parameters than full fine-tuning. Masking-based fine-tuning is one type of PEFT methods, by freezing the majority of the model parameters during fine-tuning. Existing masking-based fine-tuning methods either need to manually select the trainable parameters (heuristic-based), or perform mask learning to adaptively select the trainable parameters with high memory and computation cost. To address these problems, this paper proposes Low-Rank based Efficient Mask Learning (LoReML). LoReML performs mask learning based on low-rank decomposition and matrix reconstruction with a small ratio of new parameters. After mask learning, LoReML uses the scaled intermediate results in mask learning as warm start initialization to boost the model quality, then freezes the masked parameters accordingly, and fine-tunes the PLM. Moreover, LoReML exploits sparse training techniques to enhance the memory efficiency in masking-based fine-tuning. Experimental results across various tasks and pre-trained backbones demonstrate that LoReML can notably outperform existing heuristic-based methods. Moreover, LoReML achieves competitive or better performance compared with the adaptive mask learning methods, while improving memory and computation efficiency by over 50% in mask learning.

Local Interpretable Model-Agnostic Explanations (LIME) is a widely adopted framework for interpreting opaque models due to its simplicity and intuitiveness. However, LIME suffers from unreliability rooted in two core issues: (i) low fidelity, where the surrogate model fails to accurately approximate the target model's behavior, and (ii) instability, where the generated explanations vary significantly across runs. While prior work has proposed techniques to enhance LIME, they remain fundamentally limited by the expressiveness of linear surrogate models, which cannot adequately capture complex decision boundaries. In this work, we introduce Tilia, a novel method that employs shallow decision tree regressors as the surrogate model, leveraging its structured and deterministic nature to improve both fidelity and stability. Tilia also provides insight into the interplay between surrogate models and sampling strategies, revealing new directions for enhancing explanation reliability. Across extensive experiments on tabular and textual datasets, Tilia outperforms LIME and recent variants on both fidelity and stability, achieving up to 100% approximation of the opaque model and entirely consistent explanations (i.e., 0 Jacard distance). Tilia maintains practical efficiency, completing explanations in seconds even for datasets with over 100 features. These results position Tilia as a robust alternative for model-agnostic explanations. The code is available at https://github.com/neur1n/tilia.

Large foundation models have demonstrated remarkable success in natural language processing and computer vision. Applying the large models to downstream tasks often requires fine-tuning, in order to boost the predictive accuracy. However, the fine-tuning process relies heavily on labeled data and extensive training. This dependency makes fine-tuning impractical for niche applications, such as rare object detection or specialized medical tasks. To overcome these limitations, we propose KALE: Knowledge Aggregation for Label-free model Enhancement, a label-free method for model enhancement, leveraging knowledge aggregation via model fusion and adaptive representation alignment. Our method is powered by a carefully designed joint self-cooperative optimization function that considers (i) multi-granularity optimization (task-specific and layer-specific), (ii) self and cooperative supervision integration, and (iii) mitigation of error accumulation caused by entropy minimization. Additionally, we introduce a class cardinality-aware sample filtering to ensure the stability of the fusion process. We also design a lightweight representation alignment technique to refine the fusion coefficient in a few shots for quality enhancement. We evaluate our method on multiple image classification datasets using ViT-B/32 and ViT-L/14 backbones. Experimental results demonstrate that our label-free method consistently outperforms state-of-the-art unsupervised approaches, including TURTLE and supervised full fine-tuning, in terms of average performance. Specifically, compared to TURTLE, our method achieves average improvements of 20.7% with ViT-B/32 and 19.5% with ViT-L/14. Furthermore, on the challenging SUN397 dataset, our method surpasses supervised full fine-tuning by 4% and 2.3% with ViT-B/32 and ViT-L/14, respectively.

Gradient Boosted Decision Trees (GBDTs) are classical machine learning algorithms widely employed in recommendation systems, database queries, etc. Due to the extensive memory access involved in histogram-based GBDT training methods, high-bandwidth GPUs have been widely adopted to accelerate the training. However, when handling millions of feature data, it requires significant memory to store the training data and histograms, posing challenges for training on limited GPU memories. In this paper, we develop a GPU-based GBDT framework named ScalaGBM, aiming to accelerate high-dimensional data training with less memory usage. We first employ a CSR-like data format and CSR-based histogram construction to reduce the memory occupation of the training data. Then, we reorganize the training workflow with a double buffer structure to reduce the overall memory consumption for the histogram. Finally, we develop multi-dimensional parallel histogram construction and global optimal split point reduction to speed up the training process. Experimental results demonstrate that ScalaGBM handles real-world datasets with over 100 million instances of 50 million features with a single commercial GPU while existing GBDT frameworks all run into out-of-memory errors. Meanwhile, ScalaGBM achieves a maximum speedup of 39× over state-of-the-art GBDT counterparts without sacrificing the training quality. The code is available at https://github.com/Xtra-Computing/thundergbm.

Data science aims to solve real-world problems with the knowledge derived from data. Successfully tackling a data science problem requires practitioners to choose an appropriate solution, which potentially comprises various components such as pre-processing techniques, learning algorithms, hyper-parameters, and so on. Therefore, a problem-driven recommendation for the promising solution is invaluable, as it facilitates efficient and convenient problem-solving. However, existing solution recommendation approaches confront notable challenges when dealing with limited and sparse prior experience in practical applications. Learning from such prior easily leads to overfitting and poor generalization in solution recommendations. To address this issue, we propose a novel solution recommendation method that can predict a good-quality data science solution, including the pre-processing, the learning algorithm, and hyper-parameters, for a given problem. The foundation of our method is a carefully designed ranking model that exploits a weight-sharing structure and a newly proposed loss. The ranking model focuses on incorporating relative ranking information into the predicted performance score of each solution. With these techniques, our method can recommend the solution with the highest score and effectively mitigate the limitations of using sparse prior experience. Our experiments demonstrate the superiority of our method in predicting solutions with higher accuracy and rank, even trained on highly sparse historical performance records. It also reduces recommendation time significantly compared to the baselines, offering remarkable efficiency and convenience for practitioners.

Bandit-based methods are commonly used for hyperparameter optimization (HPO), which is significant in data analytics. When confronted with numerous configurations and high-dimensional large problems, existing bandit-based methods face challenges of high evaluation cost and poor optimization performance. To address these challenges, we introduce an improved bandit-based approach that exhibits enhanced evaluation ability and is suitable for situations with limited resources. Specifically, our method first effectively utilizes the feature and label information to conduct representative groups for further evaluation. After that, two kinds of folds (i.e., general folds and special folds) are constructed to facilitate better evaluation of the configuration in the cross-validation process. Additionally, we incorporate variance and subset size into the evaluation metric to comprehensively evaluate the configuration. We integrate our proposed method into three commonly used bandit-based methods, and experimental results on multiple datasets show that our method has advantages in stability with accuracy improvement of 1 % to 15 % on the datasets tested. In addition, since our method can avoid configurations that are low-quality but time-consuming to evaluate, it is always more efficient than the existing bandit-based methods, and can even reduce the execution time by half in some datasets. Sometimes it takes a little more time, but the improvement in accuracy can be significant.

Embedding techniques can be used to represent words using word embedding [1] , images using image-to-vector techniques [2] , [3] and even database queries [4] . As a result, many more real-world objects can be represented by matrices. For example, a matrix can represent a document where each row (i.e., each vector) of the matrix stands for a word in the document. Figure 1 shows the key steps of representing an object (e.g., a document, a video or an audio stream) by a matrix. The intermediate step is to divide the object into small pieces and to convert the small pieces into vectors. The vectors of the object are then put together to form a matrix. These objects represented by matrices require new data management systems to support efficient indexing and retrieval.

Support Vector Machines (SVMs) are a widely adopted data mining algorithm for binary and multi-class classification due to their ability to handle high-dimensional and non-linearly separable problems. However, SVM training is computationally expensive because of the heavy kernel matrix computation on large training datasets. Although much effort has been made to accelerate the training of SVMs, we find that existing libraries still suffer from inappropriate matrix multiplication methods and inefficient memory access patterns. In this paper, we propose a series of optimization approaches to address these limitations, including (i) matrix partitioning based on column density to achieve efficient kernel matrix computation; (ii) optimizing high latency memory access patterns; and (iii) dynamically selecting more suitable matrix multiplication methods based on the training dataset characteristics. Our proposed methods demonstrate significant improvements in SVM training performance without sacrificing accuracy, achieving a maximum speedup of 52x over the state-of-the-art SVMs on GPUs. These results highlight the effectiveness of our optimization in improving SVM training efficiency.

Choosing a decomposition method for multi-class classification is an important trade-off between efficiency and predictive accuracy. Trying all the decomposition methods to find the best one is too time-consuming for many applications, while choosing the wrong one may result in large loss on predictive accuracy. In this paper, we propose an automatic decomposition method selection approach called “D-Chooser”, which is lightweight and can choose the best decomposition method accurately. D-Chooser is equipped with our proposed difficulty index which consists of sub-metrics including distribution divergence, overlapping regions, unevenness degree and relative size of the solution space. The difficulty index has two intriguing properties: 1) fast to compute and 2) measuring multi-class problems comprehensively. Extensive experiments on real-world multi-class problems show that D-Chooser achieves an accuracy of 80.56% in choosing the best decomposition method. It can choose the best method in just a few seconds, while existing approaches verify the effectiveness of a decomposition method often takes a few hours. We also provide case studies on Kaggle competitions and the results confirm that D-Chooser is able to choose a better decomposition method than the winning solutions.

As data privacy increasingly becomes a critical societal concern, federated learning has been a hot research topic in enabling the collaborative training of machine learning models among different organizations under the privacy restrictions. As researchers try to support more machine learning models with different privacy-preserving approaches, there is a requirement in developing systems and infrastructures to ease the development of various federated learning algorithms. Similar to deep learning systems such as PyTorch and TensorFlow that boost the development of deep learning, federated learning systems (FLSs) are equivalently important, and face challenges from various aspects such as effectiveness, efficiency, and privacy. In this survey, we conduct a comprehensive review on federated learning systems. To understand the key design system components and guide future research, we introduce the definition of federated learning systems and analyze the system components. Moreover, we provide a thorough categorization for federated learning systems according to six different aspects, including data distribution, machine learning model, privacy mechanism, communication architecture, scale of federation and motivation of federation. The categorization can help the design of federated learning systems as shown in our case studies. By systematically summarizing the existing federated learning systems, we present the design factors, case studies, and future research opportunities.

Second-order optimization has been recently explored in neural network training. However, the recomputation of the Hessian matrix in the second-order optimization posts much extra computation and memory burden in the training. There have been some attempts to address this issue by approximation on the Hessian matrix, which unfortunately degrades the performance of the neural models. In order to tackle this issue, we propose Kernel Stochastic Gradient Descent (Kernel SGD) which solves the optimization problem in a space transformed by the Hessian matrix of the kernel machine. Kernel SGD eliminates the Hessian matrix recomputation in the training and requires a much smaller memory cost which can be controlled via the mini-batch size. We show that Kernel SGD optimization is theoretically guaranteed to converge. Our experimental results on tabular, image and text data confirm that Kernel SGD converges up to 30 times faster than the existing second-order optimization techniques, and achieves the highest test accuracy on all the tasks tested. Kernel SGD even outperforms the first-order optimization baselines in some problems tested in our experiments.

With the embedding techniques, many real-world objects can be represented using matrices. For example, a document can be represented by a matrix, where each row of the matrix represents a word. On the other hand, we have witnessed that many applications continuously generate new data represented by matrices and require real-time query answering on the data. These continuously generated matrices need to be well managed for efficient retrieval. In this paper, we propose an index for real-time matrix retrieval. Besides fast query response, the index also supports real-time insertion by exploiting the LSM-tree. Since the index is built for matrices, it consumes much more memory and requires much more time to search than the traditional index for information retrieval. To tackle the challenges, we power our proposed index with precise and fuzzy inverted lists, and propose a series of novel techniques to improve the memory consumption and the search efficiency of the index. The proposed techniques include vector signature, vector residual sorting, hashing based lookup, and dictionary initialization to guarantee the index quality. Comprehensive experimental results show that our proposed index can support real-time search on matrices and is more efficient than the state-of-the-art method.

In recent years, many data mining practitioners have treated deep neural networks (DNNs) as a standard recipe of creating the state-of-the-art solutions. As a result, models like Support Vector Machines (SVMs) have been overlooked. While the results from DNNs are encouraging, DNNs also come with their huge number of parameters in the model and overheads in long training/inference time. SVMs have excellent properties such as convexity, good generality and efficiency. In this paper, we propose techniques to enhance SVMs with an automatic pipeline which exploits the context of the learning problem. The pipeline consists of several components including data aware subproblem construction, feature customization, data balancing among subproblems with augmentation, and kernel hyper-parameter tuner. Comprehensive experiments show that our proposed solution is more efficient, while producing better results than the other SVM based approaches. Additionally, we conduct a case study of our proposed solution on a popular sentiment analysis problem---the aspect term sentiment analysis (ATSA) task. The study shows that our SVM based solution can achieve competitive predictive accuracy to DNN (and even majority of the BERT) based approaches. Furthermore, our solution is about 40 times faster in inference and has 100 times fewer parameters than the models using BERT. Our findings can encourage more research work on conventional machine learning techniques which may be a good alternative for smaller model size and faster training/inference.

Entity extraction is fundamental to many text mining tasks such as organisation name recognition. A popular approach to entity extraction is based on string matching against a dictionary of known entities. For approximate entity extraction from free text, considering solely character-based or solely token-based similarity cannot simultaneously deal with minor name variations at token-level and typos at character-level. Moreover, the tolerance of mismatch in character-level may be different from that in token-level, and the tolerance thresholds of the two levels should be able to be customised individually. In this paper, we propose an efficient character-level and token-level edit-distance based algorithm called FuzzyED. To improve the efficiency of FuzzyED, we develop various novel techniques including (i) a spanning-based candidate sub-string producing technique, (ii) a lower bound dissimilarity to determine the boundaries of candidate sub-strings, (iii) a core token based technique that makes use of the importance of tokens to reduce the number of unpromising candidate sub-strings, and (iv) a shrinking technique to reuse computation. Empirical results on real world datasets show that FuzzyED can efficiently extract entities and produce a high F1score in the range of [0.91, 0.97].

This paper demonstrates a real-time search system called Aucher for live audio streams. Audio streaming services (e.g., Mixlr, Ximalaya, Lizhi and Facebook Live Audio) have become increasingly popular with the wide use of smart phones. Because of the popularity of audio broadcasting, the data volume of live audio streams is also ever increasing. Searching and indexing these audio streams is an important and challenging problem. Aucher is a system prototype which can support both voice search and keyword search on audio streams. We achieve the real-time response for queries by our novel index which exploits log structured merge-trees and supports multi-modal search. Moreover, our system can handle insertion about four times faster and more memory efficient than the state-of-the-art solution. We plan to demonstrate searching live audio streams by keywords and voice, illustrate the trade-off of freshness, popularity and relevance on query results, perform searching hot terms, and show the ability of searching live audio streams in real-time.

Multi-class SVMs with the probabilistic output (MP-SVMs) are important techniques in pattern recognition. Two key challenges for efficient GPU accelerations for MP-SVM are: (i) many kernel values are repeatedly computed as a binary SVM classifier is trained iteratively, resulting in repeated accesses to the high latency GPU memory; (ii) performing training or estimating probability in parallel requires a much larger memory footprint than the GPU memory. To overcome the challenges, we propose GMP-SVM to reduce high latency memory accesses and memory consumption through batch processing, computation/data reusing and sharing. Experimental results show that our solution (available in https://github.com/Xtra-Computing/thundersvm) outperforms LibSVM by 100 times while retaining the same accuracy.

Recently, many researchers have been working on improving other traditional machine learning algorithms (besides deep learning) using high-performance hardware such as Graphics Processing Units (GPUs). The recent success of machine learning is not only due to more effective algorithms, but also more efficient systems and implementations. In this paper, we propose a novel and efficient solution to multi-class SVMs with probabilistic output (MP-SVMs) accelerated by GPUs. MP-SVMs are an important technique for many pattern recognition applications. However, MP-SVMs are very time-consuming to use, because using an MP-SVM classifier requires training many binary SVMs and performing probability estimation by combining results of all the binary SVMs. GPUs have much higher computation capability than CPUs and are potentially excellent hardware to accelerate MP-SVMs. Still, two key challenges for efficient GPU accelerations for MP-SVM are: (i) many kernel values are repeatedly computed as a binary SVM classifier is trained iteratively, resulting in repeated accesses to the high latency GPU memory; (ii) performing training or estimating probability in a highly parallel way requires a much larger memory footprint than the GPU memory. To overcome the challenges, we propose a solution called GMP-SVM which exploits two-level (i.e., binary SVM level and MP-SVM level) optimization for training MP-SVMs and high parallelism for estimating probability. GMP-SVM reduces high latency memory accesses and memory consumption through batch processing, kernel value reusing and sharing, and support vector sharing. Experimental results show that GMP-SVM outperforms the GPU baseline by two to five times, and LibSVM with OpenMP by an order of magnitude. Also, GMP-SVM produces the same SVM classifier as LibSVM.

Audio streaming services have become increasingly popular due to the wide use of smart phones. More and more people are enjoying live audio broadcasting while they are doing various kinds of activities. Meanwhile, the data volume of live audio streams is also ever increasing. Searching and indexing these audio streams is still an important and open problem, with the following challenges: (i) queries on the large number of audio streams need to be answered in real-time; (ii) a live audio stream is inserted into the index continuously to enable live audio streams to appear in query results, and the number of insertions is large which often becomes a performance issue. In this application paper, we propose a multi-modal and unified log structured merge-tree (a.k.a. LSM-tree which consists of multiple inverted indices) based index to support intensive insertions and real-time search on live audio stream applications. Our index natively supports two major types of indexing techniques in audio search: text based indexing and sound based indexing. To address the challenges of live audio indexing and search, we propose an index (called RTSI) which avoids traversing multiple inverted indices to compute the score of an audio stream. In RTSI, we propose various techniques to address the technical challenges. First, for each term we use three inverted lists which contain the sorted score of popularity, freshness and relevance, respectively, such that we can compute the top-k query results efficiently. Second, we devise an upper bound for the unchecked audio streams, such that the query answering process can be terminated earlier. Third, we create mirrors for the indices that need to be merged, such that queries can be answered in real-time when the indices are merging. We conduct extensive experiments on audio streams obtained from Ximalaya. The experimental results show that RTSI can answer a large number of queries in a real-time manner while concurrently handling massive insertions.

We define and study Euclidean and spatial network variants of a new path finding problem: given a set of safe zones, find paths that minimize the distance traveled outside the safe zones. In this problem, the entire space with the exception of the safe zones is unsafe, but passable, and it differs from problems that involve unsafe regions to be strictly avoided. As a result, existing algorithms are not effective solutions to the new problem. To solve the Euclidean variant, we devise a transformation of the continuous data space with safe zones into a discrete graph upon which shortest path algorithms apply. A naïve transformation yields a very large graph that is expensive to search. In contrast, our transformation exploits properties of hyperbolas in the Euclidean space to safely eliminate graph edges, thus improving performance without affecting the shortest path results. To solve the spatial network variant, we propose a different graph-to-graph transformation that identifies critical points that serve the same purpose as do the hyperbolas, thus avoiding the creation of extraneous edges. This transformation can be extended to support a weighted version of the problem, where travel in safe zones has non-zero cost. We conduct extensive experiments using both real and synthetic data. The results show that our approaches outperform baseline approaches by more than an order of magnitude in graph construction time, storage space and query response time.

Semi-supervised learning is an essential approach to classification when the available labeled data is insufficient and we need to also make use of unlabeled data in the learning process. Numerous research efforts have focused on designing algorithms to improve the F1 score, but have any mechanism to control precision or recall individually. However, many applications have precision/recall preferences. For instance, an email spam classifier requires a precision of 0.9 to mitigate the false dismissal of useful emails. In this paper, we propose a method that allows to specify a precision/recall preference while maximising the F1 score. Our key idea is that we divide the semi-supervised learning process into multiple rounds of supervised learning, and the classifier learned at each round is calibrated using a sub-set of the labeled dataset before we use it on the unlabeled dataset for enlarging the training dataset. Our idea is applicable to a number of learning models such as Support Vector Machines (SVMs), Bayesian networks and neural networks. We focus our research and the implementation of our idea on SVMs. We conduct extensive experiments to validate the effectiveness of our method. The experimental results show that our method can train classifiers with a precision/recall preference, while the popular semi-supervised SVM training algorithm (which we use as the baseline) cannot. When we specify the precision preference and the recall preference to be the same, which indicates to maximise the F1 score only as the baseline does, our method achieves better or similar F1 scores to the baseline. An additional advantage of our method is that it converges much faster than the baseline.

Cross-validation is a commonly used method for evaluating the effectiveness of Support Vector Machines (SVMs). However, existing SVM cross-validation algorithms are not scalable to large datasets because they have to (i) hold the whole dataset in memory and/or (ii) perform a very large number of kernel value computation. In this paper, we propose a scheme to dramatically improve the scalability and efficiency of SVM cross-validation through the following key ideas. (i) To avoid holding the whole dataset in the memory and avoid performing repeated kernel value computation, we precompute the kernel values and reuse them. (ii) We store the precomputed kernel values to a high-speed storage framework, consisting of CPU memory extended by solid state drives (SSDs) and GPU memory as a cache, so that reusing (i.e., Reading) kernel values takes much lesser time than computing them on-the-fly. (iii) To further improve the efficiency of the SVM training, we apply a number of techniques for the extreme example search algorithm, design a parallel kernel value read algorithm, propose a caching strategy well-suited to the characteristics of the storage framework, and parallelize the tasks on the GPU and the CPU. For datasets of sizes that existing algorithms can handle, our scheme achieves several orders of magnitude of speedup. More importantly, our scheme enables SVM cross-validation on datasets of very large scale that existing algorithms are unable to handle.

We propose and study a new type of facility location selection query, the top-k most influential location selection query. Given a set M of customers and a set F of existing facilities, this query finds k locations from a set C of candidate locations with the largest influence values, where the influence of a candidate location c (c in C) is defined as the number of customers in M who are the reverse nearest neighbors of c. We first present a naive algorithm to process the query. However, the algorithm is computationally expensive and not scalable to large datasets. This motivates us to explore more efficient solutions. We propose two branch and bound algorithms, the Estimation Expanding Pruning (EEP) algorithm and the Bounding Influence Pruning (BIP) algorithm. These algorithms exploit various geometric properties to prune the search space, and thus achieve much better performance than that of the naive algorithm. Specifically, the EEP algorithm estimates the distances to the nearest existing facilities for the customers and the numbers of influenced customers for the candidate locations, and then gradually refines the estimation until the answer set is found, during which distance metric based pruning techniques are used to improve the refinement efficiency. BIP only estimates the numbers of influenced customers for the candidate locations. But it uses the existing facilities to limit the space for searching the influenced customers and achieve a better estimation, which results in an even more efficient algorithm. Extensive experiments conducted on both real and synthetic datasets validate the efficiency of the algorithms.