Unsupervised cross-modal hashing has achieved great success in various information retrieval applications owing to its efficient storage usage and fast retrieval speed. Recent studies have primarily focused on training the hash-encoded networks by calculating a sample-based similarity matrix to improve the retrieval performance. However, there are two issues remain to solve: (1) The current sample-based similarity matrix only considers the similarity between image-text pairs, ignoring the different information densities of each modality, which may introduce additional noise and fail to mine key information for retrieval; (2) Most existing unsupervised cross-modal hashing methods only consider alignment between different modalities, while ignoring consistency between each modality, resulting in semantic conflicts. To tackle these challenges, a novel Deep High-level Concept-mining Jointing Hashing (DHCJH) model for unsupervised cross-modal retrieval is proposed in this study. DHCJH is able to capture the essential high-level semantic information from image modalities and integrate into the text modalities to improve the accuracy of guidance information. Additionally, a new hashing loss with a regularization term is introduced to avoid the cross-modal semantic collision and false positive pairs problems. To validate the proposed method, extensive comparison experiments on benchmark datasets are conducted. Experimental findings reveal that DHCJH achieves superior performance in both accuracy and efficiency. The code of DHCJH is available at Github.

Clustering is one of the most fundamental tools in artificial intelligence, machine learning, and data mining. In this paper, we follow one of the recent mainstream topics of clustering, Sum of Radii (SoR), which naturally arises as a balance between the folklore k-center and k-median. SoR aims to determine a set of k balls, each centered at a point in a given dataset, such that their union covers the entire dataset while minimizing the sum of radii of the k balls. We propose a general technical framework to overcome the challenge posed by varying radii in SoR, which yields fixed-parameter tractable (fpt) algorithms with respect to k (i.e., whose running time is f(k) ploy(n) for some f). Our framework is versatile and obtains fpt approximation algorithms with constant approximation ratios for SoR as well as its variants in general metrics, such as Fair SoR and Matroid SoR, which significantly improve the previous results.

The Connected Sensor Problem (CSP) presents a prevalent challenge in the realms of communication and Internet of Things (IoT) applications. Its primary aim is to maximize the coverage of users while maintaining connectivity among K sensors. Addressing the challenge of managing a large user base alongside a finite number of candidate locations, this paper proposes an extension to the CSP: the h-hop independently submodular maximization problem characterized by curvature α. We have developed an approximation algorithm that achieves a ratio of 1−e−α(2h+3)α. The efficacy of this algorithm is demonstrated on the CSP, where it shows superior performance over existing algorithms, marked by an average enhancement of 8.4%.

In this paper, we study approximation algorithms for several classes of DR-submodular optimization problems, where DR is short for diminishing return. Following a newly introduced algorithm framework for zeroth-order stochastic approximation methods, we first propose algorithms {\bf CG-ZOSA} and {\bf RG-ZOSA} for smooth DR-submodular optimization based on the coordinate-wise gradient estimator and the randomized gradient estimator, respectively. Our theoretical analysis proves that \rm{\bf{CG-ZOSA}} can reach a solution whose expected objective value exceeds $(1-e^{-1}-\epsilon^{2})$OPT$-\epsilon$ after $\mathcal{O}(\epsilon^{-2})$ iterations and $\mathcal{O}(N^{2/3}d\epsilon^{-2})$ oracle calls, where $d$ represents the problem dimension. On the other hand, \rm{\bf{RG-ZOSA}} improves the approximation ratio to $(1-e^{-1}-\epsilon^{2}/d)$ while maintaining the same overall oracle complexity. For non-smooth up-concave maximization problems, we propose a novel auxiliary function based on a smoothed objective function and introduce the \rm{\bf{NZOSA}} algorithm. This algorithm achieves an approximation ratio of $(1-e^{-1}-\epsilon \ln \epsilon^{-1}- \epsilon^{2}\ln \epsilon^{-1})$ with $\mathcal{O}(d\epsilon^{-2})$ iterations and $\mathcal{O}(N^{2/3}d^{3/2} \epsilon^{-3})$ oracle calls. We also extend \rm{\bf{NZOSA}} to handle a class of robust DR-submodular maximization problems. To validate the effectiveness of our proposed algorithms, we conduct experiments on both synthetic and real-world problems. The results demonstrate the superior performance and efficiency of our methods in solving DR-submodular optimization problems.

Summary The problem of maximizing the sum of a constrained submodular and a supermodular function has many applications such as social networks, machine learning, and artificial intelligence. In this article, we study the monotone submodular + supermodular maximization problem under a cardinality constraint and a p‐system constraint, respectively. For each problem, we provide a stochastic algorithm and prove the approximation ratio of each algorithm theoretically. Since the algorithm of the latter problem can also solve the former problem, we do some numerical experiments of the two algorithms to compare the time as well as the quality of the two algorithms in solving the former problem.

In this paper, we consider the perfect demand matching problem ( PDM ) which combines aspects of the knapsack problem along with the b -matching problem. It is a generalization of the maximum weight matching problem which has been fundamental in the development of theory of computer science and operations research . This problem is NP-hard and there exists a constant ϵ > 0 such that the problem admits no 1 + ϵ -approximation algorithm, unless P=NP. Here, we investigate the performance of a distributed message passing algorithm called Max-sum belief propagation for computing the problem of finding the optimal perfect demand matching. As the main result, we demonstrate the rigorous theoretical analysis of the Max-sum BP algorithm for PDM , and establish that within pseudo-polynomial-time, our algorithm could converge to the optimal solution of PDM , provided that the optimal solution of its LP relaxation is unique and integral. Different from the techniques used in previous literature, our analysis is based on primal-dual complementary slackness conditions , and thus the number of iterations of the algorithm is independent of the structure of the given graph. Moreover, to the best of our knowledge, this is one of a very few instances where BP algorithm is proved correct for NP-hard problems.

Abstract In the k-means problem with penalties, we are given a data set $${\cal D} \subseteq \mathbb{R}^\ell $$ of n points where each point $$j \in {\cal D}$$ is associated with a penalty cost pj and an integer k. The goal is to choose a set $${\rm{C}}S \subseteq {{\cal R}^\ell }$$ with |CS| ≤ k and a penalized subset $${{\cal D}_p} \subseteq {\cal D}$$ to minimize the sum of the total squared distance from the points in D / Dp to CS and the total penalty cost of points in Dp, namely $$\sum\nolimits_{j \in {\cal D}\backslash {{\cal D}_p}} {d^2}(j,{\rm{C}}S) + \sum\nolimits_{j \in {{\cal D}_p}} {p_j}$$ . We employ the primal-dual technique to give a pseudo-polynomial time algorithm with an approximation ratio of (6.357+ε) for the k-means problem with penalties, improving the previous best approximation ratio 19.849+∊ for this problem given by Feng et al. in Proceedings of FAW (2019).

It is well-known that second-order optimizer can accelerate the training of deep neural networks, however, the huge computation cost of second-order optimization makes it impractical to apply in real practice. In order to reduce the cost, many methods have been proposed to approximate a second-order matrix. Inspired by KFAC, we propose a novel Trace-based Hardware-driven layer-ORiented Natural Gradient Descent Computation method, called THOR, to make the second-order optimization applicable in the real application models. Specifically, we gradually increase the update interval and use the matrix trace to determine which blocks of Fisher Information Matrix (FIM) need to be updated. Moreover, by resorting the power of hardware, we have designed a Hardware-driven approximation method for computing FIM to achieve better performance. To demonstrate the effectiveness of THOR, we have conducted extensive experiments. The results show that training ResNet-50 on ImageNet with THOR only takes 66.7 minutes to achieve a top-1 accuracy of 75.9 % under an 8 Ascend 910 environment with MindSpore, a new deep learning computing framework. Moreover, with more computational resources, THOR can only takes 2.7 minutes to 75.9 % with 256 Ascend 910.

Second-order optimization methods have the ability to accelerate convergence by modifying the gradient through the curvature matrix. There have been many attempts to use second-order optimization methods for training deep neural networks. In this work, inspired by diagonal approximations and factored approximations such as Kronecker-factored Approximate Curvature (KFAC), we propose a new approximation to the Fisher information matrix (FIM) called Trace-restricted Kronecker-factored Approximate Curvature (TKFAC), which can hold the certain trace relationship between the exact and the approximate FIM. In TKFAC, we decompose each block of the approximate FIM as a Kronecker product of two smaller matrices and scaled by a coefficient related to trace. We theoretically analyze TKFAC's approximation error and give an upper bound of it. We also propose a new damping technique for TKFAC on convolutional neural networks to maintain the superiority of second-order optimization methods during training. Experiments show that our method has better performance compared with several state-of-the-art algorithms on some deep network architectures.

Emerging IoT applications have brought up new coverage problems with sink-based mobile sensors. In this paper, we first focus on the MinSum Sink-based Line Barrier Coverage (SLBC) problem of covering a line barrier with mobile sensors originated at sink stations distributed on the plane. The objective is to minimize the movement sum of the sensors for the sake of energy efficiency. When the sinks emit sensors with non-uniform radii, we prove the MinSum SLBC problem is$\mathcal{NP}$-complete via reducing from the Partition problem that is known$\mathcal{NP}$- complete. Then for the MinSum Sink-based on-a-Line Target Coverage (SLTC) problem of covering targets on a line, an exact algorithm is presented based on grouping the targets and transforming to the shortest path problem in the auxiliary graph induced by the vertices corresponding to the groups. The algorithm runs in time$O(n^{2})$when sinks emit sensors of uniform sensing radius, and in time$O(\vert R\vert ^{2}n^{2})$for sensors of non-uniform radii, where$n$and$\vert R\vert$are respectively the number of targets and different radii. Eventually for SLBC, we propose a pseudo additive fully polynomial-time approximation scheme by extending the algorithm for SLTC. The algorithm runs in$O(k^{2}(\frac{L}{\epsilon})^{2})$time and computes a coverage with total movement provably bounded by$opt+\epsilon$for any fixed sufficiently small$\epsilon > 0$, where$opt, k$and$L$are respectively the movement of an optimum solution, the number of sinks and the length of the barrier. At last, experiments are carried out to demonstrate the practical performance gain of our algorithms.

Most existing facility location models assume that the facility cost is either a fixed setup cost or made up of a fixed setup and a problem-specific concave or submodular cost term. This structural property plays a critical role in developing fast branch-and-price, Lagrangian relaxation, constant ratio approximation, and conic integer programming reformulation approaches for these NP-hard problems. Many practical considerations and complicating factors, however, can make the facility cost no longer concave or submodular. By removing this restrictive assumption, we study a new location model that considers general nonlinear costs to operate facilities in the facility location framework. The general model does not even admit any approximation algorithms unless P = NP because it takes the unsplittable hard-capacitated metric facility location problem as a special case. We first reformulate this general model as a set-partitioning model and then propose a branch-and-price approach. Although the corresponding pricing problem is NP-hard, we effectively analyze its structural properties and design an algorithm to solve it efficiently. The numerical results obtained from two implementation examples of the general model demonstrate the effectiveness of the solution approach, reveal the managerial implications, and validate the importance to study the general framework.

Motivated by the need for analyzing the rapidly producing data streams, such as images, videos, sensor data, etc, in a timely manner, the study on the streaming algorithms to extract representative information from massive data to maximize some objective function is therefore important and urgent. Most of previous works are assumed under a noise-free environment, while in many realistic applications obtaining the exact function value is hard or computing the function value may cost much, which brings the noisy version. Hence in this paper, we address a more general problem to select a subset of at most k elements from the stream to maximize a noisy set function (not necessarily submodular). To be specific, we cast our problem as the streaming submodular maximization problem under multiplicative and additive noise models. We develop an efficient thresholding streaming algorithm, which calls several copies of a subroutine in parallel. Therefore, this algorithm only requires two passes over data and has a memory independent of data size. For both of noisy models, its approximation guarantee approaches 2/k. In our numerical experiments, we extensively evaluate the effectiveness of our thresholding streaming algorithm on some applications in real data set.

In this paper, we study approximation algorithms for two supply chain network design problems, namely, the warehouse-retailer network design problem (WRND) and the stochastic transportation-inventory network design problem (STIND). These two problems generalize the classical uncapacitated facility location problem by incorporating, respectively, the warehouse-retailer echelon inventory cost and the warehouse cycle inventory together with the safety stock costs. The WRND and the STIND were initially studied, respectively, by Teo and Shu (Teo CP, Shu J (2004) Warehouse-retailer network design problem. Oper. Res. 52(3):396–408) and Shu et al. (Shu J, Teo CP, Shen ZJM (2005) Stochastic transportation-inventory network design problem. Oper. Res. 53(1):48–60), where they are formulated as set-covering problems, and column-generation algorithms were used to solve their linear programming relaxations. Both problems can be regarded as special cases of the so-called facility location with submodular facility costs proposed by Svitkina and Tardos (Svitkina Z, Tardos É (2010) Facility location with hierarchical facility costs. ACM Trans. Algorithms 6(2), Article No. 37), for which only a logarithmic-factor approximation algorithm is known. Our main contribution is to obtain efficient constant-factor approximation algorithms for the WRND and the STIND, which are capable of solving large-scale instances of these problems efficiently.