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Research on heuristic approximation algorithm of the densest k-subgraph discovery in large-scale dynamic graphs 认领 引用
1
作者 HAN Tao TIAN Yuxi +1 位作者 ZHAO Jianwei WANG Senzhang 《Journal of Southeast University(English Edition)》 EI CAS 2026年第1期74-79,共6页
To address the issue that static densest subgraph mining algorithms often exhibit low efficiency when handling large scale dynamic graphs,this paper proposes a heuristic approximation algorithm.The algorithm approxima... To address the issue that static densest subgraph mining algorithms often exhibit low efficiency when handling large scale dynamic graphs,this paper proposes a heuristic approximation algorithm.The algorithm approximates the densest k-subgraphs of the entire graph through four steps:partitioning the large-scale dynamic graph,constructing a partial set of the densest k-subgraphs,heuristically merging the subgraph sets,and finally extracting the densest k-subgraphs.This approach significantly reduces the computational time for large-scale dynamic graphs while simultaneously improving the quality of the resulting subgraphs.This algorithm is applicable to various definitions of“density”and can accommodate diverse requirements on the number of edges.When integrated with existing static densest subgraph detection algorithms,it achieves scalability and computational efficiency.Theoretical analysis demonstrates that the optimal density of the densest k-subgraphs extracted by the proposed algorithm reaches 0.9.To evaluate the performance of the algorithm,experiments were conducted on four billion-scale datasets:Friendster,Orkut,YouTube,and DBLP.The results indicate that the proposed algorithm outperforms static methods in both runtime efficiency and subgraph quality on large-scale dynamic graphs. 展开更多
关键词 the densest k-subgraph features heuristic approximation algorithm optimal density
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Approximation Algorithms for the Priority Facility Location Problem with Penalties 认领 引用 被引量：1
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作者 WANG Fengmin XU Dachuan WU Chenchen 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2015年第5期1102-1114,共13页
develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining... develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining with the greedy aug- previous ratio 3 to 1.8526. 展开更多
关键词 Approximation algorithm facility location problem greedy augmentation primal-dual
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Bicriteria Approximation Algorithm for Quarantining-vaccination-cure Problem 认领 引用
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作者 WANG Le-le ZHANG Zhao 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第1期99-104,共6页
In this paper, we propose a model for the epidemic control problem, the goal of which is to minimize the total cost of quarantining, vaccination and cure under the constraint on the maximum number of infected people a... In this paper, we propose a model for the epidemic control problem, the goal of which is to minimize the total cost of quarantining, vaccination and cure under the constraint on the maximum number of infected people allowed. A (1+ε+ε3 , 1+ ε+1/ε )- bicriteria approximation algorithm is given. 展开更多
关键词 epidemic control quarantining vaccination cure bicriteria approximation algorithm
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An Approximation Algorithm for the Common Due Date Scheduling Problem 认领 引用
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作者 Li Wenquan Song Rui Chengdu 6 1 003 1. China 《Journal of Modern Transportation》 1995年第2期180-186,共7页
In this paper,attention is paid to study an algorithm for the common due datetotal weighted tardiness problem of single machine scheduling. Anapproximation alsorithm is given. It performs well in the sense of worst-ca... In this paper,attention is paid to study an algorithm for the common due datetotal weighted tardiness problem of single machine scheduling. Anapproximation alsorithm is given. It performs well in the sense of worst-casebehaviour and its worst-case performance ratio is 2. 展开更多
关键词 scheduling tardiness. approximation algorithm
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Approximation Algorithms for the Connected Dominating Set Problem in Unit Disk Graphs 认领 引用
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作者 Gang Lu Ming-Tian Zhou +3 位作者 Yong Tang Ming-Yuan Zhao Xin-Zheng Niu Kun She 《Journal of Electronic Science and Technology of China》 2009年第3期214-222,共9页
The connected dominating set(CDS)problem,which consists of finding a smallest connected dominating set for graphs is an NP-hard problem in the unit disk graphs(UDGs).This paper focuses on the CDS problem in wireless n... The connected dominating set(CDS)problem,which consists of finding a smallest connected dominating set for graphs is an NP-hard problem in the unit disk graphs(UDGs).This paper focuses on the CDS problem in wireless networks.Investigation of some properties of independent set(IS)in UDGs shows that geometric features of nodes distribution like angle and area can be used to design efficient heuristics for the approximation algorithms.Several constant factor approximation algorithms are presented for the CDS problem in UDGs.Simulation results show that the proposed algorithms perform better than some known ones. 展开更多
关键词 Approximation algorithm connecteddominating set unit disk graph
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Approximation Algorithms for k-Submodular Maximization Subject to a Knapsack Constraint 认领 引用
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作者 Hao Xiao Qian Liu +1 位作者 Yang Zhou Min Li 《Journal of the Operations Research Society of China》 EI CSCD 2026年第2期397-412,共16页
In this paper,we study the problem of maximizing k-submodular functions subject to a knapsack constraint.For monotone objective functions,we present a 1/2(1−e-2)≈0.432 greedy approximation algorithm,improving the ... In this paper,we study the problem of maximizing k-submodular functions subject to a knapsack constraint.For monotone objective functions,we present a 1/2(1−e-2)≈0.432 greedy approximation algorithm,improving the previous best-known ratio1(1-e-1)≈0.316.We also consider the non-monotone knapsack problem and provide two algorithms.The first is a greedy-type combinatorial algorithm with approximation ratio 1/3(1−e-3)≈0.317,while the second is a multilinear-extension-based algorithm with approximation ratio 1/3-ε,whereε>0. 展开更多
关键词 k-submodular Knapsack Approximation algorithm
Approximation Algorithms for Solving the k-Chinese Postman Problem Under Interdiction Budget Constraints 认领 引用
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作者 Peng-Xiang Pan Jun-Ran Lichen +2 位作者 Wen-Cheng Wang Li-Jian Cai Jian-Ping Li 《Journal of the Operations Research Society of China》 EI CSCD 2025年第2期535-554,共20页
In this paper,we address the k-Chinese postman problem under interdiction budget constraints(the k-CPIBC problem,for short),which is a further generalization of the k-Chinese postman problem and has many practical app... In this paper,we address the k-Chinese postman problem under interdiction budget constraints(the k-CPIBC problem,for short),which is a further generalization of the k-Chinese postman problem and has many practical applications in real life.Specifically,given a weighted graph G=(V,E;w,c;v1)equipped with a weight function w:E→R+that satisfies the triangle inequality,an interdiction cost function c:E→Z+,a fixed depot v1∈V,an integer k∈^Z+and a budget B∈N,we are asked to find a subset SK■E such that c(SK)=∑e∈S_(kce)≤B and that the subgraph G\Skis connected,the objective is to minimize the value minC_(E\Sk)max{w(Ci)|Ci∈CE\SK}among such all aforementioned subsets Sk,where CESkis a set of k-tours(of G\Sk)starting and ending at the depot v1,jointly traversing each edge in G\Skat least once,and w(Ci)=∑e∈Ciw(e)for each tour Ci∈CE\Sk.We obtain the following main results:(1)Given an-approximation algorithm to solve the minimization knapsack problem,we design an(α+β)-approximation algorithm to solve the k-CPIBC problem,whereβ=7/2-1/k-[1/k].(2)We present aβ-approximation algorithm to solve the special version of the k-CPIBC problem,where c(e)1 for each edge e in G and is defined in(1). 展开更多
关键词 Combinatorial optimization Arc routing k-Chinese postman problem Interdiction Approximation algorithms
A Lasserre SDP Rounding Approximation Algorithm for Max Directed 3-Section 认领 引用
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作者 Guangfeng Li Jian Sun +1 位作者 Donglei Du Xiaoyan Zhang 《Tsinghua Science and Technology》 SCIE EI CAS CSCD 2025年第4期1885-1896,共12页
We consider the Max Directed 3-Section problem,which is closely connected to other well-known graph partition problems,such as Max Cut and Max Bisection.Given an arc-weighted directed graph,the goal of the Max Directe... We consider the Max Directed 3-Section problem,which is closely connected to other well-known graph partition problems,such as Max Cut and Max Bisection.Given an arc-weighted directed graph,the goal of the Max Directed 3-Section problem is to partition the vertex set into three disjoint subsets with equal size,while maximizing the total weight of arcs crossing different vertex subsets.By combining the Lasserre hierarchy with the random hyperplane rounding strategy,we propose a polynomial-time algorithm with approximation ratio of 0.489. 展开更多
关键词 Semi-Definite Programming(SDP) Lasserre hierarchy approximation algorithm Max Cut Max Bisection
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A new approximation algorithm for two-machine flow shop scheduling with transporter coordinate 认领 引用
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作者 Yinling Wang Yuping Ge +1 位作者 Yubai Zhang Hui Tian 《CCF Transactions on High Performance Computing》 EI CSCD 2025年第6期623-631,共9页
This paper investigates a two-stage flow shop scheduling model incorporating transportation after the job is complete.The system configuration comprises dual processing machines and a single automated transporter with... This paper investigates a two-stage flow shop scheduling model incorporating transportation after the job is complete.The system configuration comprises dual processing machines and a single automated transporter with unit capacity.Each job in the production sequence is defined by distinct physical size,and the transporter can load multiple jobs in a batch at the same time.All jobs follow identical processing order across both machines before they are transported to the destination.The goal of this problem is to determine a schedule and the batch scheme for transport,such that the makespan is minimum,where the makespan represents the minimum completion time required for full job processing and delivery operations.We present a novel approximation algorithm achieving a performance ratio of(1+ε+2B∗−1/2),where is an arbitrary positive number in(0,1]and B∗is the number of batches in an optimal solution.The ratio is asymptotically optimal when B∗tends toward infinity and the parameter approaches 0.Empirical validation through numerical simulations confirms that our methodology efficiently produces solutions approaching optimality within practical computation times. 展开更多
关键词 Flow shop Batch and transporter Approximation algorithms
Approximation Algorithm for the k-Product Uncapacitated Facility Location Problem with Penalties 认领 引用
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作者 Pei-Jia Yang Wen-Chang Luo 《Journal of the Operations Research Society of China》 EI CSCD 2025年第1期287-296,共10页
In the k-product uncapacitated facility location problem with penalties,we are given a set of demand points where clients are located and a set of potential sites where facilities with unlimited capacities can be open... In the k-product uncapacitated facility location problem with penalties,we are given a set of demand points where clients are located and a set of potential sites where facilities with unlimited capacities can be opened.There are k different kinds of products to be supplied by a set of open facilities.Each open facility can supply only a distinct product with a non-negative fixed cost determined by the product it wants to supply.Each client is either supplied with k kinds of products by a set of k different open facilities or completely rejected.There is a non-negative service cost between each pair of locations and also a penalty cost for each client if its service is rejected.These service costs are assumed to be symmetric and satisfy the triangle inequality.The goal is to select a set of clients to reject their service and then choose a set of facilities to be opened to service the remaining clients so that the total cost of opening facilities,servicing the clients,and the penalty is minimized.We address two different integer programs to describe the problem.Based on the linear programming rounding technique,we propose a(2k+1)-approximation algorithm for this problem. 展开更多
关键词 k-product Facility location Penalty LP-rounding Approximation algorithm
Exact and Approximation Algorithms for the Multi-Depot Capacitated Arc Routing Problems 认领 引用 被引量：5
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作者 Wei Yu Yujie Liao Yichen Yang 《Tsinghua Science and Technology》 SCIE EI CAS CSCD 2023年第5期916-928,共13页
In this work,we investigate a generalization of the classical capacitated arc routing problem,called the Multi-depot Capacitated Arc Routing Problem(MCARP).We give exact and approximation algorithms for different vari... In this work,we investigate a generalization of the classical capacitated arc routing problem,called the Multi-depot Capacitated Arc Routing Problem(MCARP).We give exact and approximation algorithms for different variants of the MCARP.First,we obtain the first constant-ratio approximation algorithms for the MCARP and its nonfixed destination version.Second,for the multi-depot rural postman problem,i.e.,a special case of the MCARP where the vehicles have infinite capacity,we develop a(2-1/2k+1)-approximation algorithm(k denotes the number of depots).Third,we show the polynomial solvability of the equal-demand MCARP on a line and devise a 2-approximation algorithm for the multi-depot capacitated vehicle routing problem on a line.Lastly,we conduct extensive numerical experiments on the algorithms for the multi-depot rural postman problem to show their effectiveness. 展开更多
关键词 approximation algorithm multi-depot vehicle routing problem arc routing problem rural postman problem
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An SDP randomized approximation algorithm for max hypergraph cut with limited unbalance 认领 引用 被引量：3
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作者 XU BaoGang YU XingXing +1 位作者 ZHANG XiaoYan ZHANG Zan-Bo 《Science China Mathematics》 SCIE 2014年第12期2437-2462,共26页
We consider the design of semidefinite programming （SDP） based approximation algorithm for the problem Max Hypergraph Cut with Limited Unbalance （MHC-LU）： Find a partition of the vertices of a weighted hypergraph... We consider the design of semidefinite programming （SDP） based approximation algorithm for the problem Max Hypergraph Cut with Limited Unbalance （MHC-LU）： Find a partition of the vertices of a weighted hypergraph H = （V, E） into two subsets V1, V2 with ｜｜V2｜ - ｜1/1 ｜｜ ≤ u for some given u and maximizing the total weight of the edges meeting both V1 and V2. The problem MHC-LU generalizes several other combinatorial optimization problems including Max Cut, Max Cut with Limited Unbalance （MC-LU）, Max Set Splitting, Max Ek-Set Splitting and Max Hypergraph Bisection. By generalizing several earlier ideas, we present an SDP randomized approximation algorithm for MHC-LU with guaranteed worst-case performance ratios for various unbalance parameters τ = u/｜V｜. We also give the worst-case performance ratio of the SDP-algorithm for approximating MHC-LU regardless of the value of τ. Our strengthened SDP relaxation and rounding method improve a result of Ageev and Sviridenko （2000） on Max Hypergraph Bisection （MHC-LU with u = 0）, and results of Andersson and Engebretsen （1999）, Gaur and Krishnamurti （2001） and Zhang et al. （2004） on Max Set Splitting （MHC-LU with u = ｜V｜）. Furthermore, our new formula for the performance ratio by a tighter analysis compared with that in Galbiati and Maffioli （2007） is responsible for the improvement of a result of Galbiati and Maffioli （2007） on MC-LU for some range of τ. 展开更多
关键词 max hypergraph cut with limited unbalance approximation algorithm performance ratio semidefinite programming relaxation
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A primal-dual approximation algorithm for the k-prize-collecting minimum vertex cover problem with submodular penalties 认领 引用 被引量：2
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作者 Xiaofei LIU Weidong LI Jinhua YANG 《Frontiers of Computer Science》 SCIE EI CSCD 2023年第3期125-132,共8页
In this paper,we consider the-prize-collecting minimum vertex cover problem with submodular penalties,which generalizes the well-known minimum vertex cover problem,minimum partial vertex cover problem and minimum vert... In this paper,we consider the-prize-collecting minimum vertex cover problem with submodular penalties,which generalizes the well-known minimum vertex cover problem,minimum partial vertex cover problem and minimum vertex cover problem with submodular penalties.We are given a cost graph and an integer.This problem determines a vertex set such that covers at least edges.The objective is to minimize the total cost of the vertices in plus the penalty of the uncovered edge set,where the penalty is determined by a submodular function.We design a two-phase combinatorial algorithm based on the guessing technique and the primal-dual framework to address the problem.When the submodular penalty cost function is normalized and nondecreasing,the proposed algorithm has an approximation factor of.When the submodular penalty cost function is linear,the approximation factor of the proposed algorithm is reduced to,which is the best factor if the unique game conjecture holds. 展开更多
关键词 vertex cover k-prize-collecting primal-dual approximation algorithm
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Approximation Algorithm for Weighted Weak Vertex Cover 认领 引用 被引量：5
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作者 YongZhang HongZhu 《Journal of Computer Science & Technology》 SCIE EI 2004年第6期782-786,共5页
The problem of efficiently monitoring the network flow is regarded as the problem to find out the minimum weighted weak vertex cover set for a given graphG=(V,E). In this paper, we give an approximation algorithm to s... The problem of efficiently monitoring the network flow is regarded as the problem to find out the minimum weighted weak vertex cover set for a given graphG=(V,E). In this paper, we give an approximation algorithm to solve it, which has the approximation ratio lnd+1, whered is the maximum degree of the vertex in graphG, and improve the previous work. Keywords weak vertex cover - NP-hard - approximation algorithm NoteThis work is supported by the Ministry of Science and Technology of China (Grant No.2001CCA03000), the National Natural Science Foundation of China (Grant No.60273045), and the Shanghai Science and Technology Development Foundation (Grant No.025115032). 展开更多
关键词 weak vertex cover NP-hard approximation algorithm
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Approximation Algorithms for Discrete Polynomial Optimization 认领 引用 被引量：2
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作者 Simai He Zhening Li Shuzhong Zhang 《Journal of the Operations Research Society of China》 EI 2013年第1期3-36,共34页
In this paper,we consider approximation algorithms for optimizing a generic multivariate polynomial function in discrete(typically binary)variables.Such models have natural applications in graph theory,neural networks... In this paper,we consider approximation algorithms for optimizing a generic multivariate polynomial function in discrete(typically binary)variables.Such models have natural applications in graph theory,neural networks,error-correcting codes,among many others.In particular,we focus on three types of optimization models:(1)maximizing a homogeneous polynomial function in binary variables;(2)maximizing a homogeneous polynomial function in binary variables,mixed with variables under spherical constraints;(3)maximizing an inhomogeneous polynomial function in binary variables.We propose polynomial-time randomized approximation algorithms for such polynomial optimizationmodels,and establish the approximation ratios(or relative approximation ratios whenever appropriate)for the proposed algorithms.Some examples of applications for these models and algorithms are discussed as well. 展开更多
关键词 Polynomial optimization problem Binary integer programming Mixed integer programming Approximation algorithm Approximation ratio
Improved Approximation Algorithm for Scheduling on a Serial Batch Machine with Split-Allowed Delivery 认领 引用 被引量：1
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作者 Ru-Bing Chen Ling-Fa Lu +1 位作者 Jin-Jiang Yuan Li-Qi Zhang 《Journal of the Operations Research Society of China》 EI CSCD 2020年第1期133-143,共11页
This paper considers the integrated production and delivery scheduling on a serial batch machine,in which split is allowed in the delivery of the jobs.The objective is to minimize the makespan,i.e.,the maximum deliver... This paper considers the integrated production and delivery scheduling on a serial batch machine,in which split is allowed in the delivery of the jobs.The objective is to minimize the makespan,i.e.,the maximum delivery completion time of the jobs.Lu et al.(Theor Comput Sci 572:50–57,2015)showed that this problem is strongly NP-hard,and presented a 32-approximation algorithm.In this paper,we present an improved 43-approximation algorithm for this problem.We also present a polynomial-time algorithm for the special case when all jobs have the identical weight. 展开更多
关键词 Scheduling Production and delivery Serial batch Approximation algorithm
Approximation Algorithms for Stochastic Combinatorial Optimization Problems 认领 引用 被引量：2
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作者 Jian Li Yu Liu 《Journal of the Operations Research Society of China》 EI CSCD 2016年第1期1-47,共47页
Stochastic optimization has established itself as a major method to handle uncertainty in various optimization problems by modeling the uncertainty by a probability distribution over possible realizations.Traditionall... Stochastic optimization has established itself as a major method to handle uncertainty in various optimization problems by modeling the uncertainty by a probability distribution over possible realizations.Traditionally,the main focus in stochastic optimization has been various stochastic mathematical programming(such as linear programming,convex programming).In recent years,there has been a surge of interest in stochastic combinatorial optimization problems from the theoretical computer science community.In this article,we survey some of the recent results on various stochastic versions of classical combinatorial optimization problems.Since most problems in this domain are NP-hard(or#P-hard,or even PSPACE-hard),we focus on the results which provide polynomial time approximation algorithms with provable approximation guarantees.Our discussions are centered around a few representative problems,such as stochastic knapsack,stochastic matching,multi-armed bandit etc.We use these examples to introduce several popular stochastic models,such as the fixed-set model,2-stage stochastic optimization model,stochastic adaptive probing model etc,as well as some useful techniques for designing approximation algorithms for stochastic combinatorial optimization problems,including the linear programming relaxation approach,boosted sampling,content resolution schemes,Poisson approximation etc.We also provide some open research questions along the way.Our purpose is to provide readers a quick glimpse to the models,problems,and techniques in this area,and hopefully inspire new contributions. 展开更多
关键词 Approximation algorithms Stochastic optimization Combinatorial optimization
An Approximation Algorithm for P-prize-collecting Set Cover Problem 认领 引用 被引量：1
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作者 Jin-Shuang Guo Wen Liu Bo Hou 《Journal of the Operations Research Society of China》 EI CSCD 2023年第1期207-217,共11页
In this paper,we consider the P-prize-collecting set cover(P-PCSC)problem,which is a generalization of the set cover problem.In this problem,we are given a set system(U,S),where U is a ground set and S⊆2U is a collect... In this paper,we consider the P-prize-collecting set cover(P-PCSC)problem,which is a generalization of the set cover problem.In this problem,we are given a set system(U,S),where U is a ground set and S⊆2U is a collection of subsets satisfying∪S∈SS=U.Every subset in S has a nonnegative cost,and every element in U has a nonnegative penalty cost and a nonnegative profit.Our goal is to find a subcollection C⊆S such that the total cost,consisting of the cost of subsets in C and the penalty cost of the elements not covered by C,is minimized and at the same time the combined profit of the elements covered by C is at least P,a specified profit bound.Our main work is to obtain a 2f+ε-approximation algorithm for the P-PCSC problem by using the primal-dual and Lagrangian relaxation methods,where f is the maximum frequency of an element in the given set system(U,S)andεis a fixed positive number. 展开更多
关键词 P-prize-collecting set cover problem Approximation algorithm Primal-dual Lagrangian relaxation
Approximation Algorithm for Bottleneck Steiner Tree Problem in the Euclidean Plane 认领 引用 被引量：3
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作者 Zi-MaoLi Da-MingZhu Shao-HanMa 《Journal of Computer Science & Technology》 SCIE EI 2004年第6期791-794,共4页
A special case of the bottleneck Steiner tree problem in the Euclidean plane was considered in this paper. The problem has applications in the design of wireless communication networks, multifacility location, VLSI ro... A special case of the bottleneck Steiner tree problem in the Euclidean plane was considered in this paper. The problem has applications in the design of wireless communication networks, multifacility location, VLSI routing and network routing. For the special case which requires that there should be no edge connecting any two Steiner points in the optimal solution, a 3-restricted Steiner tree can be found indicating the existence of the performance ratio root2. In this paper, the special case of the problem is proved to be NP-hard and cannot be approximated within ratio root2. First a simple polynomial time approximation algorithm with performance ratio root3 is presented. Then based on this algorithm and the existence of the 3-restricted Steiner tree, a polynomial time approximation algorithm with performance ratio-root2 + epsilon is proposed, for any epsilon > 0. 展开更多
关键词 bottleneck Steiner tree approximation algorithm performance ratio algorithm design and analysis
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Approximation algorithms for nonnegative polynomial optimization problems over unit spheres 认领 引用
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作者 Xinzhen ZHANG Guanglu ZHOU +1 位作者 Louis CACCETTA Mohammed ALQAHTANI 《Frontiers of Mathematics in China》 SCIE CSCD 2017年第6期1409-1426,共18页
We consider approximation algorithms for nonnegative polynomial optimization problems over unit spheres. These optimization problems have wide applications e.g., in signal and image processing, high order statistics, ... We consider approximation algorithms for nonnegative polynomial optimization problems over unit spheres. These optimization problems have wide applications e.g., in signal and image processing, high order statistics, and computer vision. Since these problems are NP-hard, we are interested in studying on approximation algorithms. In particular, we propose some polynomial-time approximation algorithms with new approximation bounds. In addition, based on these approximation algorithms, some efficient algorithms are presented and numerical results are reported to show the efficiency of our proposed algorithms. 展开更多
关键词 Approximation algorithm polynomial optimization approximationbound
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