Pub Date : 2023-02-03DOI: 10.1142/s012905412246008x
Ao Zhao, Yang Zhou, Qian Liu
Both matroid means and knapsack means are variations of the classic [Formula: see text]-means problem in which we replace the cardinality constraint by matroid constraint or knapsack constraint respectively. In this paper, we give a 64-approximation algorithm for the matroid means problem and a [Formula: see text]-approximation algorithm for the knapsack means problem by using a simpler and more efficient rounding method. We improve previous 304 approximate ratio for the former and 20016 approximate ratio for the latter. In the rounding process, the application of integrality of the intersection of submodular (or matroid) polyhedra provides strong theoretical support. Moreover, we extend this method to matroid means problem with penalties, and give 64 and 880-approximate algorithms for uniform penalties and nonuniform penalties problem.
{"title":"Improved Approximation Algorithms for Matroid and Knapsack Means Problems","authors":"Ao Zhao, Yang Zhou, Qian Liu","doi":"10.1142/s012905412246008x","DOIUrl":"https://doi.org/10.1142/s012905412246008x","url":null,"abstract":"Both matroid means and knapsack means are variations of the classic [Formula: see text]-means problem in which we replace the cardinality constraint by matroid constraint or knapsack constraint respectively. In this paper, we give a 64-approximation algorithm for the matroid means problem and a [Formula: see text]-approximation algorithm for the knapsack means problem by using a simpler and more efficient rounding method. We improve previous 304 approximate ratio for the former and 20016 approximate ratio for the latter. In the rounding process, the application of integrality of the intersection of submodular (or matroid) polyhedra provides strong theoretical support. Moreover, we extend this method to matroid means problem with penalties, and give 64 and 880-approximate algorithms for uniform penalties and nonuniform penalties problem.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47347263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-01DOI: 10.1142/s012905412344001x
Mikhail Mrykhin, Alexander Okhotin
This paper establishes an analogue of Greibach’s hardest language theorem (“The hardest context-free language”, SIAM J. Comp., 1973, http://dx.doi.org/10.1137/0202025 ) for the classical family of LL([Formula: see text]) languages. The first result is that there is a language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form, to which every language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form can be reduced by a homomorphism, that is, [Formula: see text] if and only if [Formula: see text]. Then it is shown that this statement does not hold for the full class of LL([Formula: see text]) languages. The other hardest language theorem is then established in the following form: there is a language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form, such that, for every language [Formula: see text] defined by an LL([Formula: see text]) grammar, with [Formula: see text], there exists a homomorphism [Formula: see text], for which [Formula: see text] if and only if [Formula: see text] [Formula: see text] [Formula: see text], where [Formula: see text] is a new symbol. The results lead to two robust language families: the closures of the languages defined by LL(1) grammars in the Greibach normal form under inverse homomorphisms and under inverse finite transductions.
本文建立了一个类似于Greibach最难语言定理(“最难上下文无关语言”，SIAM J. Comp.， 1973, http://dx.doi.org/10.1137/0202025)的经典LL(公式:见文本)语言族。第一个结果是存在一种由Greibach范式的LL(1)语法定义的语言[公式:见文]，而每一种由Greibach范式的LL(1)语法定义的语言[公式:见文]都可以被同态约简，即当且仅当[公式:见文]。然后证明，这一说法并不适用于LL([公式:见文本])语言的整个类。然后其他困难的语言定理是成立于以下形式:有一个语言(公式:看到文本)定义为一种LL(1)文法Greibach范式,这样,每一个语言(公式:看到文本)定义为一个会([公式:看到文本])语法,(公式:看到文本),存在一个同态(公式:看到文本),因为(公式:看到文本)当且仅当[公式:看到文本][公式:看到文本][公式:看到文本],在[公式:看到文本]是一个新的象征。这些结果导致了两个鲁棒语系:在逆同态和逆有限转导下，由LL(1)语法在Greibach范式下定义的语言闭包。
{"title":"The Hardest LL(k) Language","authors":"Mikhail Mrykhin, Alexander Okhotin","doi":"10.1142/s012905412344001x","DOIUrl":"https://doi.org/10.1142/s012905412344001x","url":null,"abstract":"This paper establishes an analogue of Greibach’s hardest language theorem (“The hardest context-free language”, SIAM J. Comp., 1973, http://dx.doi.org/10.1137/0202025 ) for the classical family of LL([Formula: see text]) languages. The first result is that there is a language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form, to which every language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form can be reduced by a homomorphism, that is, [Formula: see text] if and only if [Formula: see text]. Then it is shown that this statement does not hold for the full class of LL([Formula: see text]) languages. The other hardest language theorem is then established in the following form: there is a language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form, such that, for every language [Formula: see text] defined by an LL([Formula: see text]) grammar, with [Formula: see text], there exists a homomorphism [Formula: see text], for which [Formula: see text] if and only if [Formula: see text] [Formula: see text] [Formula: see text], where [Formula: see text] is a new symbol. The results lead to two robust language families: the closures of the languages defined by LL(1) grammars in the Greibach normal form under inverse homomorphisms and under inverse finite transductions.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136019615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-30DOI: 10.1142/s0129054122500290
Tayssir Touili, Xin Ye
A Self modifying code is code that modifies its own instructions during execution time. It is nowadays widely used, especially in malware to make the code hard to analyse and to detect by anti-viruses. Thus, the analysis of such self modifying programs is a big challenge. Pushdown systems (PDSs) is a natural model that is extensively used for the analysis of sequential programs because they allow to accurately model procedure calls and mimic the program’s stack. In this work, we propose to extend the PushDown System model with self-modifying rules. We call the new model Self-Modifying PushDown System (SM-PDS). A SM-PDS is a PDS that can modify its own set of transitions during execution. We show how SM-PDSs can be used to naturally represent self-modifying programs and provide efficient algorithms to compute the backward and forward reachable configurations of SM-PDSs. We implemented our techniques in a tool and obtained encouraging results. In particular, we successfully applied our tool for the detection of self-modifying malware.
{"title":"Reachability Analysis of Self Modifying Code","authors":"Tayssir Touili, Xin Ye","doi":"10.1142/s0129054122500290","DOIUrl":"https://doi.org/10.1142/s0129054122500290","url":null,"abstract":"A Self modifying code is code that modifies its own instructions during execution time. It is nowadays widely used, especially in malware to make the code hard to analyse and to detect by anti-viruses. Thus, the analysis of such self modifying programs is a big challenge. Pushdown systems (PDSs) is a natural model that is extensively used for the analysis of sequential programs because they allow to accurately model procedure calls and mimic the program’s stack. In this work, we propose to extend the PushDown System model with self-modifying rules. We call the new model Self-Modifying PushDown System (SM-PDS). A SM-PDS is a PDS that can modify its own set of transitions during execution. We show how SM-PDSs can be used to naturally represent self-modifying programs and provide efficient algorithms to compute the backward and forward reachable configurations of SM-PDSs. We implemented our techniques in a tool and obtained encouraging results. In particular, we successfully applied our tool for the detection of self-modifying malware.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135489749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-26DOI: 10.1142/s0129054122460029
Xiaoyan Zhang, Hong Chang, Longkun Guo, D. Du, Gaokai Zou, Yu-Si Xiong
Sparsest cut problems are very important graph partitions, which have been widely applied in expander graphs, Markov chains, and image segmentation. In this paper, we study the edge-weighted version of the Sparse Cut Problem, which minimizes the ratio of the total weight of edges between blocks and the total weight of edges incident to vertices in one block. We first prove that the problem is even NP-hard for an edge-weighted graph with bridges. Then, we combine and generalize submodular functions and principal partition to design a graph algorithm to improve the initial bipartition, which runs in polynomial time by using network flow as its subroutines.
{"title":"Graph Algorithm Based Submodular Function for Sparsest Cut Problem","authors":"Xiaoyan Zhang, Hong Chang, Longkun Guo, D. Du, Gaokai Zou, Yu-Si Xiong","doi":"10.1142/s0129054122460029","DOIUrl":"https://doi.org/10.1142/s0129054122460029","url":null,"abstract":"Sparsest cut problems are very important graph partitions, which have been widely applied in expander graphs, Markov chains, and image segmentation. In this paper, we study the edge-weighted version of the Sparse Cut Problem, which minimizes the ratio of the total weight of edges between blocks and the total weight of edges incident to vertices in one block. We first prove that the problem is even NP-hard for an edge-weighted graph with bridges. Then, we combine and generalize submodular functions and principal partition to design a graph algorithm to improve the initial bipartition, which runs in polynomial time by using network flow as its subroutines.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49026439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-25DOI: 10.1142/s0129054122460054
Zhihua Huang, An Zhang, G. Dósa, Yong Chen, Chenling Xiong
Given a set of items, and a conflict graph defined on the item set, the problem of bin packing with conflicts asks for a partition of items into a minimum number of independent sets so that the total size of items in each independent set does not exceed the bin capacity. As a generalization of both classic bin packing and classic vertex coloring, it is hard to approximate the problem on general graphs. We present new approximation algorithms for bipartite graphs and split graphs. The absolute approximation ratios are shown to be [Formula: see text] and [Formula: see text] respectively, both improving the existing results.
{"title":"Improved Approximation Algorithms for Bin Packing with Conflicts","authors":"Zhihua Huang, An Zhang, G. Dósa, Yong Chen, Chenling Xiong","doi":"10.1142/s0129054122460054","DOIUrl":"https://doi.org/10.1142/s0129054122460054","url":null,"abstract":"Given a set of items, and a conflict graph defined on the item set, the problem of bin packing with conflicts asks for a partition of items into a minimum number of independent sets so that the total size of items in each independent set does not exceed the bin capacity. As a generalization of both classic bin packing and classic vertex coloring, it is hard to approximate the problem on general graphs. We present new approximation algorithms for bipartite graphs and split graphs. The absolute approximation ratios are shown to be [Formula: see text] and [Formula: see text] respectively, both improving the existing results.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41465456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-21DOI: 10.1142/s0129054122460091
Hongxiang Zhang, C. Hao, Yu Cao, Gaidi Li
In this paper, we propose a concept of a lattice pseudo-submodular (LPS) function and consider maximizing a monotone continuous real LPS function [Formula: see text] under a convex polytope constraint. The concept of LPS function was proposed to describe the properties of some discrete functions or nonconvex continuous functions. It is a generalization of the lattice submodular function. For the real LPS maximization problem, we design the monotone Pseudo Frank-Wolfe (PFW) algorithm by taking advantage of the second derivative bound. The PFW algorithm iterates by constantly optimize linear gradient function [Formula: see text], and finally outputs the solution. We theoretically prove that PFK algorithm has an approximation ratio of [Formula: see text] (where [Formula: see text]), and it needs at least [Formula: see text] rounds (where [Formula: see text] is a parameter given in advance). The PFW algorithm is also useful for multilinear extension of discrete lattice pseudo-submodular maximization problems.
{"title":"Properties and Algorithm of Lattice Pseudo-Submodular Functions","authors":"Hongxiang Zhang, C. Hao, Yu Cao, Gaidi Li","doi":"10.1142/s0129054122460091","DOIUrl":"https://doi.org/10.1142/s0129054122460091","url":null,"abstract":"In this paper, we propose a concept of a lattice pseudo-submodular (LPS) function and consider maximizing a monotone continuous real LPS function [Formula: see text] under a convex polytope constraint. The concept of LPS function was proposed to describe the properties of some discrete functions or nonconvex continuous functions. It is a generalization of the lattice submodular function. For the real LPS maximization problem, we design the monotone Pseudo Frank-Wolfe (PFW) algorithm by taking advantage of the second derivative bound. The PFW algorithm iterates by constantly optimize linear gradient function [Formula: see text], and finally outputs the solution. We theoretically prove that PFK algorithm has an approximation ratio of [Formula: see text] (where [Formula: see text]), and it needs at least [Formula: see text] rounds (where [Formula: see text] is a parameter given in advance). The PFW algorithm is also useful for multilinear extension of discrete lattice pseudo-submodular maximization problems.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41846178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-19DOI: 10.1142/s0129054122460078
Long Zhang, Jiguo Yu, Yuzhong Zhang, D. Du
We consider the scheduling game with activation cost, where jobs as selfish agents compete for processing on serial-batching identical machines. Each job selects a machine (more precisely, a batch on a machine) for processing to minimize his disutility composed of the load of his machine and the fraction of activation cost. We claim that such a game may not admit any Nash equilibrium under the uniform sharing rule. We present an algorithm and prove that the schedule produced by the algorithm is a tight approximate Nash equilibria.
{"title":"Approximate Nash Equilibria for Scheduling Game on Serial-Batching-Machines with Activation Cost","authors":"Long Zhang, Jiguo Yu, Yuzhong Zhang, D. Du","doi":"10.1142/s0129054122460078","DOIUrl":"https://doi.org/10.1142/s0129054122460078","url":null,"abstract":"We consider the scheduling game with activation cost, where jobs as selfish agents compete for processing on serial-batching identical machines. Each job selects a machine (more precisely, a batch on a machine) for processing to minimize his disutility composed of the load of his machine and the fraction of activation cost. We claim that such a game may not admit any Nash equilibrium under the uniform sharing rule. We present an algorithm and prove that the schedule produced by the algorithm is a tight approximate Nash equilibria.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48110467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-19DOI: 10.1142/s0129054122460066
Xinru Guo, Sijia Dai, Guichen Gao, Ruikang Ma, Yicheng Xu, Li Ning, Jianping Fan
This paper studies the problem of dividing [Formula: see text] indivisible items among [Formula: see text] agents fairly and efficiently. Specifically, this research concentrates on pairwise maximin share (PMMS), which is defined to be the maximum value that an agent can guarantee for herself if she were to repartition the items with another agent and receive the bundle with the minimum value. PMMS is an important concept in the fair division. However, whether PMMS for indivisible items exists is still open. This work concentrates on PMMS by proving the existence of PMMS on linear graphs with binary valuation functions. Besides, this paper designs an algorithm to approximate PMMS in the case where different agents have identical valuations among the same items, achieving a ratio strictly greater than 0.8, which outperforms the state-of-the-art ratio of 0.781 from Kurokawa [22]. The time complexity of our FFD-based algorithm is [Formula: see text].
{"title":"Restricted Existence and Approximation Algorithms for PMMS","authors":"Xinru Guo, Sijia Dai, Guichen Gao, Ruikang Ma, Yicheng Xu, Li Ning, Jianping Fan","doi":"10.1142/s0129054122460066","DOIUrl":"https://doi.org/10.1142/s0129054122460066","url":null,"abstract":"This paper studies the problem of dividing [Formula: see text] indivisible items among [Formula: see text] agents fairly and efficiently. Specifically, this research concentrates on pairwise maximin share (PMMS), which is defined to be the maximum value that an agent can guarantee for herself if she were to repartition the items with another agent and receive the bundle with the minimum value. PMMS is an important concept in the fair division. However, whether PMMS for indivisible items exists is still open. This work concentrates on PMMS by proving the existence of PMMS on linear graphs with binary valuation functions. Besides, this paper designs an algorithm to approximate PMMS in the case where different agents have identical valuations among the same items, achieving a ratio strictly greater than 0.8, which outperforms the state-of-the-art ratio of 0.781 from Kurokawa [22]. The time complexity of our FFD-based algorithm is [Formula: see text].","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47110880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-14DOI: 10.1142/s0129054122460042
Jiaming Hu, C. Hao, Cuixia Miao, Bo Zhao
We consider the problem of local privacy where actions are subsets of a ground multiset and expectation rewards are modeled by a [Formula: see text]decomposable monotone submodular function. For the DR-submodular maximization problem under a polymatroid constraint, Soma and Yoshida [26] provide a continuous greedy algorithm for no-privacy setting. In this paper, we obtain the first differentially private algorithm for DR-submodular maximization subject to a polymatroid constraint. Our algorithm achieves a [Formula: see text]approximation with a little loss and runs in [Formula: see text][Formula: see text] times where [Formula: see text] is the rank of the base polymatroid and [Formula: see text] is the size of ground set. Along the way, we analyze the utility and privacy of our algorithm. A concrete experiment to simulate the privacy Uber pickups location problem is provided, and our algorithm performs well within the agreed range.
{"title":"A Differentially Private Approximation Algorithm for Submodular Maximization Under a Polymatroid Constraint Over the Integer Lattice","authors":"Jiaming Hu, C. Hao, Cuixia Miao, Bo Zhao","doi":"10.1142/s0129054122460042","DOIUrl":"https://doi.org/10.1142/s0129054122460042","url":null,"abstract":"We consider the problem of local privacy where actions are subsets of a ground multiset and expectation rewards are modeled by a [Formula: see text]decomposable monotone submodular function. For the DR-submodular maximization problem under a polymatroid constraint, Soma and Yoshida [26] provide a continuous greedy algorithm for no-privacy setting. In this paper, we obtain the first differentially private algorithm for DR-submodular maximization subject to a polymatroid constraint. Our algorithm achieves a [Formula: see text]approximation with a little loss and runs in [Formula: see text][Formula: see text] times where [Formula: see text] is the rank of the base polymatroid and [Formula: see text] is the size of ground set. Along the way, we analyze the utility and privacy of our algorithm. A concrete experiment to simulate the privacy Uber pickups location problem is provided, and our algorithm performs well within the agreed range.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42455228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-31DOI: 10.1142/s0129054122460030
Jie Gao, Juan Zou, Yuzhong Zhang
In this paper, we study the single-machine scheduling problems with DeJong’s learning effect and deteriorating maintenance activity, where DeJong’s learning effect is a special position-based learning effect and the duration of the deteriorating maintenance activity is a linear increasing function of its starting time. Our goal is to determine the job sequence of all jobs and the position of the maintenance activity to minimize some performance measures. When the performance measures are the makespan and the total completion time, we show that both of them can be solved in polynomial time. When the performance measure is the total weighted completion time, we develop a pseudo-polynomial time dynamic programming algorithm under a special case. When the performance measure is the maximum lateness, we show that the earliest due date first (EDD) order is a bad algorithm for the general case, and develop a polynomial time algorithm under a special case.
{"title":"Single-Machine Scheduling with a Deteriorating Maintenance Activity and DeJong’s Learning Effect","authors":"Jie Gao, Juan Zou, Yuzhong Zhang","doi":"10.1142/s0129054122460030","DOIUrl":"https://doi.org/10.1142/s0129054122460030","url":null,"abstract":"In this paper, we study the single-machine scheduling problems with DeJong’s learning effect and deteriorating maintenance activity, where DeJong’s learning effect is a special position-based learning effect and the duration of the deteriorating maintenance activity is a linear increasing function of its starting time. Our goal is to determine the job sequence of all jobs and the position of the maintenance activity to minimize some performance measures. When the performance measures are the makespan and the total completion time, we show that both of them can be solved in polynomial time. When the performance measure is the total weighted completion time, we develop a pseudo-polynomial time dynamic programming algorithm under a special case. When the performance measure is the maximum lateness, we show that the earliest due date first (EDD) order is a bad algorithm for the general case, and develop a polynomial time algorithm under a special case.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43160624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：