Pub Date : 2024-02-27DOI: 10.1142/s0129626423400170
Saber Gholami, Hovhannes A. Harutyunyan
Broadcasting is a fundamental problem in the information dissemination area. In classical broadcasting, a message must be sent from one network member to all other members as rapidly as feasible. Although it has been demonstrated that this problem is NP-Hard for arbitrary graphs, it has several applications in various fields. As a result, the universal lists model, replicating real-world restrictions like the memory limits of nodes in large networks, is introduced as a branch of this problem in the literature. In the universal lists model, each node is equipped with a fixed list and has to follow the list regardless of the originator. In this study, we focus on the non-adaptive branch of universal lists broadcasting. In this regard, we establish the optimal broadcast time of [Formula: see text]-ary trees and binomial trees under the non-adaptive model and provide an upper bound for complete bipartite graphs. We also improved a general upper bound for trees under the same model and showed that our upper bound cannot be improved in general.
{"title":"A Note to Non-adaptive Broadcasting","authors":"Saber Gholami, Hovhannes A. Harutyunyan","doi":"10.1142/s0129626423400170","DOIUrl":"https://doi.org/10.1142/s0129626423400170","url":null,"abstract":"Broadcasting is a fundamental problem in the information dissemination area. In classical broadcasting, a message must be sent from one network member to all other members as rapidly as feasible. Although it has been demonstrated that this problem is NP-Hard for arbitrary graphs, it has several applications in various fields. As a result, the universal lists model, replicating real-world restrictions like the memory limits of nodes in large networks, is introduced as a branch of this problem in the literature. In the universal lists model, each node is equipped with a fixed list and has to follow the list regardless of the originator. In this study, we focus on the non-adaptive branch of universal lists broadcasting. In this regard, we establish the optimal broadcast time of [Formula: see text]-ary trees and binomial trees under the non-adaptive model and provide an upper bound for complete bipartite graphs. We also improved a general upper bound for trees under the same model and showed that our upper bound cannot be improved in general.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"56 1","pages":"2340017:1-2340017:19"},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140427744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-05DOI: 10.1142/s012962642340008x
Jin Li, Yisong Huang, Xinlong Chen, Yanglan Fu
As a kind of generalization of Transformers in the graph domain, Global Graph Transformers are good at learning distant knowledge by directly doing information interactions on complete graphs, which differs from Local Graph Transformers interacting on the original structures. However, we find that most prior works focus only on graph-level tasks (e.g., graph classification) and few Graph Transformer models can effectively solve node-level tasks, especially semi-supervised node classification, which obviously has important practical significance due to the limitation and expensiveness of these node labels. In order to fill this gap, this paper first summarizes the theoretical advantages of Graph Transformers. And based on some exploring experiments, we give some discussions on the main cause of their poor practical performance in semi-supervised node classifications. Secondly, based on this analysis, we design a three-stage homogeneity augmentation framework and propose a Semi-Global Graph Transformer. Considering both global and local perspectives, the proposed model combines various technologies including self-distillation, pseudo-label filtering, pre-training and fine-tuning, and metric learning. Furthermore, it simultaneously enhances the structure and the optimization, improving its effectiveness, scalability, and generalizability. Finally, extensive experiments on seven public homogeneous and heterophilous graph benchmarks show that the proposed method can achieve competitive or much better results compared to many baseline models including state-of-the-arts.
{"title":"Semi-Supervised Node Classification via Semi-Global Graph Transformer Based on Homogeneity Augmentation","authors":"Jin Li, Yisong Huang, Xinlong Chen, Yanglan Fu","doi":"10.1142/s012962642340008x","DOIUrl":"https://doi.org/10.1142/s012962642340008x","url":null,"abstract":"As a kind of generalization of Transformers in the graph domain, Global Graph Transformers are good at learning distant knowledge by directly doing information interactions on complete graphs, which differs from Local Graph Transformers interacting on the original structures. However, we find that most prior works focus only on graph-level tasks (e.g., graph classification) and few Graph Transformer models can effectively solve node-level tasks, especially semi-supervised node classification, which obviously has important practical significance due to the limitation and expensiveness of these node labels. In order to fill this gap, this paper first summarizes the theoretical advantages of Graph Transformers. And based on some exploring experiments, we give some discussions on the main cause of their poor practical performance in semi-supervised node classifications. Secondly, based on this analysis, we design a three-stage homogeneity augmentation framework and propose a Semi-Global Graph Transformer. Considering both global and local perspectives, the proposed model combines various technologies including self-distillation, pseudo-label filtering, pre-training and fine-tuning, and metric learning. Furthermore, it simultaneously enhances the structure and the optimization, improving its effectiveness, scalability, and generalizability. Finally, extensive experiments on seven public homogeneous and heterophilous graph benchmarks show that the proposed method can achieve competitive or much better results compared to many baseline models including state-of-the-arts.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"2011 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131653748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-25DOI: 10.1142/s0129626423400078
Bingshi Li, Jin Li, Yanglan Fu
Over the past few years, graph contrastive learning (GCL) has gained great success in processing unlabeled graph-structured data, but most of the existing GCL methods are based on instance discrimination task which typically learns representations by minimizing the distance between two versions of the same instance. However, different from images, which are assumed to be independently and identically distributed, graphs present relational information among data instances, in which each instance is related to others by links. Furthermore, the relations are heterogeneous in many cases. The instance discrimination task cannot make full use of the relational information inherent in the graph-structured data. To solve the above-mentioned problems, this paper proposes a relation-aware graph contrastive learning method, called RGCL. Aiming to capture the most important heterogeneous relations in the graph, RGCL explicitly models the edges, and then pulls semantically similar pairs of edges together and pushes dissimilar ones apart with contrastive regularization. By exploiting the full potential of the relationship among nodes, RGCL overcomes the limitations of previous GCL methods based on instance discrimination. The experimental results demonstrate that the proposed method outperforms a series of graph contrastive learning frameworks on widely used benchmarks, which justifies the effectiveness of our work.
{"title":"Relation-aware Graph Contrastive Learning","authors":"Bingshi Li, Jin Li, Yanglan Fu","doi":"10.1142/s0129626423400078","DOIUrl":"https://doi.org/10.1142/s0129626423400078","url":null,"abstract":"Over the past few years, graph contrastive learning (GCL) has gained great success in processing unlabeled graph-structured data, but most of the existing GCL methods are based on instance discrimination task which typically learns representations by minimizing the distance between two versions of the same instance. However, different from images, which are assumed to be independently and identically distributed, graphs present relational information among data instances, in which each instance is related to others by links. Furthermore, the relations are heterogeneous in many cases. The instance discrimination task cannot make full use of the relational information inherent in the graph-structured data. To solve the above-mentioned problems, this paper proposes a relation-aware graph contrastive learning method, called RGCL. Aiming to capture the most important heterogeneous relations in the graph, RGCL explicitly models the edges, and then pulls semantically similar pairs of edges together and pushes dissimilar ones apart with contrastive regularization. By exploiting the full potential of the relationship among nodes, RGCL overcomes the limitations of previous GCL methods based on instance discrimination. The experimental results demonstrate that the proposed method outperforms a series of graph contrastive learning frameworks on widely used benchmarks, which justifies the effectiveness of our work.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"2006 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117044555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-25DOI: 10.1142/s0129626423500044
Qifan Zhang, Liqiong Xu, Yuqing Lin
Directed cycles in digraphs are useful in embedding linear arrays and rings, and are suitable for designing simple algorithm with low communication costs in parallel computer systems, thus the existence of directed cycles on digraphs has been largely investigated. Let [Formula: see text], [Formula: see text] be integers. Bermond et al. [Journal of Graph Theory 4(3) (1980) 337–341] proved that if the size of a strong digraph [Formula: see text] with order [Formula: see text] is at least [Formula: see text], then the girth of [Formula: see text] is no more than [Formula: see text]. Consequently, when [Formula: see text] is a 4-free strong digraph with order [Formula: see text], which means that every directed cycle in [Formula: see text] has length at least [Formula: see text], then the maximum size of [Formula: see text] is [Formula: see text]. In this paper, we mainly give the structural characterizations for all 4-free strong digraphs of order [Formula: see text] whose arc number exactly is [Formula: see text].
有向图上的有向环用于嵌入线性阵列和环，并且适合设计并行计算机系统中通信成本低的简单算法，因此对有向图上的有向环的存在性进行了大量的研究。设[公式:见文]，[公式:见文]为整数。Bermond等[Journal of Graph Theory 4(3)(1980) 337-341]证明了如果有序的强有向图[公式:见文]的大小至少为[公式:见文]，则[公式:见文]的周长不大于[公式:见文]。因此，当[Formula: see text]是一个顺序为[Formula: see text]的4-free强有向图时，这意味着[Formula: see text]中的每个有向循环的长度至少为[Formula: see text]，则[Formula: see text]的最大大小为[Formula: see text]。本文主要给出了所有阶[公式:见文]且弧数恰好为[公式:见文]的4-自由强有向图的结构刻画。
{"title":"4-Free Strong Digraphs with the Maximum Size","authors":"Qifan Zhang, Liqiong Xu, Yuqing Lin","doi":"10.1142/s0129626423500044","DOIUrl":"https://doi.org/10.1142/s0129626423500044","url":null,"abstract":"Directed cycles in digraphs are useful in embedding linear arrays and rings, and are suitable for designing simple algorithm with low communication costs in parallel computer systems, thus the existence of directed cycles on digraphs has been largely investigated. Let [Formula: see text], [Formula: see text] be integers. Bermond et al. [Journal of Graph Theory 4(3) (1980) 337–341] proved that if the size of a strong digraph [Formula: see text] with order [Formula: see text] is at least [Formula: see text], then the girth of [Formula: see text] is no more than [Formula: see text]. Consequently, when [Formula: see text] is a 4-free strong digraph with order [Formula: see text], which means that every directed cycle in [Formula: see text] has length at least [Formula: see text], then the maximum size of [Formula: see text] is [Formula: see text]. In this paper, we mainly give the structural characterizations for all 4-free strong digraphs of order [Formula: see text] whose arc number exactly is [Formula: see text].","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114745602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-14DOI: 10.1142/s0129626423300015
Baohua Niu, Shuming Zhou, Hong Zhang
In this work, we determine all the eigenvalues and their corresponding multiplicities of the normalized Laplacian matrix for folded hypercubes. Furthermore, we establish the explicit formula to calculate Kemeny’s constant for random walks on the folded hypercube, which indicates that its growth is roughly consistent with the network order. In addition, we also determine the number of spanning trees and degree-Kirchhoff index of folded hypercubes. Especially, we make some comparisons with that of hypercubes to verify that folded hypercubes have superior properties than hypercubes.
{"title":"The Normalized Laplacian Spectrum of Folded Hypercube with Applications","authors":"Baohua Niu, Shuming Zhou, Hong Zhang","doi":"10.1142/s0129626423300015","DOIUrl":"https://doi.org/10.1142/s0129626423300015","url":null,"abstract":"In this work, we determine all the eigenvalues and their corresponding multiplicities of the normalized Laplacian matrix for folded hypercubes. Furthermore, we establish the explicit formula to calculate Kemeny’s constant for random walks on the folded hypercube, which indicates that its growth is roughly consistent with the network order. In addition, we also determine the number of spanning trees and degree-Kirchhoff index of folded hypercubes. Especially, we make some comparisons with that of hypercubes to verify that folded hypercubes have superior properties than hypercubes.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125301442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-21DOI: 10.1142/s0129626423500032
Hengji Qiao, Mingzu Zhang, Wenhuan Ma, Xing Yang
An interconnection network can be modelled as a connected graph [Formula: see text]. The reliability of interconnection networks is critical for multiprocessor systems. Several conditional edge-connectivities have been introduced in the past for accurately reflecting various realistic network situations, with the [Formula: see text]-extra edge-connectivity being one such conditional edge-connectivity. The [Formula: see text]-extra edge-connectivity of [Formula: see text], denoted by [Formula: see text], is the minimum cardinality of faulty edges whose deletion disconnects the graph [Formula: see text] with each resulting component containing at least [Formula: see text] processors. In general, for a connected graph [Formula: see text], determining whether the graph exists an [Formula: see text]-extra edge-cut is [Formula: see text]-hard. The folded-crossed hypercube [Formula: see text] is a variation of the crossed hypercube [Formula: see text] with [Formula: see text] processors. In this paper, after excavating the layer structure of folded-crossed hypercube, we investigate some recursive properties of [Formula: see text], based on some recursive properties, an effective [Formula: see text] algorithm of [Formula: see text]-extra edge-connectivity of folded-crossed hypercube is designed, which can determine the exact value and the [Formula: see text]-optimality of [Formula: see text] for each positive integer [Formula: see text]. Our results solve this problem thoroughly.
{"title":"An O(log(N)) Algorithm View: Reliability Evaluation of Folded-crossed Hypercube in Terms of h-extra Edge-connectivity","authors":"Hengji Qiao, Mingzu Zhang, Wenhuan Ma, Xing Yang","doi":"10.1142/s0129626423500032","DOIUrl":"https://doi.org/10.1142/s0129626423500032","url":null,"abstract":"An interconnection network can be modelled as a connected graph [Formula: see text]. The reliability of interconnection networks is critical for multiprocessor systems. Several conditional edge-connectivities have been introduced in the past for accurately reflecting various realistic network situations, with the [Formula: see text]-extra edge-connectivity being one such conditional edge-connectivity. The [Formula: see text]-extra edge-connectivity of [Formula: see text], denoted by [Formula: see text], is the minimum cardinality of faulty edges whose deletion disconnects the graph [Formula: see text] with each resulting component containing at least [Formula: see text] processors. In general, for a connected graph [Formula: see text], determining whether the graph exists an [Formula: see text]-extra edge-cut is [Formula: see text]-hard. The folded-crossed hypercube [Formula: see text] is a variation of the crossed hypercube [Formula: see text] with [Formula: see text] processors. In this paper, after excavating the layer structure of folded-crossed hypercube, we investigate some recursive properties of [Formula: see text], based on some recursive properties, an effective [Formula: see text] algorithm of [Formula: see text]-extra edge-connectivity of folded-crossed hypercube is designed, which can determine the exact value and the [Formula: see text]-optimality of [Formula: see text] for each positive integer [Formula: see text]. Our results solve this problem thoroughly.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126515702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-13DOI: 10.1142/s0129626423400030
Na Li, Ran Ma
In the production scheduling of prefabricated components, we study an online [Formula: see text] parallel-batch machines scheduling model considering learning effect jobs with [Formula: see text] incompatible job families to minimize the makespan in this paper, where the capacity of batch is unbounded. Job families indicate that a job must belong to some job family and jobs of distinct job families are incapable to be executed in the same batch. The information of each job including its basic processing time [Formula: see text] and release time [Formula: see text] is unknown in advance and is revealed at the instant of its arrival. Moreover, the actual processing time of job [Formula: see text] with learning effect is [Formula: see text], where [Formula: see text] and [Formula: see text] are non-negative parameters and [Formula: see text] denotes the starting time of prefabricated job [Formula: see text], respectively. When [Formula: see text], we propose an online algorithm with a competitive ratio of [Formula: see text]. Furthermore, the performance of the online algorithm is demonstrated by numerical experiments.
{"title":"Online Parallel-Batch Scheduling of Learning Effect Jobs with Incompatible Job Families for Prefabricated Components","authors":"Na Li, Ran Ma","doi":"10.1142/s0129626423400030","DOIUrl":"https://doi.org/10.1142/s0129626423400030","url":null,"abstract":"In the production scheduling of prefabricated components, we study an online [Formula: see text] parallel-batch machines scheduling model considering learning effect jobs with [Formula: see text] incompatible job families to minimize the makespan in this paper, where the capacity of batch is unbounded. Job families indicate that a job must belong to some job family and jobs of distinct job families are incapable to be executed in the same batch. The information of each job including its basic processing time [Formula: see text] and release time [Formula: see text] is unknown in advance and is revealed at the instant of its arrival. Moreover, the actual processing time of job [Formula: see text] with learning effect is [Formula: see text], where [Formula: see text] and [Formula: see text] are non-negative parameters and [Formula: see text] denotes the starting time of prefabricated job [Formula: see text], respectively. When [Formula: see text], we propose an online algorithm with a competitive ratio of [Formula: see text]. Furthermore, the performance of the online algorithm is demonstrated by numerical experiments.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128049658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-29DOI: 10.1142/s0129626423400029
Xiao‐hai Yang, Ran Ma
With the popularization of energy conservation and emission reduction, amounts of industrial production has taken energy conservation as a goal to achieve. The paper considers an online parallel-batch scheduling problem with deteriorating and incompatible families on identical machines to minimize the makespan, which minimizes the maximum energy consumption of machines. Specifically, the processing time of job [Formula: see text] is defined by an increasing function of its starting time [Formula: see text], i.e., [Formula: see text], where [Formula: see text] is the deterioration rate of job [Formula: see text]. For the problem, we propose an online algorithm with a competitive ratio of [Formula: see text], where [Formula: see text] is the largest deterioration rate in an instance. Furthermore, the paper presents a concise computational study of the numerical experiment to show that our algorithm performs very well in practice of this model.
随着节能减排的普及，大量的工业生产已经把节能作为一个目标来实现。为了使机器的最大能耗最小，研究了同一机器上具有劣化和不相容家族的在线并行批调度问题。具体来说，作业的加工时间[公式:见文]是其开始时间[公式:见文]的递增函数，即[公式:见文]，其中[公式:见文]是作业[公式:见文]的劣化率。针对该问题，我们提出了一种竞争比为[Formula: see text]的在线算法，其中[Formula: see text]是一个实例中最大的劣化率。此外，本文还对数值实验进行了简明的计算研究，表明该算法在该模型的实际应用中具有良好的性能。
{"title":"A Production Plan Considering Parallel Machines and Deteriorating Effects: Minimizing the Makespan in the Section of Steel Box Girder Processing","authors":"Xiao‐hai Yang, Ran Ma","doi":"10.1142/s0129626423400029","DOIUrl":"https://doi.org/10.1142/s0129626423400029","url":null,"abstract":"With the popularization of energy conservation and emission reduction, amounts of industrial production has taken energy conservation as a goal to achieve. The paper considers an online parallel-batch scheduling problem with deteriorating and incompatible families on identical machines to minimize the makespan, which minimizes the maximum energy consumption of machines. Specifically, the processing time of job [Formula: see text] is defined by an increasing function of its starting time [Formula: see text], i.e., [Formula: see text], where [Formula: see text] is the deterioration rate of job [Formula: see text]. For the problem, we propose an online algorithm with a competitive ratio of [Formula: see text], where [Formula: see text] is the largest deterioration rate in an instance. Furthermore, the paper presents a concise computational study of the numerical experiment to show that our algorithm performs very well in practice of this model.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125177201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-20DOI: 10.1142/s0129626423500020
V. Dimakopoulos, Aggelos Mourelis
Auto-scoping in OpenMP has been proposed as a means for relieving the programmer from the non-trivial effort of identifying the data sharing attributes of variables used within code regions that produce concurrency, such as parallel and task constructs. In this work we reconsider autoscoping on parallel constructs, including combined parallel-worksharing constructs. We first show that the current implementations do not always scope variables correctly in the presence of nested parallel constructs. We then proceed to extend the set of rules that guide the autoscoping decisions so as to handle nested constructs successfully. We also discuss how this functionality is implemented in the OMPi source-to-source OpenMP compiler.
{"title":"Revisiting OpenMP Auto-Scoping Rules","authors":"V. Dimakopoulos, Aggelos Mourelis","doi":"10.1142/s0129626423500020","DOIUrl":"https://doi.org/10.1142/s0129626423500020","url":null,"abstract":"Auto-scoping in OpenMP has been proposed as a means for relieving the programmer from the non-trivial effort of identifying the data sharing attributes of variables used within code regions that produce concurrency, such as parallel and task constructs. In this work we reconsider autoscoping on parallel constructs, including combined parallel-worksharing constructs. We first show that the current implementations do not always scope variables correctly in the presence of nested parallel constructs. We then proceed to extend the set of rules that guide the autoscoping decisions so as to handle nested constructs successfully. We also discuss how this functionality is implemented in the OMPi source-to-source OpenMP compiler.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125693511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-31DOI: 10.1142/s0129626423400017
S. Chopra, Hyunwoo Park, Sangho Shim
Mehrotra, Johnson, and Nemhauser (1998) [Management Science 44, pp. 1100–1114] addressed a problem for political districting and developed an optimization based heuristic to find good districting plans which partition the population units into contiguous districts with equal populations. Their case study found a good South Carolina plan at a penalty cost of 68. This paper develops a strong integer programming model identifying the exact optimal solution. Our model identifies the optimal South Carolina plan at the minimum penalty of 64. Motivated by the 2019 lawsuit challenging the congressional plan as gerrymandering, we inspect the actual Maryland plan.
{"title":"An Exact Solution Method for the Political Districting Problem","authors":"S. Chopra, Hyunwoo Park, Sangho Shim","doi":"10.1142/s0129626423400017","DOIUrl":"https://doi.org/10.1142/s0129626423400017","url":null,"abstract":"Mehrotra, Johnson, and Nemhauser (1998) [Management Science 44, pp. 1100–1114] addressed a problem for political districting and developed an optimization based heuristic to find good districting plans which partition the population units into contiguous districts with equal populations. Their case study found a good South Carolina plan at a penalty cost of 68. This paper develops a strong integer programming model identifying the exact optimal solution. Our model identifies the optimal South Carolina plan at the minimum penalty of 64. Motivated by the 2019 lawsuit challenging the congressional plan as gerrymandering, we inspect the actual Maryland plan.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"231 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116391177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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