{"title":"贪婪自组织的拓扑方面","authors":"F. Ahmed, O. Tirkkonen","doi":"10.1109/SASO.2014.15","DOIUrl":null,"url":null,"abstract":"We consider self-organization problems, where agents try to agree about the value of a configuration space variable. Problems of consensus and synchronization belong to this category. These are the problems which would often be trivial to solve in a centralized setting, and non-trivial aspects are often directly induced by the process of self-organization itself. We discuss topological reasons as to why simple locally greedy algorithms are not able to create long-range order. The reason why greedy synchronization of a real-valued variable works in a straight forward manner, whereas greedy phase synchronization does not, is topological, in the latter non-trivial homotopy classes in mappings from the interaction graph of the agents to the configuration space exist. We identify higher dimensional configuration spaces with such non-trivial homotopy classes. However, we find that greedy self-organization is able to create long-range order for any higher-dimensional configuration space that does not possess circular components.","PeriodicalId":6458,"journal":{"name":"2014 IEEE Eighth International Conference on Self-Adaptive and Self-Organizing Systems Workshops","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2014-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Topological Aspects of Greedy Self-Organization\",\"authors\":\"F. Ahmed, O. Tirkkonen\",\"doi\":\"10.1109/SASO.2014.15\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider self-organization problems, where agents try to agree about the value of a configuration space variable. Problems of consensus and synchronization belong to this category. These are the problems which would often be trivial to solve in a centralized setting, and non-trivial aspects are often directly induced by the process of self-organization itself. We discuss topological reasons as to why simple locally greedy algorithms are not able to create long-range order. The reason why greedy synchronization of a real-valued variable works in a straight forward manner, whereas greedy phase synchronization does not, is topological, in the latter non-trivial homotopy classes in mappings from the interaction graph of the agents to the configuration space exist. We identify higher dimensional configuration spaces with such non-trivial homotopy classes. However, we find that greedy self-organization is able to create long-range order for any higher-dimensional configuration space that does not possess circular components.\",\"PeriodicalId\":6458,\"journal\":{\"name\":\"2014 IEEE Eighth International Conference on Self-Adaptive and Self-Organizing Systems Workshops\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-09-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2014 IEEE Eighth International Conference on Self-Adaptive and Self-Organizing Systems Workshops\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SASO.2014.15\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2014 IEEE Eighth International Conference on Self-Adaptive and Self-Organizing Systems Workshops","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SASO.2014.15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider self-organization problems, where agents try to agree about the value of a configuration space variable. Problems of consensus and synchronization belong to this category. These are the problems which would often be trivial to solve in a centralized setting, and non-trivial aspects are often directly induced by the process of self-organization itself. We discuss topological reasons as to why simple locally greedy algorithms are not able to create long-range order. The reason why greedy synchronization of a real-valued variable works in a straight forward manner, whereas greedy phase synchronization does not, is topological, in the latter non-trivial homotopy classes in mappings from the interaction graph of the agents to the configuration space exist. We identify higher dimensional configuration spaces with such non-trivial homotopy classes. However, we find that greedy self-organization is able to create long-range order for any higher-dimensional configuration space that does not possess circular components.