Caterina Feletti, C. Mereghetti, Beatrice Palano, Priscilla Raucci
In the field of robotics, a lot of theoretical models have been settled to formalize multi-agent systems and design distributed algorithms for autonomous robots. Among the most investigated problems for such systems, the study of the Uniform Circle Formation (UCF problem earned a lot of attention for the properties of such a convenient disposition. Such a problem asks robots to move on the plane to form a regular polygon, running a deterministic and distributed algorithm by executing a sequence of look–compute–move cycles. This work aims to solve the UCF problem for a very restrictive model of robots: they are punctiform, anonymous, and indistinguishable. They are completely disoriented, i.e., they share neither the coordinate system nor chirality. Additionally, they are opaque, so collinearities can hide important data for a proper computation. To tackle these system limitations, robots are equipped with a persistent light used to communicate and store a constant amount of information. For such a robot model, this paper presents a solution for UCF for each of the three scheduling modes usually studied in the literature: fully synchronous, semi-synchronous, and asynchronous. Regarding the time complexity, the proposed algorithms use a constant number of cycles (epochs) for fully synchronous (semi-synchronous) robots, and linearly, many epochs in the worst case for asynchronous robots.
{"title":"Uniform Circle Formation for Fully Semi-, and Asynchronous Opaque Robots with Lights","authors":"Caterina Feletti, C. Mereghetti, Beatrice Palano, Priscilla Raucci","doi":"10.3390/app13137991","DOIUrl":"https://doi.org/10.3390/app13137991","url":null,"abstract":"In the field of robotics, a lot of theoretical models have been settled to formalize multi-agent systems and design distributed algorithms for autonomous robots. Among the most investigated problems for such systems, the study of the Uniform Circle Formation (UCF problem earned a lot of attention for the properties of such a convenient disposition. Such a problem asks robots to move on the plane to form a regular polygon, running a deterministic and distributed algorithm by executing a sequence of look–compute–move cycles. This work aims to solve the UCF problem for a very restrictive model of robots: they are punctiform, anonymous, and indistinguishable. They are completely disoriented, i.e., they share neither the coordinate system nor chirality. Additionally, they are opaque, so collinearities can hide important data for a proper computation. To tackle these system limitations, robots are equipped with a persistent light used to communicate and store a constant amount of information. For such a robot model, this paper presents a solution for UCF for each of the three scheduling modes usually studied in the literature: fully synchronous, semi-synchronous, and asynchronous. Regarding the time complexity, the proposed algorithms use a constant number of cycles (epochs) for fully synchronous (semi-synchronous) robots, and linearly, many epochs in the worst case for asynchronous robots.","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122641494","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}
We study the parameterized complexity of the $s$-Club Cluster Edge Deletion problem: Given a graph $G$ and two integers $s ge 2$ and $k ge 1$, is it possible to remove at most $k$ edges from $G$ such that each connected component of the resulting graph has diameter at most $s$? This problem is known to be NP-hard already when $s = 2$. We prove that it admits a fixed-parameter tractable algorithm when parameterized by $s$ and the treewidth of the input graph.
我们研究了$s$-Club聚类边删除问题的参数化复杂性:给定一个图$G$和两个整数$s ge 2$和$k ge 1$，是否有可能从$G$中删除最多$k$条边，使得结果图的每个连通成分的直径最多$s$?当$s = 2$时，这个问题已知是np困难的。我们证明了当参数化为$s$和输入图的树宽时，它允许一个固定参数的可处理算法。
{"title":"On the Parametrized Complexity of the s-Club Cluster Edge Deletion Problem","authors":"Fabrizio Montecchiani, Giacomo Ortali, Tommaso Piselli, Alessandra Tappini","doi":"10.48550/arXiv.2205.10834","DOIUrl":"https://doi.org/10.48550/arXiv.2205.10834","url":null,"abstract":"We study the parameterized complexity of the $s$-Club Cluster Edge Deletion problem: Given a graph $G$ and two integers $s ge 2$ and $k ge 1$, is it possible to remove at most $k$ edges from $G$ such that each connected component of the resulting graph has diameter at most $s$? This problem is known to be NP-hard already when $s = 2$. We prove that it admits a fixed-parameter tractable algorithm when parameterized by $s$ and the treewidth of the input graph.","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125420220","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}
Motivated by the work on the domination number of directed de Bruijn graphs and some of its generalizations, in this paper we introduce a natural generalization of de Bruijn graphs (directed and undirected), namely $t$-constrained de Bruijn graphs, where $t$ is a positive integer, and then study the domination number of these graphs. Within the definition of $t$-constrained de Bruijn graphs, de Bruijn and Kautz graphs correspond to 1-constrained and 2-constrained de Bruijn graphs, respectively. This generalization inherits many structural properties of de Bruijn graphs and may have similar applications in interconnection networks or bioinformatics. We establish upper and lower bounds for the domination number on $t$-constrained de Bruijn graphs both in the directed and in the undirected case. These bounds are often very close and in some cases we are able to find the exact value.
{"title":"On the Domination Number of t-Constrained de Bruijn Graphs","authors":"T. Calamoneri, A. Monti, B. Sinaimeri","doi":"10.46298/dmtcs.8879","DOIUrl":"https://doi.org/10.46298/dmtcs.8879","url":null,"abstract":"Motivated by the work on the domination number of directed de Bruijn graphs\u0000and some of its generalizations, in this paper we introduce a natural\u0000generalization of de Bruijn graphs (directed and undirected), namely\u0000$t$-constrained de Bruijn graphs, where $t$ is a positive integer, and then\u0000study the domination number of these graphs.\u0000 Within the definition of $t$-constrained de Bruijn graphs, de Bruijn and\u0000Kautz graphs correspond to 1-constrained and 2-constrained de Bruijn graphs,\u0000respectively. This generalization inherits many structural properties of de\u0000Bruijn graphs and may have similar applications in interconnection networks or\u0000bioinformatics.\u0000 We establish upper and lower bounds for the domination number on\u0000$t$-constrained de Bruijn graphs both in the directed and in the undirected\u0000case. These bounds are often very close and in some cases we are able to find\u0000the exact value.","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"152 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123010266","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 : 2019-01-27DOI: 10.1007/978-3-030-10801-4_14
S. Das, R. Focardi, F. Luccio, Euripides Markou, D. Moro, M. Squarcina
{"title":"Gathering of Robots in a Ring with Mobile Faults","authors":"S. Das, R. Focardi, F. Luccio, Euripides Markou, D. Moro, M. Squarcina","doi":"10.1007/978-3-030-10801-4_14","DOIUrl":"https://doi.org/10.1007/978-3-030-10801-4_14","url":null,"abstract":"","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132517421","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 : 2016-08-17DOI: 10.1007/978-3-319-44543-4_11
T. Calamoneri, Mattia Gastaldello, A. Mary, M. Sagot, B. Sinaimeri
{"title":"On Maximal Chain Subgraphs and Covers of Bipartite Graphs","authors":"T. Calamoneri, Mattia Gastaldello, A. Mary, M. Sagot, B. Sinaimeri","doi":"10.1007/978-3-319-44543-4_11","DOIUrl":"https://doi.org/10.1007/978-3-319-44543-4_11","url":null,"abstract":"","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"84 5-6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120913735","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 : 2015-08-24DOI: 10.1007/978-3-662-48057-1_14
C. Dima, Bastien Maubert, S. Pinchinat
{"title":"Relating Paths in Transition Systems: the Fall of the Modal mu-Calculus","authors":"C. Dima, Bastien Maubert, S. Pinchinat","doi":"10.1007/978-3-662-48057-1_14","DOIUrl":"https://doi.org/10.1007/978-3-662-48057-1_14","url":null,"abstract":"","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"125 33","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114046854","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}
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：