Serafino Cicerone , Alessia Di Fonso , Gabriele Di Stefano , Alfredo Navarra
{"title":"测地线相互可见性问题:网格和树木上的遗忘机器人","authors":"Serafino Cicerone , Alessia Di Fonso , Gabriele Di Stefano , Alfredo Navarra","doi":"10.1016/j.pmcj.2023.101842","DOIUrl":null,"url":null,"abstract":"<div><p>The <span>Mutual Visibility</span> is a well-known problem in the context of mobile robots. For a set of <span><math><mi>n</mi></math></span> robots disposed in the Euclidean plane, it asks for moving the robots without collisions so as to achieve a placement ensuring that no three robots are collinear. For robots moving on graphs, we consider the <span>Geodesic Mutual Visibility</span>\n(<span><math><mi>GMV</mi></math></span>) problem. Robots move along the edges of the graph, without collisions, so as to occupy some vertices that guarantee they become pairwise geodesic mutually visible. This means that there is a shortest path (i.e., a “geodesic”) between each pair of robots along which no other robots reside. We study this problem in the context of trees and (finite or infinite) square grids, for robots operating under the standard Look–Compute–Move model. In both scenarios, we provide resolution algorithms along with formal correctness proofs, highlighting the most relevant peculiarities arising within the different contexts, while optimizing the time complexity.</p></div>","PeriodicalId":49005,"journal":{"name":"Pervasive and Mobile Computing","volume":"95 ","pages":"Article 101842"},"PeriodicalIF":3.0000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The geodesic mutual visibility problem: Oblivious robots on grids and trees\",\"authors\":\"Serafino Cicerone , Alessia Di Fonso , Gabriele Di Stefano , Alfredo Navarra\",\"doi\":\"10.1016/j.pmcj.2023.101842\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The <span>Mutual Visibility</span> is a well-known problem in the context of mobile robots. For a set of <span><math><mi>n</mi></math></span> robots disposed in the Euclidean plane, it asks for moving the robots without collisions so as to achieve a placement ensuring that no three robots are collinear. For robots moving on graphs, we consider the <span>Geodesic Mutual Visibility</span>\\n(<span><math><mi>GMV</mi></math></span>) problem. Robots move along the edges of the graph, without collisions, so as to occupy some vertices that guarantee they become pairwise geodesic mutually visible. This means that there is a shortest path (i.e., a “geodesic”) between each pair of robots along which no other robots reside. We study this problem in the context of trees and (finite or infinite) square grids, for robots operating under the standard Look–Compute–Move model. In both scenarios, we provide resolution algorithms along with formal correctness proofs, highlighting the most relevant peculiarities arising within the different contexts, while optimizing the time complexity.</p></div>\",\"PeriodicalId\":49005,\"journal\":{\"name\":\"Pervasive and Mobile Computing\",\"volume\":\"95 \",\"pages\":\"Article 101842\"},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pervasive and Mobile Computing\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1574119223001001\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, INFORMATION SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pervasive and Mobile Computing","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1574119223001001","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
The geodesic mutual visibility problem: Oblivious robots on grids and trees
The Mutual Visibility is a well-known problem in the context of mobile robots. For a set of robots disposed in the Euclidean plane, it asks for moving the robots without collisions so as to achieve a placement ensuring that no three robots are collinear. For robots moving on graphs, we consider the Geodesic Mutual Visibility
() problem. Robots move along the edges of the graph, without collisions, so as to occupy some vertices that guarantee they become pairwise geodesic mutually visible. This means that there is a shortest path (i.e., a “geodesic”) between each pair of robots along which no other robots reside. We study this problem in the context of trees and (finite or infinite) square grids, for robots operating under the standard Look–Compute–Move model. In both scenarios, we provide resolution algorithms along with formal correctness proofs, highlighting the most relevant peculiarities arising within the different contexts, while optimizing the time complexity.
期刊介绍:
As envisioned by Mark Weiser as early as 1991, pervasive computing systems and services have truly become integral parts of our daily lives. Tremendous developments in a multitude of technologies ranging from personalized and embedded smart devices (e.g., smartphones, sensors, wearables, IoTs, etc.) to ubiquitous connectivity, via a variety of wireless mobile communications and cognitive networking infrastructures, to advanced computing techniques (including edge, fog and cloud) and user-friendly middleware services and platforms have significantly contributed to the unprecedented advances in pervasive and mobile computing. Cutting-edge applications and paradigms have evolved, such as cyber-physical systems and smart environments (e.g., smart city, smart energy, smart transportation, smart healthcare, etc.) that also involve human in the loop through social interactions and participatory and/or mobile crowd sensing, for example. The goal of pervasive computing systems is to improve human experience and quality of life, without explicit awareness of the underlying communications and computing technologies.
The Pervasive and Mobile Computing Journal (PMC) is a high-impact, peer-reviewed technical journal that publishes high-quality scientific articles spanning theory and practice, and covering all aspects of pervasive and mobile computing and systems.