Pub Date : 2018-09-28DOI: 10.1016/J.COMGEO.2020.101680
A. Bhattacharya, A. Mondal
{"title":"Covering the plane by a sequence of circular disks with a constraint","authors":"A. Bhattacharya, A. Mondal","doi":"10.1016/J.COMGEO.2020.101680","DOIUrl":"https://doi.org/10.1016/J.COMGEO.2020.101680","url":null,"abstract":"","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"1 1","pages":"101680"},"PeriodicalIF":0.0,"publicationDate":"2018-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91395211","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 : 2018-08-01DOI: 10.4230/LIPIcs.ESA.2018.73
Bo Zhou, Yi-Jen Chiang, C. Yap
The design and implementation of theoretically-sound robot motion planning algorithms is challenging. Within the framework of resolution-exact algorithms, it is possible to exploit soft predicates for collision detection. The design of soft predicates is a balancing act between easily implementable predicates and their accuracy/effectivity. In this paper, we focus on the class of planar polygonal rigid robots with arbitrarily complex geometry. We exploit the remarkable decomposability property of soft collision-detection predicates of such robots. We introduce a general technique to produce such a decomposition. If the robot is an m-gon, the complexity of this approach scales linearly in m. This contrasts with the O(m^3) complexity known for exact planners. It follows that we can now routinely produce soft predicates for any rigid polygonal robot. This results in resolution-exact planners for such robots within the general Soft Subdivision Search (SSS) framework. This is a significant advancement in the theory of sound and complete planners for planar robots. We implemented such decomposed predicates in our open-source Core Library. The experiments show that our algorithms are effective, perform in real time on non-trivial environments, and can outperform many sampling-based methods.
{"title":"Soft Subdivision Motion Planning for Complex Planar Robots","authors":"Bo Zhou, Yi-Jen Chiang, C. Yap","doi":"10.4230/LIPIcs.ESA.2018.73","DOIUrl":"https://doi.org/10.4230/LIPIcs.ESA.2018.73","url":null,"abstract":"The design and implementation of theoretically-sound robot motion planning algorithms is challenging. Within the framework of resolution-exact algorithms, it is possible to exploit soft predicates for collision detection. The design of soft predicates is a balancing act between easily implementable predicates and their accuracy/effectivity.\u0000In this paper, we focus on the class of planar polygonal rigid robots with arbitrarily complex geometry. We exploit the remarkable decomposability property of soft collision-detection predicates of such robots. We introduce a general technique to produce such a decomposition. If the robot is an m-gon, the complexity of this approach scales linearly in m. This contrasts with the O(m^3) complexity known for exact planners. It follows that we can now routinely produce soft predicates for any rigid polygonal robot. This results in resolution-exact planners for such robots within the general Soft Subdivision Search (SSS) framework. This is a significant advancement in the theory of sound and complete planners for planar robots.\u0000We implemented such decomposed predicates in our open-source Core Library. The experiments show that our algorithms are effective, perform in real time on non-trivial environments, and can outperform many sampling-based methods.","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"38 1","pages":"101683"},"PeriodicalIF":0.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73694222","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 : 2018-07-31DOI: 10.1007/978-3-030-04414-5_29
Marcel Radermacher, Ignaz Rutter
{"title":"Inserting an Edge into a Geometric Embedding","authors":"Marcel Radermacher, Ignaz Rutter","doi":"10.1007/978-3-030-04414-5_29","DOIUrl":"https://doi.org/10.1007/978-3-030-04414-5_29","url":null,"abstract":"","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"439 1","pages":"101843"},"PeriodicalIF":0.0,"publicationDate":"2018-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76672465","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 : 2018-03-06DOI: 10.1016/J.COMGEO.2020.101653
Ahmad Biniaz, Alfredo García
{"title":"Packing Plane Spanning Trees into a Point Set","authors":"Ahmad Biniaz, Alfredo García","doi":"10.1016/J.COMGEO.2020.101653","DOIUrl":"https://doi.org/10.1016/J.COMGEO.2020.101653","url":null,"abstract":"","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"09 1","pages":"101653"},"PeriodicalIF":0.0,"publicationDate":"2018-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86222109","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 : 2018-02-19DOI: 10.1007/978-3-030-00256-5_26
Linda Kleist, Boris Klemz, A. Lubiw, Lena Schlipf, F. Staals, Darren Strash
{"title":"Convexity-Increasing Morphs of Planar Graphs","authors":"Linda Kleist, Boris Klemz, A. Lubiw, Lena Schlipf, F. Staals, Darren Strash","doi":"10.1007/978-3-030-00256-5_26","DOIUrl":"https://doi.org/10.1007/978-3-030-00256-5_26","url":null,"abstract":"","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"11 1","pages":"69-88"},"PeriodicalIF":0.0,"publicationDate":"2018-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88350996","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 : 2017-08-01DOI: 10.1016/j.comgeo.2017.03.002
Gerald L. Orick, Kenneth Stephenson, Charles R. Collins
{"title":"A linearized circle packing algorithm","authors":"Gerald L. Orick, Kenneth Stephenson, Charles R. Collins","doi":"10.1016/j.comgeo.2017.03.002","DOIUrl":"https://doi.org/10.1016/j.comgeo.2017.03.002","url":null,"abstract":"","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"23 1","pages":"13-29"},"PeriodicalIF":0.0,"publicationDate":"2017-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90580673","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 : 2017-03-17DOI: 10.4230/LIPIcs.ISAAC.2016.9
O. Aichholzer, T. Hackl, Matias Korman, Alexander Pilz, G. Rote, André van Renssen, Marcel Roeloffzen, B. Vogtenhuber
Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is very long (when compared to the minimum length needed to obtain a spanning graph). We consider two different approaches: first we show an almost optimal centralized approach to extract two trees. Then we show a constant factor approximation for a distributed model in which each point can compute its adjacencies using only local information. This second approach may create cycles, but maintains planarity.
{"title":"Packing Short Plane Spanning Trees in Complete Geometric Graphs","authors":"O. Aichholzer, T. Hackl, Matias Korman, Alexander Pilz, G. Rote, André van Renssen, Marcel Roeloffzen, B. Vogtenhuber","doi":"10.4230/LIPIcs.ISAAC.2016.9","DOIUrl":"https://doi.org/10.4230/LIPIcs.ISAAC.2016.9","url":null,"abstract":"Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is very long (when compared to the minimum length needed to obtain a spanning graph). We consider two different approaches: first we show an almost optimal centralized approach to extract two trees. Then we show a constant factor approximation for a distributed model in which each point can compute its adjacencies using only local information. This second approach may create cycles, but maintains planarity.","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"14 1","pages":"1-15"},"PeriodicalIF":0.0,"publicationDate":"2017-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78843844","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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