V. Polishchuk, E. Arkin, A. Efrat, Christian Knauer, Joseph B. M. Mitchell, G. Rote, Lena Schlipf, Topi Talvitie
{"title":"Shortest path to a segment and quickest visibility queries","authors":"V. Polishchuk, E. Arkin, A. Efrat, Christian Knauer, Joseph B. M. Mitchell, G. Rote, Lena Schlipf, Topi Talvitie","doi":"10.20382/jocg.v7i2a5","DOIUrl":null,"url":null,"abstract":"We show how to preprocess a polygonal domain with a fixed starting point $s$ in order to answer efficiently the following queries: Given a point $q$, how should one move from $s$ in order to see $q$ as soon as possible? This query resembles the well-known shortest-path-to-a-point query, except that the latter asks for the fastest way to reach $q$, instead of seeing it. Our solution methods include a data structure for a different generalization of shortest-path-to-a-point queries, which may be of independent interest: to report efficiently a shortest path from $s$ to a query segment in the domain.","PeriodicalId":43044,"journal":{"name":"Journal of Computational Geometry","volume":"6 1","pages":"658-673"},"PeriodicalIF":0.4000,"publicationDate":"2015-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.20382/jocg.v7i2a5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 13
Abstract
We show how to preprocess a polygonal domain with a fixed starting point $s$ in order to answer efficiently the following queries: Given a point $q$, how should one move from $s$ in order to see $q$ as soon as possible? This query resembles the well-known shortest-path-to-a-point query, except that the latter asks for the fastest way to reach $q$, instead of seeing it. Our solution methods include a data structure for a different generalization of shortest-path-to-a-point queries, which may be of independent interest: to report efficiently a shortest path from $s$ to a query segment in the domain.
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