{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,6]],"date-time":"2024-04-06T17:13:33Z","timestamp":1712423613169},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2008,4]]},"abstract":"This paper deals with an important problem of mobile communication. The objective is to place k base stations of equal range on the boundary of a convex polygonal region P such that each point inside P is covered by at least one base station. We name this problem as region-cover(k) problem. A simplified form of this problem is the vertex-cover(k) problem, where the objective is to communicate with only the vertices of P instead of covering the entire polygon. We first present efficient algorithms for vertex-cover(2) and region-cover(2) problems, where the base stations are to be installed on a pair of specified edges. The time complexity of these algorithms are O(n log n) and O(n2<\/jats:sup>) respectively, where n is the number of vertices in the polygon P. Next, we consider the case where k \u2265 3. We first concentrate on a restricted version of the vertex-cover(k) and region-cover(k) problems, where all the k base stations are to be installed on the same edge of P. Our proposed algorithm for the restricted vertex-cover(k) problem produces optimum result in O(min(n2<\/jats:sup>,nk log n)) time, whereas the algorithm for the restricted region-cover(k) problem produces an (1 + \u220a)-factor approximation result in [Formula: see text] time. Finally, we propose efficient heuristic algorithm for the unrestricted version of the region-cover(k) problem for k \u2265 3. Experimental results demonstrate that our proposed algorithm runs fast and produces near optimum solutions.<\/jats:p>","DOI":"10.1142\/s0129054108005747","type":"journal-article","created":{"date-parts":[[2008,4,10]],"date-time":"2008-04-10T11:30:22Z","timestamp":1207827022000},"page":"405-427","source":"Crossref","is-referenced-by-count":15,"title":["VARIATIONS OF BASE-STATION PLACEMENT PROBLEM ON THE BOUNDARY OF A CONVEX REGION"],"prefix":"10.1142","volume":"19","author":[{"given":"GAUTAM K.","family":"DAS","sequence":"first","affiliation":[{"name":"Indian Statistical Institute, Kolkata - 700 108, India"}]},{"given":"SASANKA","family":"ROY","sequence":"additional","affiliation":[{"name":"Tata Research Development and Design Centre, Pune-411103, India"}]},{"given":"SANDIP","family":"DAS","sequence":"additional","affiliation":[{"name":"Indian Statistical, Institute, Kolkata - 700 108, India"}]},{"given":"SUBHAS C.","family":"NANDY","sequence":"additional","affiliation":[{"name":"Indian Statistical Institute, Kolkata - 700 108, India"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf5","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03427-9","volume-title":"Computational Geometry Algorithms and Applications","author":"de Berg M.","year":"1997"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(99)00019-X"},{"key":"rf8","first-page":"379","volume":"6","author":"Elzinga J.","journal-title":"Transputer Sciences"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01228511"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1287\/moor.10.2.180"},{"key":"rf12","first-page":"17","volume":"15","author":"Hurtado F.","journal-title":"Studies in Locational Analysis"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.comnet.2004.08.012"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1137\/0212052"},{"key":"rf19","volume-title":"The LEDA Platform of Combinatorial and Geometric Computing","author":"Mehlhorn K.","year":"1999"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(87)90029-1"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009311"},{"key":"rf24","first-page":"79","volume":"1","author":"Sylvester J. J.","journal-title":"Quarterly Journal of Mathematics"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054108005747","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,4]],"date-time":"2020-05-04T01:25:39Z","timestamp":1588555539000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054108005747"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,4]]},"references-count":12,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,4]]}},"alternative-id":["10.1142\/S0129054108005747"],"URL":"https:\/\/doi.org\/10.1142\/s0129054108005747","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,4]]}}}