{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T02:15:57Z","timestamp":1770516957957,"version":"3.49.0"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:p> This paper studies two types of reverse 1-center problems under uniform linear cost function where edge lengths are allowed to reduce. In the first type, the aim is that the objective value is bounded by a prescribed fixed value [Formula: see text] at minimum cost. The aim of the other is to improve the objective value as much as possible within a given budget. An algorithm based on dynamic programming is proposed to solve the first problem in linear time. Then, this algorithm is applied as a subroutine to design an algorithm to solve the second type of the problem in [Formula: see text] time in which [Formula: see text] is a fixed number dependent on the problem parameters. Under the similarity assumption, this algorithm has a better complexity than the Nguyen algorithm (2013) with quadratic-time complexity. Some numerical experiments are conducted to validate this fact in practice. <\/jats:p>","DOI":"10.1142\/s0217595920500347","type":"journal-article","created":{"date-parts":[[2020,6,18]],"date-time":"2020-06-18T14:32:37Z","timestamp":1592490757000},"page":"2050034","source":"Crossref","is-referenced-by-count":7,"title":["Further Study on Reverse 1-Center Problem on Trees"],"prefix":"10.1142","volume":"37","author":[{"given":"Ali Reza","family":"Sepasian","sequence":"first","affiliation":[{"name":"Faculty of Basic Science, Department of Mathematics, Fasa University, Fasa, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Javad","family":"Tayyebi","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, Birjand University of Technology, Birjand, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,9,15]]},"reference":[{"key":"S0217595920500347BIB001","volume-title":"Network 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