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2-Medians in trees with pos/neg weights

Rainer E. Burkard, Eranda Çela, Helidon Dollani
2000 Discrete Applied Mathematics  
For the p-median problem with pos=neg weights on a path we give an O(pn 2 ) algorithm.  ...  For the pos=neg 2-median problem on a network with n vertices, these properties can be exploited to derive an O(n 2 ) algorithm for trees, an O(n log n) algorithm for stars and a linear algorithm for paths  ...  This research has been supported by the Spezialforschungsbereich F003 "Optimierung und Kontrolle", Projektbereich Diskrete Optimierung.  ... 
doi:10.1016/s0166-218x(00)00177-3 fatcat:heksuhjebvfcfkkxso2kxrg2ci

Finding a core of a tree with pos/neg weight

Mehdi Zaferanieh, Jafar Fathali
2012 Mathematical Methods of Operations Research  
Morgan and Slater [Journal of Algorithms 1 (1980) 247] presented a linear time algorithm for finding the core of a tree with only positive weights of vertices.  ...  We show that their algorithm also works for semi-obnoxious problems.  ...  Acknowledgment The authors would like to express their sincere gratitude to the anonymous referees for their careful reading of the manuscript and their constructive comments which resulted in the improvement  ... 
doi:10.1007/s00186-012-0394-5 fatcat:2h4v7jhux5hf3muhhhz2vgh4rq

An ant colony algorithm for the pos/neg weighted p-median problem

Jafar Fathali, Hossein T. Kakhki, Rainer E. Burkard
2006 Central European Journal of Operations Research  
In this paper an Ant Colony algorithm with a tabu restriction is designed for both problems.  ...  The classical graph version of the p-median problem asks for a subset X ⊆ V of cardinality p, so that the (weighted) sum of the minimum distances from X to all other vertices in V is minimized.  ...  Burkard et al. (2000) considered p-median problems with pos/neg weights in graphs and noted that there are two different models: In the first model (P1) the sum of the minimum weighted distances is minimized  ... 
doi:10.1007/s10100-006-0001-z fatcat:nas75yx7ovdfbd4d5lbxsk255u

The pos/neg-weighted 1-median problem on tree graphs with subtree-shaped customers

Yukun Cheng, Liying Kang, Changhong Lu
2010 Theoretical Computer Science  
Based on this property we devise a polynomial time algorithm for the pos/neg-weighted 1-median problem on a tree with subtree-shaped customers.  ...  In this paper we consider the pos/neg-weighted median problem on a tree graph where the customers are modeled as continua subtrees.  ...  Acknowledgements The authors are grateful to the referees for their valuable comments, which have led to improvements in the presentation of the paper.  ... 
doi:10.1016/j.tcs.2009.11.009 fatcat:cj4t6xzzbncgtd3giebyujbmqa

Page 2909 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
(A-TGRZ-IM; Graz); Krarup, J. (DK-CPNH-CS; Copenhagen) A linear algorithm for the pos/neg-weighted |-median problem on a cactus. (English summary) Computing 60 (1998), no. 3, 193-215.  ...  We allow for negative weights as well and devise an exact algorithm for the resulting ‘pos/neg-weightedproblem defined on a cactus.  ... 

On the finding 2-(k,l)-core of a tree with arbitrary real weight

S. M. Ashkezari, J. Fathali
2019 Iranian journal of numerical analysis and optimization  
Then an algorithm for finding the 2-(k, l)-core of a tree with the pos/neg weight is presented.  ...  In this paper, we first investigate the problem of finding 2-(k, l)-core on an unweighted tree and show that there exists a solution that none of (k, l)-cores is a vertex.  ...  Acknowledgements Authors are grateful to there anonymous referees and editor for their constructive comments.  ... 
doi:10.22067/ijnao.v9i1.65852 doaj:7e255b30d0f14a229027f45e22c0d0be fatcat:agfgewndungkdipzhkd5dfori4

Page 5034 of Mathematical Reviews Vol. , Issue 2004f [page]

2004 Mathematical Reviews  
(A-TGRZ-B; Graz); Dollani, Helidon (A-TGRZ-B; Graz) Center problems with pos/neg weights on trees. (English summary) European J. Oper. Res. 145 (2003), no. 3, 483-495.  ...  We focus on row-column aggregations, and make use of aggregation results for 1-median problems on the line to do aggregation for l-median problems in the plane.  ... 

Discrete location problems with push–pull objectives

Jakob Krarup, David Pisinger, Frank Plastria
2002 Discrete Applied Mathematics  
away from the places a ected by the facilities' nearness.  ...  The discussion is restricted to models of combinatorial optimisation and includes indications of reduction to standard models and=or algorithmic approaches where possible. ?  ...  Acknowledgements The third author thanks E. Carrizosa for some fruitful modelling discussions. Furthermore, the useful suggestions made by two anonymous referees are gratefully acknowledged.  ... 
doi:10.1016/s0166-218x(01)00346-8 fatcat:oj3fe4w3m5fstbrjasnt5conbi

Page 2193 of Mathematical Reviews Vol. 31, Issue Index [page]

Mathematical Reviews  
(with Krarup, Jakob) A linear algorithm for the pos/neg-weighted 1- median problem on a cactus.  ...  A.; Woeginger, Gerhard J.) On-line and off-line approximation algorithms for vector covering problems.  ... 

Unweighted p-center problem on extended stars

Jafar Fathali, Jafari Rad, Rahimi Sadegh, Sherbaf
unpublished
In this paper we consider the p-center problem on the unweighted extended stars, and present some properties to find solution.  ...  The p-center problem in a graph G asks to find a subset X of the vertices of G of cardinality p such that the maximum weighted distances from X to all vertices is minimized.  ...  In [8] , Tamir algorithm for p -center problem on a tree. They also presented a linear time algorithm for 1-center problem with pos/neg weights on paths and star graphs.  ... 
fatcat:fpw2kafz6vfolohvgwuyeoflsi