Abstract
This paper deals with the p-maxian problem on block graphs with unit edge length. It is shown that the two points with maximum distance provide an optimal solution for the 2-maxian problem of block graphs except for K 3. It can easily be extended to the p-maxian problem of block graphs. So we solve the p-maxian problem on block graphs in linear time.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aho AV, Hopcropt JE, Ullman JD (1974) The design and analysis of computer algorithms. Addison-Wesley, Reading
Burkard RE, Fathali J (2007) A polynomial method for the pos/neg weighted 3-medians problem on a tree. Math Meth Oper Res 65:229–238
Burkard RE, Krarup J (1998) A linear algorithm for the pos/neg-weighted median problem on a cactus. Computing 60:193–215
Burkard RE, Cela E, Dollani H (2000) 2-median in trees with pos/neg weights. Discrete Appl Math 105:51–71
Burkard RE, Fathali J, Kakhki HT (2007) The p-maxian problem on a tree. Oper Res Lett 35:331–335
Church RL, Garfinkel RS (1978) Locating an obnoxious facility on a network. Transp Sci 12:107–118
Gassner E (2008) The inverse 1-maxian problem with edge length modification. J Comb Optim 16:50–67
Handler GY (1973) Minimax location of a facility in an undirected tree networks. Transp Sci 7:287–293
Tamir A (1991) Obnoxious facility location on graphs. SIAM J Discrete Math 4:550–567
Ting SS (1984) A linear-time algorithm for maxisum facility location on tree networks. Transp Sci 18:76–84
Zelinka B (1968) Medians and peripherians of trees. Arch Math 4:87–95
Author information
Authors and Affiliations
Corresponding author
Additional information
Research was partially supported by the National Nature Science Foundation of China (Nos. 10571117, 60773078), the ShuGuang Plan of Shanghai Education Development Foundation (No. 06SG42) and Shanghai Leading Academic Discipline Project (No. J50101).
Rights and permissions
About this article
Cite this article
Kang, L., Cheng, Y. The p-maxian problem on block graphs. J Comb Optim 20, 131–141 (2010). https://doi.org/10.1007/s10878-008-9198-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10878-008-9198-1