TY - JOUR
T1 - Conditional location of path and tree shaped facilities on trees
AU - Tamir, A.
AU - Puerto, J.
AU - Mesa, J. A.
AU - Rodríguez-Chía, A. M.
N1 - Funding Information:
was supported by Spanish MCyT grant numbers BFM2000-1052-C02-01 and BFM2003-04062.
Funding Information:
The research of the second and fourth authors was partially supported by Spanish MCyT grant numbers BFM2001-2378, HA2003-0121, BFM2004-0909. The third author
PY - 2005/7
Y1 - 2005/7
N2 - In this paper we deal with the location of extensive facilities on trees, both discrete and continuous, under the condition that existing facilities are already located. We require that the selected new server is a subtree, although we also specialize to the case of paths. We study the problem with the two most widely used criteria in Location Analysis: center and median. Our main results under the center criterion are nestedness properties of the solution and subquadratic algorithms for the location of paths and subtrees. For the case of the median criterion we prove that unlike the case where there is no existing facility, the continuous conditional median subtree problem is NP-hard and we develop a corresponding fully polynomial approximation algorithm. We also present subquadratic algorithms for almost all other models.
AB - In this paper we deal with the location of extensive facilities on trees, both discrete and continuous, under the condition that existing facilities are already located. We require that the selected new server is a subtree, although we also specialize to the case of paths. We study the problem with the two most widely used criteria in Location Analysis: center and median. Our main results under the center criterion are nestedness properties of the solution and subquadratic algorithms for the location of paths and subtrees. For the case of the median criterion we prove that unlike the case where there is no existing facility, the continuous conditional median subtree problem is NP-hard and we develop a corresponding fully polynomial approximation algorithm. We also present subquadratic algorithms for almost all other models.
UR - http://www.scopus.com/inward/record.url?scp=20344403957&partnerID=8YFLogxK
U2 - 10.1016/j.jalgor.2005.01.005
DO - 10.1016/j.jalgor.2005.01.005
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AN - SCOPUS:20344403957
SN - 0196-6774
VL - 56
SP - 50
EP - 75
JO - Journal of Algorithms
JF - Journal of Algorithms
IS - 1
ER -