Compact location problems with budget and communication constraints
- Wuerzburg Univ. (Germany). Dept. of Computer Science
- State Univ., of New York, Albany, NY (United States). Dept. of Computer Science
- Los Alamos National Lab., NM (United States)
We consider the problem of placing a specified number p of facilities on the nodes of a given network with two nonnegative edge-weight functions so as to minimize the diameter of the placement with respect to the first distance function under diameter or sum-constraints with respect to the second weight function. Define an ({alpha}, {beta})-approximation algorithm as a polynomial-time algorithm that produces a solution within a times the optimal function value, violating the constraint with respect to the second distance function by a factor of at most {beta}. We observe that in general obtaining an ({alpha}, {beta})-approximation for any fixed {alpha}, {beta} {ge} 1 is NP-hard for any of these problems. We present efficient approximation algorithms for the case, when both edge-weight functions obey the triangle inequality. For the problem of minimizing the diameter under a diameter Constraint with respect to the second weight-function, we provide a (2,2)-approximation algorithm. We. also show that no polynomial time algorithm can provide an ({alpha},2 {minus} {var_epsilon})- or (2 {minus} {var_epsilon},{beta})-approximation for any fixed {var_epsilon} > 0 and {alpha},{beta} {ge} 1, unless P = NP. This result is proved to remain true, even if one fixes {var_epsilon}{prime} > 0 and allows the algorithm to place only 2p/{vert_bar}VI{vert_bar}/{sup 6 {minus} {var_epsilon}{prime}} facilities. Our techniques can be extended to the case, when either the objective or the constraint is of sum-type and also to handle additional weights on the nodes of the graph.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 62641
- Report Number(s):
- LA-UR-95-1293; CONF-9508113-1; ON: DE95010876
- Resource Relation:
- Journal Volume: 959; Conference: 1. annual international computing and combinatorics conference, Xian (China), 24 Aug 1995; Other Information: PBD: [1995]
- Country of Publication:
- United States
- Language:
- English
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