Compact location problems with budget and communication constraints

Krumke, S O; Noltemeier, H; Ravi, S S; Marathe, M V

doi:10.1007/BFb0030872

Compact location problems with budget and communication constraints

Conference · Mon May 01 00:00:00 EDT 1995

DOI:https://doi.org/10.1007/BFb0030872· OSTI ID:62641

Krumke, S O; Noltemeier, H ^[1]; Ravi, S S ^[2]; Marathe, M V ^[3]

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.

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Research Organization:: Los Alamos National Lab., 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

Country of Publication:: United States

Language:: English

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