Several practical instances of network design problems often require the network to satisfy multiple constraints. In this paper, we focus on the following problem (and its variants): find a low-cost network, under one cost function, that services every node in the graph, under another cost function, (i,e., every node of the graph is within a prespecified distance from the network). This study has important applications to the problems of optical network design and the efficient maintenance of distributed databases. We utilize the framework developed in [MR+95] to formulate these problems as bicriteria network design problems. We present the first known approximation algorithms for the class of service-constrained network design problems. We provide a (Formula Presented)-approximation algorithm for the (Service cost, Total edge cost, Tree)-bicriteria problem (where,∆ is the maximum service-degree of any node in the graph). We counterbalance this by showing that the problem does not have an (α, β)-approximation algorithm for any α ≥ 1 andβ < In n unless NP ⊆ DTIME(n log log n). When both the objectives are evaluated under the same cost function we provide a (Formula Presented)-approximation algorithm, for any ɛ> 0. In the opposite direction we provide a hardness result showing that even in the restricted case where the two cost functions are the same the problem does not have an (α, β)-approximation algorithm for α = 1 andβ < In n unless NP ⊆ (Formula Presented). We also consider a generalized Steiner forest version of the problem along with other variants involving diameter and bottleneck cost.
CITATION STYLE
Marathe, M. V., Ravi, R., & Sundaram, R. (1996). Service-constrained network design problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1097, pp. 28–40). Springer Verlag. https://doi.org/10.1007/3-540-61422-2_118
Mendeley helps you to discover research relevant for your work.