Approximability of capacitated network design
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Routing for power minimization in the speed scaling model
IEEE/ACM Transactions on Networking (TON)
Energy-Efficient network routing with discrete cost functions
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Multicast routing for energy minimization using speed scaling
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
Optimal Cost Sharing for Resource Selection Games
Mathematics of Operations Research
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Given a network, a set of demands and a cost function f(.), the min-cost network design problem is to route all demands with the objective of minimizing sum_e f(l_e), where l_e is the total traffic load under the routing. We focus on cost functions of the form f(x) = s + x^a for x >, 0, with f(0) = 0. For a 1 with a positive startup cost s >, 0. Now, the cost function f(.) is neither sub additive nor super additive. This is motivated by minimizing network-wide energy consumption when supporting a set of traffic demands. It is commonly accepted that, for some computing and communication devices, doubling processing speed more than doubles the energy consumption. Hence, in Economics parlance, such a cost function reflects diseconomies of scale. We begin by discussing why existing routing techniques such as randomized rounding and tree-metric embedding fail to generalize directly. We then present our main contribution, which is a polylogarithmic approximation algorithm. We obtain this result by first deriving a bicriteria approximation for a related capacitated min-cost flow problem that we believe is interesting in its own right. Our approach for this problem builds upon the well-linked decomposition due to Chekuri-Khanna-Shepherd, the construction of expanders via matchings due to Khandekar-Rao-Vazirani, and edge-disjoint routing in well-connected graphs due to Rao-Zhou. However, we also develop new techniques that allow us to keep a handle on the total cost, which was not a concern in the aforementioned literature.