Randomized oblivious integral routing for minimizing power cost

Given an undirected network G ( V , E ) and a set of traffic requests R , the minimum power-cost routing problem requires that each R k ? R be routed along a single path to minimize ? e ? E ( l e ) α , where l e is the traffic load on edge e and α is a constant greater than 1. Typically, α ? ( 1 , 3 . This problem is important in optimizing the energy consumption of networks.To address this problem, we propose a randomized oblivious routing algorithm. An oblivious routing algorithm makes decisions independently of the current traffic in the network. This feature enables the efficient implementation of our algorithm in a distributed manner, which is desirable for large-scale high-capacity networks.An important feature of our work is that our algorithm can satisfy the integral constraint, which requires that each traffic request R k should follow a single path. We prove that, given this constraint, no randomized oblivious routing algorithm can guarantee a competitive ratio bounded by o ( | E | α - 1 α + 1 ) . By contrast, our approach provides a competitive ratio of O ( | E | α - 1 α + 1 log 2 α α + 1 ? | V | ? log α - 1 ? D ) , where D is the maximum demand of traffic requests. Furthermore, our results also hold for a more general case where the objective is to minimize ? e ( l e ) p , where p ? 1 is an arbitrary unknown parameter with a given upper bound α 1 .The theoretical results established in proving these bounds can be further generalized to a framework of designing and analyzing oblivious integral routing algorithms, which is significant for research on minimizing ? e ( l e ) α in specific scenarios with simplified problem settings. For instance, we prove that this framework can generate an oblivious integral routing algorithm whose competitive ratio can be bounded by O ( log α ? | V | ? log α - 1 ? D ) and O ( log 3 α ? | V | ? log α - 1 ? D ) on expanders and hypercubes, respectively. Original study on energy saving in oblivious integral routing.An ? ( | E | α - 1 α + 1 ) lower bound on competitive ratio.A random oblivious integral routing algorithm with polylog-tight competitive ratio.A general framework to design and analyze oblivious integral routing algorithms.Polylog bound on competitive ratio for expanders and hypercubes.