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Given a network infrastructure (e.g., data-center or on-chip-network) and adistribution on the source-destination requests, the expected path (route)length is an important measure for the performance, efficiency and powerconsumption of the network. In this work we initiate a study on self-adjustingnetworks: networks that use local-distributed mechanisms to adjust the positionof the nodes (e.g., virtual machines) in the network to best fit the routerequests distribution. Finding the optimal placement of nodes is defined as theminimum expected path length (MEPL) problem. This is a generalization of theminimum linear arrangement (MLA) problem where the network infrastructure is aline and the computation is done centrally. In contrast to previous work, westudy the distributed version and give efficient and simple approximationalgorithms for interesting and practically relevant special cases of theproblem. In particular, we consider grid networks in which the distribution ofrequests is a symmetric product distribution. In this setting, we show that asimple greedy policy of position switching between neighboring nodes to locallyminimize an objective function, achieves good approximation ratios. We are ableto prove this result using the useful notions of expected rank of thedistribution and the expected distance to the center of the graph.

Self-Adjusting Networks to Minimize Expected Path Length