Self-Adjusting Networks to Minimize Expected Path Length

Given a network infrastructure (e.g., a grid, datacenter or on-chip-network) and a distribution on the sourcedestination requests, the expected path (route) length is an important measure for the performance, efficiency and power consumption of the network. In this work we initiate a study on self-adjusting networks: networks that use local-distributed mechanisms to adjust the position of the nodes in the network to any distribution of route requests. Finding the optimal placement of nodes is defined as the minimum expected path length (MEPL) problem. While, as we show, the MEPL problem is NP-hard to solve exactly in general we give efficient and simple approximation algorithms for interesting and practically relevant special cases of the problem. E.g., we consider grid networks in which the distribution of requests is a symmetric product distribution. In this setting we show that simple greedy switches, which locally minimize an objective function, achieve good approximation ratios. We are able to prove this result using the useful notions of expected rank of the distribution and the expected distance to the center of the graph.