Self-Adjusting Networks to Minimize Expected Path Length

TL;DR

This paper introduces self-adjusting networks that use local mechanisms to optimize node placement, minimizing expected path length based on request distributions, with practical algorithms for grid networks.

Contribution

It studies the distributed version of the MEPL problem, providing efficient approximation algorithms for grid networks with symmetric request distributions.

Findings

A simple greedy policy achieves good approximation ratios.

The approach uses expected rank and distance to the graph center.

Distributed algorithms are effective for practical network optimization.

Abstract

Given a network infrastructure (e.g., data-center or on-chip-network) and a distribution on the source-destination 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 (e.g., virtual machines) in the network to best fit the route requests distribution. Finding the optimal placement of nodes is defined as the minimum expected path length (MEPL) problem. This is a generalization of the minimum linear arrangement (MLA) problem where the network infrastructure is a line and the computation is done centrally. In contrast to previous work, we study the distributed version and give efficient and simple approximation algorithms for interesting and practically relevant special cases of the problem. In particular, we consider grid networks in which the distribution of requests is a symmetric product distribution. In this setting, we show that a simple greedy policy of position switching between neighboring nodes to locally minimize an objective function, achieves 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.