Deterministic Self-Adjusting Tree Networks Using Rotor Walks

We revisit the design of self-adjusting single-source tree networks. The problem can be seen as a generalization of the classic list update problem to trees, and finds applications in reconfigurable datacenter networks. We are given a balanced binary tree T connecting n nodes V = {v 1 ,..., v n }. A...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the International Conference on Distributed Computing Systems pp. 67 - 77
Main Authors: Avin, Chen, Bienkowski, Marcin, Salem, Iosif, Sama, Robert, Schmid, Stefan, Schmidt, Pawel
Format: Conference Proceeding
Language:English
Published: IEEE 01.07.2022
Subjects:
Behavioral sciences
Binary trees
competitive analysis
Costs
Distributed computing
list update
online algorithms
rotor walks
Rotors
self adjusting networks
Source coding
ISSN:2575-8411
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We revisit the design of self-adjusting single-source tree networks. The problem can be seen as a generalization of the classic list update problem to trees, and finds applications in reconfigurable datacenter networks. We are given a balanced binary tree T connecting n nodes V = {v 1 ,..., v n }. A source node v 0 , attached to the root of the tree, issues communication requests to nodes in V , in an online and adversarial manner; the access cost of a request to a node v, is given by the current depth of v in T . The online algorithm can try to reduce the access cost by performing swap operations, with which the position of a node is exchanged with the position of its parent in the tree; a swap operation costs one unit. The objective is to design an online algorithm which minimizes the total access cost plus adjustment cost (swapping). Avin et al. [12] (LATIN 2020) recently presented RANDOM-PUSH, a constant competitive online algorithm for this problem, based on random walks, together with a sophisticated analysis exploiting the working set property.This paper studies analytically and empirically, online algorithms for this problem. In particular, we explore how to derandomize RANDOM-PUSH. In the analytical part, we consider a simple derandomized algorithm which we call ROTOR-PUSH, as its behavior is reminiscent of rotor walks. Our first contribution is a proof that ROTOR-PUSH is constant competitive: its competitive ratio is 12 and hence by a factor of five lower than the best existing competitive ratio. Interestingly, in contrast to RANDOM-PUSH, the algorithm does not feature the working set property, which requires a new analysis. We further present a significantly improved and simpler analysis for the randomized algorithm, showing that it is 16-competitive.In the empirical part, we compare all self-adjusting single-source tree networks, using both synthetic and real data. In particular, we shed light on the extent to which these self-adjusting trees can exploit temporal and spatial structure in the workload. Our experimental artefacts and source codes are publicly available.
ISSN:2575-8411
DOI:10.1109/ICDCS54860.2022.00016