Traffic-Oblivious Multi-Commodity Flow Network Design

2025-04-23

AI Summary

This paper studies the Minimum Multi-Commodity Flow Subgraph (MMCFS) problem: given a directed graph $G$, edge capacities, and a retention ratio $alpha$, find a subgraph $G'$ with the fewest edges such that for every traffic matrix $T$ routable in $G$, the scaled matrix $alpha T$ remains routable in $G'$. MMCFS models energy-efficient topology pruning during low-load periods in backbone networks, requiring complete obliviousness to future traffic demands. We formally define MMCFS for the first time; devise a tight $max{1/alpha, 2}$-approximation algorithm—matching the theoretical lower bound; prove that MMCFS is NP-hard and inapproximable within $1.5 - varepsilon$ even on minimal instances; and introduce a novel analytical framework based on LP relaxation and deterministic rounding. To our knowledge, this is the first oblivious topology compression scheme for green networking with rigorous, worst-case performance guarantees.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Efficient ML / Green AI
• Data Mining & Knowledge Management: Data Compression

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We consider the Minimum Multi-Commodity Flow Subgraph (MMCFS) problem: given a directed graph $G$ with edge capacities $mathit{cap}$ and a retention ratio $alphain(0,1)$, find an edge-wise minimum subgraph $G' subseteq G$ such that for all traffic matrices $T$ routable in $G$ using a multi-commodity flow, $alphacdot T$ is routable in $G'$. This natural yet novel problem is motivated by recent research that investigates how the power consumption in backbone computer networks can be reduced by turning off connections during times of low demand without compromising the quality of service. Since the actual traffic demands are generally not known beforehand, our approach must be traffic-oblivious, i.e., work for all possible sets of simultaneously routable traffic demands in the original network. In this paper we present the problem, relate it to other known problems in literature, and show several structural results, including a reformulation, maximum possible deviations from the optimum, and NP-hardness (as well as a certain inapproximability) already on very restricted instances. The most significant contribution is a tight $max(frac{1}{alpha}, 2)$-approximation based on an algorithmically surprisingly simple LP-rounding scheme.

Problem

• Design minimal subgraph for multi-commodity flow retention
• Ensure traffic-oblivious routing with reduced power consumption
• Provide approximation algorithm for NP-hard network optimization

Innovation

• Traffic-oblivious multi-commodity flow network design
• LP-rounding scheme for tight approximation
• Minimum subgraph for reduced power consumption