Forwarding Packets Greedily

2026-03-06

AI Summary

This work addresses the online packet scheduling problem in a line network of routers, where packets arrive over time and each traverses either one or two consecutive routers, with the objective of minimizing the maximum flow time—the duration from a packet’s release to its arrival at the destination. The paper proposes a novel greedy algorithm that, at each step, prioritizes scheduling a specific packet to reduce overall delay. This strategy is the first to be explicitly designed and rigorously analyzed for this setting, achieving a tight competitive ratio of $2 - 2^{1-k}$ for $k$ active routers. Furthermore, the study establishes a general lower bound of $4/3$ for any randomized algorithm. These results constitute the first substantial progress toward resolving the long-standing open question of whether an $O(1)$-competitive algorithm exists for this problem.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Algorithm Configuration
• Machine Learning: Online Learning & Bandits

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We consider the problem of forwarding packets arriving online with their destinations in a line network. In each time step, each router can forward one packet along the edge to its right. Each packet that is forwarded arrives at the next router one time step later. Packets are forwarded until they reach their destination. The flow time of a packet is the difference between its release time and the time of its arrival at its destination. The goal is to minimize the maximum flow time. This problem was introduced by Antoniadis et al.~in 2014. They propose a collection of natural algorithms and prove for one, and claim for others, that none of them are $O(1)$-competitive. It was posed as an open problem whether such an algorithm exists. We make the first progress on answering this question. We consider the special case where each packet needs to be forwarded by exactly one or two routers. We show that a greedy algorithm, which was not previously considered for this problem, achieves a competitive ratio of exactly $2-2^{1-k}$, where $k$ is the number of active routers in the network. We also give a general lower bound of $4/3$, even for randomized algorithms.

Problem

• online packet forwarding
• flow time minimization
• line network
• competitive ratio
• scheduling

Innovation

• online packet forwarding
• greedy algorithm
• competitive ratio
• flow time minimization
• line network