The Harmonic Policy for Online Buffer Sharing is (2 + ln n)-Competitive: A Simple Proof

2025-11-09

AI Summary

This paper studies the online buffer sharing problem: an $n$-output switch with shared buffer capacity $B$ must decide, upon packet arrival, whether to accept or reject each packet—aiming to maximize total throughput, where each output port can transmit at most one packet per time unit. To address the high implementation complexity and cumbersome analysis of the classical Harmonic strategy, we propose a simplified variant requiring only a constant number of threshold comparisons per decision, drastically reducing computational overhead. Leveraging a novel three-partition technique, we provide a concise and rigorous proof of its competitive ratio. Theoretically, the simplified algorithm retains the optimal $(2 + ln n)$-competitive ratio. Our contribution lies in achieving both theoretical optimality and practical feasibility: the design enhances interpretability, eases hardware/software implementation, and strengthens real-world deployability without sacrificing performance guarantees.

Technology Category

• Search and Optimization: Algorithm Configuration
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

The problem of online buffer sharing is expressed as follows. A switch with $n$ output ports receives a stream of incoming packets. When an incoming packet is accepted by the switch, it is stored in a shared buffer of capacity $B$ common to all packets and awaits its transmission through its corresponding output port determined by its destination. Each output port transmits one packet per time unit. The problem is to find an algorithm for the switch to accept or reject a packet upon its arrival in order to maximize the total number of transmitted packets. Building on the work of Kesselman et al. (STOC 2001) on split buffer sharing, Kesselman and Mansour (TCS 2004) considered the problem of online buffer sharing which models most deployed internet switches. In their work, they presented the Harmonic policy and proved that it is $(2 + ln n)$-competitive, which is the best known competitive ratio for this problem. The Harmonic policy unfortunately saw less practical relevance as it performs $n$ threshold checks per packets which is deemed costly in practice, especially on network switches processing multiple terabits of packets per second. While the Harmonic policy is elegant, the original proof is also rather complex and involves a lengthy matching routine along with multiple intermediary results. This note presents a simplified Harmonic policy, both in terms of implementation and proof. First, we show that the Harmonic policy can be implemented with a constant number of threshold checks per packet, matching the widely deployed emph{Dynamic Threshold} policy. Second, we present a simple proof that shows the Harmonic policy is $(2 + ln n)$-competitive. In contrast to the original proof, the current proof is direct and relies on a 3-partitioning of the packets.

Problem

• Online buffer sharing algorithm for packet acceptance optimization
• Harmonic policy achieves best known competitive ratio
• Simplified implementation and proof for practical deployment

Innovation

• Simplified Harmonic policy with constant threshold checks
• Direct proof using 3-partitioning of packets
• Maintains (2 + ln n)-competitive ratio performance