An optimal algorithm for 2-bounded delay buffer management with lookahead

TL;DR

This paper presents an optimal online algorithm for the 2-bounded delay buffer management problem with lookahead, achieving the best possible competitive ratio matching the known lower bound.

Contribution

It introduces a new algorithm for the 2-bounded delay buffer management with lookahead that attains the optimal competitive ratio, resolving a longstanding conjecture.

Findings

Achieves a competitive ratio of (1 + sqrt(17))/4 ≈ 1.281

Matches the known lower bound for deterministic algorithms in this setting

Advances understanding of buffer management with lookahead in online algorithms

Abstract

The bounded delay buffer management problem, which was proposed by Kesselman et~al.\ (STOC 2001 and SIAM Journal on Computing 33(3), 2004), is an online problem focusing on buffer management of a switch supporting Quality of Service (QoS). The problem definition is as follows: Packets arrive to a buffer over time and each packet is specified by the {\em release time}, {\em deadline} and {\em value}. An algorithm can transmit at most one packet from the buffer at each integer time and can gain its value as the {\em profit} if transmitting a packet by its deadline after its release time. The objective of this problem is to maximize the gained profit. We say that an instance of the problem is $s$-bounded if for any packet, an algorithm has at most $s$ chances to transmit it. For any $s \geq 2$, Hajek (CISS 2001) showed that the competitive ratio of any deterministic algorithm is at least $(1 + \sqrt{5})/2 \approx 1.619$. It is conjectured that there exists an algorithm whose competitive ratio matching this lower bound for any $s$. However, it has not been shown yet. Then, when $s = 2$, B{\"o}hm et al.~(ISAAC 2016) introduced the {\em lookahead} ability to an online algorithm, that is the algorithm can gain information about future arriving packets, and showed that the algorithm achieves the competitive ratio of $(-1 + \sqrt{13})/2 \approx 1.303$. Also, they showed that the competitive ratio of any deterministic algorithm is at least $(1 + \sqrt{17})/4 \approx 1.281$. In this paper, for the 2-bounded model with lookahead, we design an algorithm with a matching competitive ratio of $(1 + \sqrt{17})/4$.