One to Rule Them All: a General Randomized Algorithm for Buffer Management with Bounded Delay

TL;DR

This paper introduces a memoryless, scale-invariant randomized algorithm for buffer management with bounded delay, achieving optimal competitive ratios and extending to a more general collecting items problem.

Contribution

It presents a novel, optimal, memoryless randomized algorithm with strong guarantees for buffer management with bounded delay and related problems.

Findings

Achieves e/(e-1)-competitiveness against adaptive adversaries.

Attains the optimal 4/3 competitive ratio on 2-bounded instances.

Extends to a general collecting items problem with optimal performance.

Abstract

We give a memoryless scale-invariant randomized algorithm for the Buffer Management with Bounded Delay problem that is e/(e-1)-competitive against an adaptive adversary, together with better performance guarantees for many restricted variants, including the s-bounded instances. In particular, our algorithm attains the optimum competitive ratio of 4/3 on 2-bounded instances. Both the algorithm and its analysis are applicable to a more general problem, called Collecting Items, in which only the relative order between packets' deadlines is known. Our algorithm is the optimal randomized memoryless algorithm against adaptive adversary for that problem in a strong sense. While some of provided upper bounds were already known, in general, they were attained by several different algorithms.