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On the Performance of Greedy Algorithms in Packet Buffering

Summary: On the Performance of Greedy Algorithms in
Packet Buffering£
Susanne AlbersÝ Markus SchmidtÞ
We study a basic buffer management problem that arises in network switches. Consider Ñ input
ports, each of which is equipped with a buffer (queue) of limited capacity. Data packets arrive online
and can be stored in the buffers if space permits; otherwise packet loss occurs. In each time step the
switch can transmit one packet from one of the buffers to the output port. The goal is to maximize the
number of transmitted packets. Simple arguments show that any reasonable algorithm, which serves any
non-empty buffer, is 2-competitive. Azar and Richter recently presented a randomized online algorithm
and gave lower bounds for deterministic and randomized strategies.
In practice greedy algorithms are very important because they are fast, use little extra memory and
reduce packet loss by always serving a longest queue. In this paper we first settle the competitive
performance of the entire family of greedy strategies. We prove that greedy algorithms are not better than
2-competitive no matter how ties are broken. Our lower bound proof uses a new recursive construction
for building adversarial buffer configurations that may be of independent interest. We also give improved
lower bounds for deterministic and randomized online algorithms.
In the second part of the paper we present the first deterministic online algorithm that is better than
2-competitive. We develop a modified greedy algorithm, called Semi-Greedy, and prove that it achieves
a competitive ratio of ½ ½ . The new algorithm is simple, fast and uses little extra memory. Only


Source: Albers, Susanne - Institut für Informatik, Humboldt-Universität zu Berlin


Collections: Computer Technologies and Information Sciences