Title: On Packet Scheduling with Adversarial Jamming and Speedup,
Abstract: In Packet Scheduling with Adversarial Jamming packets of arbitrary sizes
arrive over time to be transmitted over a channel in which instantaneous
jamming errors occur at times chosen by the adversary and not known to the
algorithm. The transmission taking place at the time of jamming is corrupt, and
the algorithm learns this fact immediately. An online algorithm maximizes the
total size of packets it successfully transmits and the goal is to develop an
algorithm with the lowest possible asymptotic competitive ratio, where the
additive constant may depend on packet sizes.
Our main contribution is a universal algorithm that works for any speedup and
packet sizes and, unlike previous algorithms for the problem, it does not need
to know these properties in advance. We show that this algorithm guarantees
1-competitiveness with speedup 4, making it the first known algorithm to
maintain 1-competitiveness with a moderate speedup in the general setting of
arbitrary packet sizes. We also prove a lower bound of $\phi+1\approx 2.618$ on
the speedup of any 1-competitive deterministic algorithm, showing that our
algorithm is close to the optimum.
Additionally, we formulate a general framework for analyzing our algorithm
locally and use it to show upper bounds on its competitive ratio for speedups
in $[1,4)$ and for several special cases, recovering some previously known
results, each of which had a dedicated proof. In particular, our algorithm is
3-competitive without speedup, matching both the (worst-case) performance of
the algorithm by Jurdzinski et al. and the lower bound by Anta et al.