3 research outputs found
Online Algorithms with Randomly Infused Advice
We introduce a novel method for the rigorous quantitative evaluation of online algorithms that relaxes the "radical worst-case" perspective of classic competitive analysis. In contrast to prior work, our method, referred to as randomly infused advice (RIA), does not make any assumptions about the input sequence and does not rely on the development of designated online algorithms. Rather, it can be applied to existing online randomized algorithms, introducing a means to evaluate their performance in scenarios that lie outside the radical worst-case regime.
More concretely, an online algorithm ALG with RIA benefits from pieces of advice generated by an omniscient but not entirely reliable oracle. The crux of the new method is that the advice is provided to ALG by writing it into the buffer ? from which ALG normally reads its random bits, hence allowing us to augment it through a very simple and non-intrusive interface. The (un)reliability of the oracle is captured via a parameter 0 ? ? ? 1 that determines the probability (per round) that the advice is successfully infused by the oracle; if the advice is not infused, which occurs with probability 1 - ?, then the buffer ? contains fresh random bits (as in the classic online setting).
The applicability of the new RIA method is demonstrated by applying it to three extensively studied online problems: paging, uniform metrical task systems, and online set cover. For these problems, we establish new upper bounds on the competitive ratio of classic online algorithms that improve as the infusion parameter ? increases. These are complemented with (often tight) lower bounds on the competitive ratio of online algorithms with RIA for the three problems
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
On the Smoothness of Paging Algorithms
We study the smoothness of paging algorithms. How much can the number of page
faults increase due to a perturbation of the request sequence? We call a paging
algorithm smooth if the maximal increase in page faults is proportional to the
number of changes in the request sequence. We also introduce quantitative
smoothness notions that measure the smoothness of an algorithm. We derive lower
and upper bounds on the smoothness of deterministic and randomized
demand-paging and competitive algorithms. Among strongly-competitive
deterministic algorithms LRU matches the lower bound, while FIFO matches the
upper bound.
Well-known randomized algorithms like Partition, Equitable, or Mark are shown
not to be smooth. We introduce two new randomized algorithms, called
Smoothed-LRU and LRU-Random. Smoothed- LRU allows to sacrifice competitiveness
for smoothness, where the trade-off is controlled by a parameter. LRU-Random is
at least as competitive as any deterministic algorithm while smoother.Comment: Full version of paper presented at WAOA 201