Temporal Locality in Online Algorithms

TL;DR

This paper introduces time-local online algorithms where decisions depend only on recent inputs, enabling consistent distributed decisions and demonstrating their effectiveness through a variant of the online file migration problem.

Contribution

It defines time-local online algorithms, connects them to distributed graph algorithms, and provides a synthesis method for designing optimal algorithms with small horizons.

Findings

Existence of a 3-competitive time-local algorithm for two nodes with horizon T=4.

Deterministic time-local algorithms can achieve a 6-competitive ratio.

Randomized time-local algorithms can achieve a 2.62-competitive ratio.

Abstract

Online algorithms make decisions based on past inputs. In general, the decision may depend on the entire history of inputs. If many computers run the same online algorithm with the same input stream but are started at different times, they do not necessarily make consistent decisions. In this work we introduce time-local online algorithms. These are online algorithms where the output at a given time only depends on $T = O(1)$ latest inputs. The use of (deterministic) time-local algorithms in a distributed setting automatically leads to globally consistent decisions. Our key observation is that time-local online algorithms (in which the output at a given time only depends on local inputs in the temporal dimension) are closely connected to local distributed graph algorithms (in which the output of a given node only depends on local inputs in the spatial dimension). This makes it possible to interpret prior work on distributed graph algorithms from the perspective of online algorithms. We describe an algorithm synthesis method that one can use to design optimal time-local online algorithms for small values of $T$. We demonstrate the power of the technique in the context of a variant of the online file migration problem, and show that e.g. for two nodes and unit migration costs there exists a $3$-competitive time-local algorithm with horizon $T=4$, while no deterministic online algorithm (in the classic sense) can do better. We also derive upper and lower bounds for a more general version of the problem; we show that there is a $6$-competitive deterministic time-local algorithm and a $2.62$-competitive randomized time-local algorithm for any migration cost $\alpha \ge 1$.