From Amortized to Worst Case Delay in Enumeration Algorithms

TL;DR

This paper explores the relationship between amortized and worst-case delay in enumeration algorithms, proposing methods to convert algorithms with polynomial amortized delay into those with polynomial worst-case delay, supported by lower bounds.

Contribution

It introduces schemes to transform algorithms with polynomial amortized delay into those with polynomial worst-case delay, and provides lower bounds in the blackbox model.

Findings

Schemes for converting amortized delay algorithms to worst-case delay algorithms.

Lower bounds and impossibility results in the blackbox model.

Analysis of the relation between amortized and worst-case delays.

Abstract

The quality of enumeration algorithms is often measured by their delay, that is, the maximal time spent between the output of two distinct solutions. If the goal is to enumerate $t$ distinct solutions for any given $t$, then another relevant measure is the maximal time needed to output $t$ solutions divided by $t$, a notion we call the amortized delay of the algorithm, since it can be seen as the amortized complexity of the problem of enumerating $t$ elements in the set. In this paper, we study the relation between these two notions of delay, showing different schemes allowing one to transform an algorithm with polynomial amortized delay for which one has a blackbox access into an algorithm with polynomial delay. We complement our results by providing several lower bounds and impossibility theorems in the blackbox model.