A Comparison of Performance Measures via Online Search

TL;DR

This paper compares various performance measures for online algorithms, focusing on online search and Reservation Price Policies, analyzing their applicability, properties, and sensitivity, and establishing the first optimality proof for Relative Interval Analysis.

Contribution

It systematically studies multiple performance measures for online search, generalizes some measures, and provides the first optimality proof for Relative Interval Analysis.

Findings

Different measures emphasize different algorithm properties.

Some measures are sensitive to domain types (integral vs. real-valued).

Established the first optimality proof for Relative Interval Analysis.

Abstract

Though competitive analysis has been a very useful performance measure for the quality of online algorithms, it is recognized that it sometimes fails to distinguish between algorithms of different quality in practice. A number of alternative measures have been proposed, but, with a few exceptions, these have generally been applied only to the online problem they were developed in connection with. Recently, a systematic study of performance measures for online algorithms was initiated [Boyar, Irani, Larsen: Eleventh International Algorithms and Data Structures Symposium 2009], first focusing on a simple server problem. We continue this work by studying a fundamentally different online problem, online search, and the Reservation Price Policies in particular. The purpose of this line of work is to learn more about the applicability of various performance measures in different situations and the properties that the different measures emphasize. We investigate the following analysis techniques: Competitive, Relative Worst Order, Bijective, Average, Relative Interval, Random Order, and Max/Max. In addition to drawing conclusions on this work, we also investigate the measures' sensitivity to integral vs. real-valued domains, and as a part of this work, generalize some of the known performance measures. Finally, we have established the first optimality proof for Relative Interval Analysis.