A Comparison of Performance Measures for Online Algorithms

Boyar, Joan; Irani, Sandy; Larsen, Kim S.

doi:10.1007/s00453-014-9884-6

Cited by 21 publications

(12 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In terms of a direct comparison of online algorithms, we obtain that greedy has a bijective ratio of at most 2k/3 against k-Center. It is worth mentioning that our results expand the work of Boyar et al [16] who showed that greedy is bijectively optimal for the 2-server problem on a very simple, albeit discrete metric consisting of three colinear points (termed the baby server problem).…”

Section: Introductionsupporting

confidence: 80%

“…Boyar et al [16] provided a systematic study of several measures for a simple version of the k-server problem, namely, the two server problem on three colinear points. In particular, they showed that greedy is bijectively optimal.…”

Section: Related Work and Preliminariesmentioning

confidence: 99%

“…In terms of techniques, the transition from exact to approximate bijective analysis necessitates a new approach that combines bijective analysis and amortization arguments. In particular, we note that all previous work that establishes the bijective optimality of a given algorithm [3,4,5,16] is based on inductive arguments which do not immediately carry over to the bijective ratio. For instance [5] crucially exploits the fact that for ρ = 1, if A b ρ·B and B b ρ·C, then A b C. This obviously only holds for ρ = 1, i.e., for optimality.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stochastic Dominance and the Bijective Ratio of Online Algorithms

Angelopoulos

Schweitzer

2019

Algorithmica

View full text Add to dashboard Cite

Stochastic dominance is a technique for evaluating the performance of online algorithms that provides an intuitive, yet powerful stochastic order between the compared algorithms. Accordingly this holds for bijective analysis, which can be interpreted as stochastic dominance assuming the uniform distribution over requests. These techniques have been applied in problems such as paging, list update, bin coloring, routing in array mesh networks, and in connection with Bloom filters, and have provided a clear separation between algorithms whose performance varies significantly in practice. However, despite their appealing properties, there are situations in which they are not readily applicable. This is due to the fact that they stipulate a stringent relation between the compared algorithms that may be either too difficult to establish analytically, or worse, may not even exist.In this paper we propose remedies to both of these shortcomings. First, we establish sufficient conditions that allow us to prove the bijective optimality of a certain class of algorithms for a wide range of problems; we demonstrate this approach in the context of well-studied online problems such as weighted paging, reordering buffer management, and 2-server on the circle. Second, to account for situations in which two algorithms are incomparable or there is no clear optimum, we introduce the bijective ratio as a natural extension of (exact) bijective analysis. Our definition readily generalizes to stochastic dominance. This renders the concept of bijective analysis (and that of stochastic dominance) applicable to all online problems, is a broad generalization of the Max/Max ratio due to Ben-David and Borodin, and allows for the incorporation of other useful techniques such as amortized analysis. We demonstrate the applicability of the bijective ratio to one of the fundamental online problems, namely the continuous k-server problem on metrics such as the line, the circle, and the star. Among other results, we show that the greedy algorithm attains bijective ratios of O(k) consistently across these metrics. These results confirm extensive previous studies that gave evidence of the efficiency of this algorithm on said metrics in practice, which, however, is not reflected in competitive analysis.

show abstract

Section: Introductionsupporting

confidence: 80%

Section: Related Work and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic Dominance and the Bijective Ratio of Online Algorithms

Angelopoulos

Schweitzer

2019

Algorithmica

View full text Add to dashboard Cite

show abstract

“…For completeness, we include these results. Random order analysis [20] was introduced for classic bin packing, but has also been used for other problems; a server problem, for instance [8]. Max/max analysis [3] was introduced as an early step towards refining the results from competitive analysis for paging and a server problem.…”

Section: Introductionmentioning

confidence: 99%

Online bin covering: Expectations vs. guarantees

Christ

Favrholdt

Larsen

2014

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…A systematic comparison of performance measures for online algorithms was initiated in [24], comparing some measures which are applicable to many types of problems. To make this feasible, a particularly simple problem was chosen: the 2server problem on a line with three points, one point farther away from the middle point than the other.…”

Section: Comparisons Of Performance Measuresmentioning

confidence: 99%