Competitive Analysis for Multi-objective Online Algorithms

Tiedemann, Morten; Ide, Jonas; Schöbel, Anita

doi:10.1007/978-3-319-15612-5_19

Cited by 9 publications

(29 citation statements)

References 6 publications

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“…From Theorems 4.2 and 4.3, we note that (1) Theorem 5.1 gives another proof for the result that the algorithm in [8, Theorem 1] is best possible for the multi-objective time series search problem with respect to f 1 , (2) Theorem 5.2 disproves the result that the algorithm in [8,Theorem 3] is best possible for the bi-objective time series search problem with respect to f 2 , and (3) Theorem 5.3 gives a best possible online algorithm for the multi-objective time series search problem with respect to f 3 , which is an extension of the result that the algorithm in [8,Theorem 3] is best possible for the bi-objective time series search problem with respect to f 3 .…”

Section: Our Contributionmentioning

confidence: 84%

“…. , itv k = [m k , M k ] are real intervals, Tiedemann, et al [8] presented best possible online algorithms for the multi-objective time series search problem with respect to the monotone functions f 1 , f 2 , and f 3 , i.e., a best possible online algorithm for the multi-objective (k-objective) time series search problem with respect to the monotone function f 1 [8, Theorems 1 and 2], a best possible online algorithm for the bi-objective time series search problem with respect to the monotone function f 2 [8, Theorems 3 and 4] and a best possible online algorithm for the bi-objective time series search problem with respect to the monotone function f 3 [8, §3.2]. Note that the proofs of these results are correct under the assumption that all of itv 1 = [m 1 , M 1 ], .…”

Section: Previous Workmentioning

confidence: 99%

“…As mentioned in Subsection 1.1, Tiedemann, et al [8] showed best possible online algorithms for the multi-objective time series search problem with respect to the monotone continuous functions f 1 , f 2 and f 3 under the assumption that all of itv 1 = [m 1 , M 1 ], . .…”

Section: Our Contributionmentioning

confidence: 99%

“…Tiedemann, et al [8] defined a notion of competitive analysis for multi-objective online problems. In this subsection, we introduce the notion of competitive analysis for multi-objective on-line problems with respect to maximization problems (it is straightforward that the corresponding minimization problem can be defined analogously).…”

Section: Competitive Analysis For Multi-objective Online Problemsmentioning

confidence: 99%

“…We assume that prices are chosen from the interval itv = [m, M], where 0 < m ≤ M, and that m and M are known to the online player alg 1 . If the online player alg rejects the price p t for every t ∈ [1, T ], then the return for alg is defined to be m. A multi-objective time series search problem [8] can be defined by a natural extension of the single-objective time series search problem. In a multi-objective time series search problem, a price vector p t = (p 1 t , .…”

Section: Multi-objective Time Series Search Problemmentioning

confidence: 99%

See 4 more Smart Citations

Optimal Online Algorithms for the Multi-objective Time Series Search Problem

Hasegawa

Itoh

2016

WALCOM: Algorithms and Computation

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Tiedemann, et al. [Proc. of WALCOM, LNCS 8973, 2015, pp.210-221] defined multiobjective online problems and the competitive analysis for multi-objective online problems, and showed best possible online algorithms with respect to several measures of the competitive analysis. In this paper, we first point out that the definitions and frameworks of the competitive analysis due to Tiedemann, et al. do not necessarily capture the efficiency of online algorithms for multi-objective online problems and provide modified definitions of the competitive analysis for multi-objective online problems. Under the modified framework, we present a simple online algorithm Balanced Price Policy (bpp k ) for the multi-objective (k-objective) time series search problem, and show that the algorithm bpp k is best possible with respect to any measure of the competitive analysis (defined by a monotone function f ). For the modified framework, we also derive best possible values of the competitive ratio for the multi-objective time series search problem with respect to several representative measures of the competitive analysis.

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Section: Our Contributionmentioning

confidence: 84%

Section: Previous Workmentioning

confidence: 99%

Section: Our Contributionmentioning

confidence: 99%

Section: Competitive Analysis For Multi-objective Online Problemsmentioning

confidence: 99%

Section: Multi-objective Time Series Search Problemmentioning

confidence: 99%

See 3 more Smart Citations

Optimal Online Algorithms for the Multi-objective Time Series Search Problem

Hasegawa

Itoh

2016

WALCOM: Algorithms and Computation

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Optimal energy allocation policies for a high altitude flying wireless access point

Ceran

Erkilic

Uysal-Biyikoğlu

et al. 2016

Trans. Emerging Tel. Tech.

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Inspired by recent industrial efforts towards high altitude flying wireless access points powered by renewable energy, an online resource allocation problem for a mobile access point travelling at high altitude is formulated. The access point allocates its resources (available energy) to maximise the total utility (reward) provided to a sequentially observed set of users demanding service. The problem is formulated as a 0/1 dynamic knapsack problem with incremental capacity over a finite time horizon, and the solution of which is quite open in the literature. We address the problem through deterministic and stochastic formulations followed by a model where the statistics of the underlying processes are not known and learned through rule-based and neural network approaches. For the deterministic problem, several online approximations including optimisation via genetic algorithm and rule-based approach are proposed based on an instantaneous threshold that can adapt to short-time-scale dynamics. For the stochastic model, after showing the optimality of a threshold-based solution on a dynamic programming formulation, an approximate threshold-based policy is obtained. The performances of proposed policies are compared with that of the optimal solution obtained through dynamic programming

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Introducing Set-Based Regret for Online Multiobjective Optimization

Savary,

Wiecek

2023

Lecture Notes in Networks and Systems

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Competitive Analysis for Multi-objective Online Algorithms

Cited by 9 publications

References 6 publications

Optimal Online Algorithms for the Multi-objective Time Series Search Problem

Optimal Online Algorithms for the Multi-objective Time Series Search Problem

Optimal energy allocation policies for a high altitude flying wireless access point

Introducing Set-Based Regret for Online Multiobjective Optimization

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