Online Packing with Gradually Improving Capacity Estimations and Applications to Network Lifetime Maximization

Ochel, Marcel; Radke, Klaus; Vöcking, Berthold

doi:10.1007/978-3-642-31585-5_57

Cited by 1 publication

(4 citation statements)

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“…Ochel et al [5] give a Θ(ln α/α)-competitive online algorithm for their online packing LP problem and show an upper bound on the competitive ratio of any online algorithm, even randomized, of O(1/ √ α). We significantly improve the upper bound.…”

Section: Our Resultsmentioning

confidence: 99%

“…The upper bound on the competitive ratio of randomized online algorithms against oblivious adversaries is based on the construction from the previous section and uses a technique that is, at least implicitly, also used by Ochel et al [5]. Recall that each round ends when the slack of at least one active constraint drops below a certain threshold value.…”

Section: Randomized Upper Boundmentioning

confidence: 99%

“…Ochel, Radke, and Vöcking [5] introduce a related model in which b and A are initially given to the online algorithm and instead c is only gradually revealed. At each point in time, the adversary reveals a vector t , which can be seen as the current right hand side values of the LP, and the online algorithm responds by increasing variables x i .…”

Section: Introductionmentioning

confidence: 99%

“…Ochel et al [5] give the problem of lifetime optimization in wireless sensor networks as a motivating application (see, e.g., [4]). There, the right hand sides of the constraints correspond to battery lifetimes of sensors.…”

Section: Introductionmentioning

confidence: 99%

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New Bounds for Online Packing LPs

Englert

Matsakis

Mucha

2014

LATIN 2014: Theoretical Informatics

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Abstract. Solving linear programs online has been an active area of research in recent years and was used with great success to develop new online algorithms for a variety of problems. We study the setting introduced by Ochel et al. as an abstraction of lifetime optimization of wireless sensor networks. In this setting, the online algorithm is given a packing LP and has to monotonically increase LP variables in order to maximize the objective function. However, at any point in time, the adversary only provides an α-approximation of the remaining slack for each constraint. This is designed to model scenarios in which only estimates of remaining capacities (e.g. of batteries) are known, and they get more and more accurate as the remaining capacities approach 0. On the other hand, we also show that the known lower bound can be significantly improved if the number of variables in the LP is small. Specifically, we give a deterministic Θ(1/ √ α)-competitive online algorithm for packing LPs with two variables. This is tight, since the previously known upper bound of O(1/ √ α) still holds for 2-dimensional LPs.

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Section: Our Resultsmentioning

confidence: 99%

Section: Randomized Upper Boundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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