An asymptotic fully polynomial time approximation scheme for bin covering

Jansen, Klaus; Solis-Oba, Roberto

doi:10.1016/s0304-3975(03)00363-3

Cited by 44 publications

(52 citation statements)

References 3 publications

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“…Our problem of packing resizable items is closely related to the bin covering (BC) problem, which was widely studied (see, e.g., [1,5,6,13]). The input for bin covering is a set of items {a 1 , .…”

Section: Related Workmentioning

confidence: 99%

“…The first asymptotic approximation scheme (APTAS) for bin covering was introduced by Csirik et al [6]. Subsequently, Jansen and Solis-Oba [13] presented an AFPTAS for the problem. We discuss the relation between the two problems in Section 4.…”

Section: Related Workmentioning

confidence: 99%

“…Let A bc be such an AFPTAS, and let c be its asymptotic constant (such an AFPTAS with c = 4 is given in [13]). That is, given n items of sizes s(1), .…”

Section: Approximation Schemementioning

confidence: 99%

See 2 more Smart Citations

Packing resizable items with application to video delivery over wireless networks

Albagli-Kim¹,

Epstein²,

Shachnai³

et al. 2014

Theoretical Computer Science

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Motivated by fundamental optimization problems in video delivery over wireless networks, we consider the following problem of packing resizable items (PRI). Given is a bin of capacity B > 0, and a set I of items. Each item j ∈ I is of size s j > 0. A packed item must stay in the bin for a fixed time interval. To accommodate more items in the bin, each item j can be compressed to a size p j ∈ [0, s j ) for at most a fraction q j ∈ [0, 1) of the packing interval. The goal is to pack in the bin, for the given time interval, a subset of items of maximum cardinality. PRI is strongly NP-hard already for highly restricted instances.Our main result is an approximation algorithm that packs, for any instance I of PRI, at least 2 3 OP T (I) − 3 items, where OP T (I) is the number of items packed in an optimal solution. Our algorithm yields better ratio for instances in which the maximum compression time of an item is q max ∈ (0, 1 2 ). For subclasses of instances arising in realistic scenarios, we give an algorithm that packs at least OP T (I) − 2 items. Finally, we show that a non-trivial subclass of instances admits an asymptotic fully polynomial time approximation scheme (AFPTAS).

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Packing resizable items with application to video delivery over wireless networks

Albagli-Kim¹,

Epstein²,

Shachnai³

et al. 2014

Theoretical Computer Science

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show abstract

“…In contrast, the main result of Assmann et al [12] is an O(n log 2 n) time algorithm that yields an asymptotic approximation ratio of 4/3 for bin covering, while easier algorithms based on next fit and first fit decreasing are shown to yield asymptotic approximation ratios of 2 and 3/2, respectively. Later, an asymptotic PTAS [13] and an asymptotic FPTAS [14] for bin covering were developed.…”

Section: Previous Workmentioning

confidence: 99%

The generalized assignment problem with minimum quantities

Krumke

Thielen

2013

European Journal of Operational Research

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We consider a variant of the generalized assignment problem (GAP) where the amount of space used in each bin is restricted to be either zero (if the bin is not opened) or above a given lower bound (a minimum quantity). We provide several complexity results for different versions of the problem and give polynomial time exact algorithms and approximation algorithms for restricted cases. For the most general version of the problem, we show that it does not admit a polynomial time approximation algorithm (unless P = NP), even for the case of a single bin. This motivates to study dual approximation algorithms that compute solutions violating the bin capacities and minimum quantities by a constant factor. When the number of bins is fixed and the minimum quantity of each bin is at least a factor δ > 1 larger than the largest size of an item in the bin, we show how to obtain a polynomial time dual approximation algorithm that computes a solution violating the minimum quantities and bin capacities by at most a factor 1 − 1 δ and 1 + 1 δ , respectively, and whose profit is at least as large as the profit of the best solution that satisfies the minimum quantities and bin capacities strictly. In particular, for δ = 2, we obtain a polynomial time (1, 2)-approximation algorithm.

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“…The objective of the bin covering problem is to maximize the number of bins that can be filled to a minimum capacity with a set of items whose weights have been specified. Our algorithm, described in Section VI is directly inspired by recent theoretical advances in approximating the upper bounds on the optimal solution for the bin covering problem that were reported by Jansen and Solis-Oba [7].…”

Section: B Overview Of the Proposed Schemementioning

confidence: 99%

Schedulability Analysis for the Dynamic Segment of FlexRay: A Generalization to Slot Multiplexing

Tanasă

Bordoloi

Kosuch

et al. 2012

2012 IEEE 18th Real Time and Embedded Technology and Applications Symposium

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Abstract-FlexRay, developed by a consortium of over hundred automotive companies, is a real-time communication protocol for automotive networks. In this paper, we propose a new approach for timing analysis of the event-triggered component of FlexRay, known as the dynamic segment. Our technique accounts for the fact that the FlexRay standard allows slot multiplexing, i.e., the same priority can be assigned to more than one message. Existing techniques have either ignored slot multiplexing in their analysis or made simplifying assumptions that severely limit achieving high bandwidth utilization. Moreover, we show that our technique returns less pessimistic results compared to previously known techniques even in the case where slot multiplexing is ignored.

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An asymptotic fully polynomial time approximation scheme for bin covering

Cited by 44 publications

References 3 publications

Packing resizable items with application to video delivery over wireless networks

Packing resizable items with application to video delivery over wireless networks

The generalized assignment problem with minimum quantities

Schedulability Analysis for the Dynamic Segment of FlexRay: A Generalization to Slot Multiplexing

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