Approximation Schemes for Packing with Item Fragmentation

Shachnai, Hadas; Tamir, Tami; Yehezkely, Omer

doi:10.1007/11671411_26

Cited by 13 publications

(8 citation statements)

References 11 publications

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“…Other related problems were introduced by Shachnai et al [27]. They propose to model the size of an item as increasing when it is split and to ask for a global bound on the number of fragmentations.…”

Section: Related Workmentioning

confidence: 99%

Heterogeneous Resource Allocation under Degree Constraints

Beaumont

Eyraud-Dubois

Thraves

et al. 2013

IEEE Trans. Parallel Distrib. Syst.

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Abstract-In this paper, we consider the problem of assigning a set of clients with demands to a set of servers with capacities and degree constraints. The goal is to find an allocation such that the number of clients assigned to a server is smaller than the server's degree and their overall demand is smaller than the server's capacity, while maximizing the overall throughput. This problem has several natural applications in the context of independent tasks scheduling or virtual machines allocation. We consider both the offline (when clients are known beforehand) and the online (when clients can join and leave the system at any time) versions of the problem. We first show that the degree constraint on the maximal number of clients that a server can handle is realistic in many contexts. Then, our main contribution is to prove that even if it makes the allocation problem more difficult (NP-Complete), a very small additive resource augmentation on the servers degree is enough to find in polynomial time a solution that achieves at least the optimal throughput. After a set of theoretical results on the complexity of the offline and online versions of the problem, we propose several other greedy heuristics to solve the online problem and we compare the performance (in terms of throughput) and the cost (in terms of disconnections and reconnections) of proposed algorithms through a set of extensive simulation results.

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Section: Related Workmentioning

confidence: 99%

Heterogeneous Resource Allocation under Degree Constraints

Beaumont

Eyraud-Dubois

Thraves

et al. 2013

IEEE Trans. Parallel Distrib. Syst.

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“…A related problem was studied recently by Shachnai, Tamir and Yehezkely [14]. They considered an offline bin packing problem where items may be split arbitrarily.…”

Section: Opt(i) = N}mentioning

confidence: 99%

Approximation Schemes for Packing Splittable Items with Cardinality Constraints

Epstein¹,

Stee²

2008

Approximation and Online Algorithms

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We continue the study of bin packing with splittable items and cardinality constraints. In this problem, a set of items must be packed into as few bins as possible. Items may be split, but each bin may contain at most k (parts of) items, where k is some fixed constant. Complicating the problem further is the fact that items may be larger than 1, which is the size of a bin. We close this problem by providing a polynomial-time approximation scheme for it. We first present a scheme for the case k = 2 and then for the general case of constant k.Additionally, we present dual approximation schemes for k = 2 and constant k. Thus we show that for any ε > 0, it is possible to pack the items into the optimal number of bins in polynomial time, if the algorithm may use bins of size 1 + ε.

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“…For example, the problem of bin packing with item fragmentation is solved in [46] in two steps. Given the input, we need to determine the set of items that will be fragmented, as well as the fragment sizes in a feasible approximate solution.…”

Section: More On Grouping and Shiftingmentioning

confidence: 99%

“…The actual sizes of the shifted fragments are determined by solving a linear program which attempts to find a feasible packing of these fragments. A detailed description is given in [46].…”

Section: More On Grouping and Shiftingmentioning

confidence: 99%