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## A constant factor approximation algorithm for the storage allocation problem: extended abstract (2013)

Venue: | In SPAA |

Citations: | 1 - 0 self |

### Citations

1422 |
Algorithmic Graph Theory and Perfect Graphs,
- Golumbic
- 1980
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Citation Context ...he NBA. Related work. The special case of SAP-U (or UFPP-U) with unit capacities and demands is the MAXIMUM INDEPENDENT SET problem in interval graphs which is solvable in polynomial time (see, e.g., =-=[16]-=-). Both SAP-U and UFPP-U are NP-hard, since they contain KNAPSACK as the special case in which the paths of all requests share an edge. When the number of edges in P is constant, UFPP is a special cas... |

176 | A local-ratio theorem for approximating the weighted vertex cover problem, - Bar-Yehuda, Even - 1985 |

156 | A unified approach to approximating resource allocation and scheduling,
- Bar-Noy, Bar-Yehuda, et al.
- 2001
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Citation Context ...ial case in which the paths of all requests share an edge. When the number of edges in P is constant, UFPP is a special case of MUTLI-DIMENSIONAL KNAPSACK and hence admits a PTAS [14]. Bar-Noy et al. =-=[3]-=- designed local ratio algorithms for UFPP-U and SAP-U with ratio 3 and 7, respectively. The latter was obtained using a reduction from SAP-U to UFPP-U that was based on an algorithm for the DYNAMIC ST... |

55 | Approximation algorithms for the unsplittable flow problem
- Chakrabarti, Chekuri, et al.
(Show Context)
Citation Context ... for instances of UFPP, where all capacities and demands are quasi-polynomial, thereby ruling out an APX-hardness result for such instances of UFPP, unless NP ⊆ DTIME(2polylog(n)). Chakrabarti et al. =-=[9]-=- presented a constant factor approximation algorithm for UFPP under the NBA by extending the approach of [8]. Chekuri et 2 al. [11] used an LP-based deterministic algorithm to obtain a (2 + ε)-approxi... |

45 |
Approximation algorithms for the m-dimensional 0-1 knapsack problem: worst-case and probabilistic analyses
- Frieze, Clarke
- 1984
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Citation Context ... KNAPSACK as the special case in which the paths of all requests share an edge. When the number of edges in P is constant, UFPP is a special case of MUTLI-DIMENSIONAL KNAPSACK and hence admits a PTAS =-=[14]-=-. Bar-Noy et al. [3] designed local ratio algorithms for UFPP-U and SAP-U with ratio 3 and 7, respectively. The latter was obtained using a reduction from SAP-U to UFPP-U that was based on an algorith... |

41 | Improved approximation algorithms for resource allocation
- Calinescu, Chakrabarti, et al.
- 2002
(Show Context)
Citation Context ...s to find the minimum capacity c for all edges along with a SAP solution that contains all tasks. An extension of SAP-U in which each task j has a time window was studied in [3, 17]. Calinescu et al. =-=[8]-=- developed a randomized approximation algorithm for UFPP-U with expected performance ratio of 2 + ε, for every ε > 0. They obtained this result by dividing the given instance into an instance with lar... |

38 |
F.B.: Multicommodity demand flow in a tree and packing integer programs.
- Chekuri, Mydlarz, et al.
- 2007
(Show Context)
Citation Context ...instances of UFPP, unless NP ⊆ DTIME(2polylog(n)). Chakrabarti et al. [9] presented a constant factor approximation algorithm for UFPP under the NBA by extending the approach of [8]. Chekuri et 2 al. =-=[11]-=- used an LP-based deterministic algorithm to obtain a (2 + ε)-approximation algorithm for UFPP under the NBA. Bansal et al. [2] developed an O(log n)-approximation algorithm for UFPP, beating the inte... |

28 | A quasi-PTAS for unsplittable flow on line graphs
- Bansal, Chakrabarti, et al.
- 2006
(Show Context)
Citation Context ...for large instances of SAP-U, and this lead to two approximation algorithms for SAP-U, a randomized algorithm with ratio 2+ε and a deterministic algorithm with ratio 2e−1e−1 +ε < 2.582. Bansal et al. =-=[1]-=- described a deterministic quasi-polynomial time approximation scheme for instances of UFPP, where all capacities and demands are quasi-polynomial, thereby ruling out an APX-hardness result for such i... |

22 | M.: OPT versus LOAD in dynamic storage allocation - Buchsbaum, Karloff, et al. - 2004 |

22 |
Algorithms for compile-time memory optimization
- Gergov
- 1999
(Show Context)
Citation Context ...-U and SAP-U with ratio 3 and 7, respectively. The latter was obtained using a reduction from SAP-U to UFPP-U that was based on an algorithm for the DYNAMIC STORAGE ALLOCATION PROBLEM (DSA) by Gergov =-=[15]-=-. In DSA the goal is to find the minimum capacity c for all edges along with a SAP solution that contains all tasks. An extension of SAP-U in which each task j has a time window was studied in [3, 17]... |

21 | A logarithmic approximation for unsplittable flow on line graphs
- Bansal, Friggstad, et al.
- 2009
(Show Context)
Citation Context ...r UFPP under the NBA by extending the approach of [8]. Chekuri et 2 al. [11] used an LP-based deterministic algorithm to obtain a (2 + ε)-approximation algorithm for UFPP under the NBA. Bansal et al. =-=[2]-=- developed an O(log n)-approximation algorithm for UFPP, beating the integrality gap of the natural LP-relaxation, which was shown to be Ω(n) [9]. This result has been generalized to trees and uniform... |

15 | A constant factor approximation algorithm for unsplittable flow on paths
- Bonsma, Schulz, et al.
- 2011
(Show Context)
Citation Context ... We present a polynomial time (9 + ε)-approximation algorithm for SAP, for every constant ε > 0. Our algorithm is based on the recent constant factor approximation algorithm for UFPP by Bonsma et al. =-=[6]-=-. As done in [6] we partition the task set into three sets: small tasks, medium tasks, and large tasks.1 Small tasks are δ-small for some δ > 0, large tasks are δ′-large for some δ′ > δ, and medium ta... |

15 | Allocation of bandwidth and storage
- Chen, Hassin, et al.
(Show Context)
Citation Context ...ed LP-based algorithm to obtain a (1+ ε)-approximate solution for the small instance. They also present a 3-approximation algorithm for UFPP-U that is different from the one given in [3]. Chen et al. =-=[12]-=- studied the special case of SAP-U where all demands are multiples of 1/K , for some integer K . They developed an O(n(nK)K) time dynamic programming algorithm to solve this special case of SAP-U, and... |

15 |
Approximation algorithms for bandwidth and storage allocation problems under real time constraints
- Leonardi, Marchetti-Spaccamela, et al.
- 2000
(Show Context)
Citation Context ...ov [15]. In DSA the goal is to find the minimum capacity c for all edges along with a SAP solution that contains all tasks. An extension of SAP-U in which each task j has a time window was studied in =-=[3, 17]-=-. Calinescu et al. [8] developed a randomized approximation algorithm for UFPP-U with expected performance ratio of 2 + ε, for every ε > 0. They obtained this result by dividing the given instance int... |

11 | Unsplittable flow in paths and trees and columnrestricted packing integer programs.
- Chekuri, Ene, et al.
- 2009
(Show Context)
Citation Context ...oximation algorithm for UFPP, beating the integrality gap of the natural LP-relaxation, which was shown to be Ω(n) [9]. This result has been generalized to trees and uniform weights by Chekuri et al. =-=[10]-=- who also provided an O(log2 n)-approximation algorithm for the weighted case. They also developed an LP formulation for UNSPLITTABLE FLOW in trees with general weights with an O(log2 n) integrality g... |

9 |
Caching is hard - even in the fault model
- Chrobak, Woeginger, et al.
(Show Context)
Citation Context ...algorithm for UFPP, being the first constantfactor approximation algorithm for the problem. They also showed that UFPP is strongly NP-hard even for instances with demands in {1, 2, 3}. Chrobak et al. =-=[13]-=- showed that UFPP-U is strongly NP-hard even for the case of uniform weights. Paper organization. The remainder of the paper is organized as follows. Section 2 contains definitions and a few prelimina... |

5 | Resource allocation in bounded degree trees
- Bar-Yehuda, Beder, et al.
- 2006
(Show Context)
Citation Context ...height assignments. Additionally, we provide a 2-approximation algorithm for “almost uniform” instances. We do this by extending the dynamic programming algorithm for SAP with uniform capacities from =-=[4]-=- to “almost uniform” capacities. A factor 2 is lost due to the framework’s requirement from the α-approximation algorithm for “almost uniform” instances. Hence, combined with the above framework we ob... |