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## Approximation Algorithms for the Unsplittable Flow Problem ∗ (2005)

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1971 | The Probabilistic Method - Alon, Spencer, et al. - 1992 |

698 |
Network flows,
- Ahuja, Magnanti, et al.
- 1993
(Show Context)
Citation Context ... ce e ∈ E(G) xi ∈ {0, 1} i = 1, . . . , k fπ ∈ {0, 1} π ∈ ∪ k i=1Pi . The linear programming (LP) relaxation, which we shall call lpmain, is obtained by allowing xi and fπ to lie in the real interval =-=[0, 1]-=-. Let (x1, . . . , xk, fπ1 , fπ2 , . . . ) be a fractional solution to lpmain. We shall refer to �k i=1 wixi as the profit or the value of the solution. We say that the solution uses a flow path π if ... |

217 | Throughput-competitive on-line routing.
- Awerbuch, Azar, et al.
- 1993
(Show Context)
Citation Context ... the weights are proportional to the request size (wi = ρi). Such an algorithm can be obtained by combining the bounded greedy algorithm [21, 25] and the algorithm of Awerbuch, Azar and Plotkin (AAP) =-=[5]-=- for large capacities. Kleinberg [21] has previously developed and analyzed such a combined algorithm in a related context. However, to apply this idea in our context, we need the existence of (log n,... |

156 | A unified approach to approximating resource allocation and scheduling,
- Bar-Noy, Bar-Yehuda, et al.
- 2001
(Show Context)
Citation Context ...t to the task assignment problem on a single machine with fixed time windows. Generalizations of the task assignment problem to multiple machines and time windows have been studied in the recent past =-=[7, 29]-=-, and most of these problems have O(1)-approximation algorithms as well as O(1) integrality gaps. This is not the case with UFP on the line, for which no constant-factor approximation was known before... |

75 | Approximating the throughput of multiple machines in real-time scheduling.
- Bar-Noy, Guha, et al.
- 2001
(Show Context)
Citation Context ...n for UFP could be Ω(min(log ρmax, n)) (see Theorem 5.7). Furthermore, two of the standard techniques used to develop O(1) approximations for the task assignment problem, i.e., the local-ratio method =-=[8, 7]-=- and rounding fractional solutions [29], seem not to extend to the case of UFP. In this work, we build upon ideas of Calinescu et al. [13], and combine dynamic programming and randomized rounding with... |

59 | Approximation algorithms for disjoint paths and related routing and packing problems
- Baveja, Srinivasan
(Show Context)
Citation Context ... scaling, and follow that by an alteration phase to obtain a feasible solution. We prove that this yields an O(d) approximation in expectation. We note that Srinivasan [33], and Baveja and Srinivasan =-=[9]-=- showed that randomized rounding yields an O(d) approximation for UCUFP if all flow path lengths are bounded by d. However, the proof is involved and is based on the FKG inequality. While it is concei... |

56 | Hardness of the undirected edge-disjoint paths problem
- Andrews, Zhang
- 2005
(Show Context)
Citation Context ...ndirected graphs, which will be the focus of this paper, EDP is only known to be hard to approximate to within constant factors [19]. Very recently, a hardness factor of Ω(log 1/2−ε n) has been shown =-=[3, 4]-=-. Improved approximation ratios for EDP have been obtained for special classes of graphs like trees, mesh-like planar graphs, and graphs with high expansion; see, e.g., [21, 25] for references. Let ρm... |

48 | Strongly polynomial algorithms for the unsplittable problem - Azar, Regev - 2001 |

40 | Edge disjoint paths revisited - Chekuri, Khanna - 2003 |

26 |
Existence and construction of edgedisjoint paths on expander graphs
- Broder, Frieze, et al.
(Show Context)
Citation Context ...r digraphs [11]. An immediate consequence of this is an O(log n) approximation for EDP on such expanders. In 1996, Kleinberg and Rubinfeld [22] had used an earlier result of Broder, Frieze, and Upfal =-=[12]-=- to show that a deterministic online algorithm, the so-called bounded greedy algorithm (BGA), gave an O(log n log log n) approximation guarantee for EDP. (In fact, Frieze’s result mentioned above impl... |

22 |
Yuval Rabani. An improved approximation algorithm for multiway cut
- Calinescu, Karloff
- 2000
(Show Context)
Citation Context ... monotone problems. Applications of this technique to approximation algorithms were recently given by Srinivasan [34], who applied it to general packing and covering problems, and by Calinescu et al. =-=[13]-=- who applied it to a specific packing problem. In this approach, the first step is the same as above: scaling followed by randomized rounding. However, instead of desiring feasibility (i.e., that all ... |

8 |
Improvements in throughout maximization for real-time scheduling
- Berman, DasGupta
- 2000
(Show Context)
Citation Context ...ls) that contain e. Recall that we are working under the no-bottleneck assumption: ρmax ≤ 1 = cmin. The UCUFP on the line is equivalent to a resource allocation problem that has been studied recently =-=[29, 7, 10, 13]-=-; however, we will not use the resource allocation terminology. Constant factor approximation algorithms for the resource allocation problem, and consequently UCUFP on the line, have been obtained via... |

4 | Arc-disjoint paths in expander digraphs
- Bohman, Frieze
- 2001
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Citation Context ... no vertex appears in more than a constant (depending on, and less than the degree) number of pairs. This result is optimal to within constant factors, and has also been extended to expander digraphs =-=[11]-=-. An immediate consequence of this is an O(log n) approximation for EDP on such expanders. In 1996, Kleinberg and Rubinfeld [22] had used an earlier result of Broder, Frieze, and Upfal [12] to show th... |

3 |
Multicommodity demand flow in a tree (extended abstract
- Chekuri, Mydlarz, et al.
(Show Context)
Citation Context ...and low capacity edges is borrowed from earlier work of Kleinberg [21]. For UFP on the line and the ring, a (2 + ε)-approximation has been obtained in subsequent work by Chekuri, Mydlarz and Shepherd =-=[15]-=-. The improvement is based on a different algorithm for small demands which builds on certain grouping and scaling ideas for packing problems from the work of Kolliopoulos and Stein [23]. 21sAcknowled... |