## Off-Line and On-Line Call-Scheduling in Stars and Trees (1997)

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Venue: | in Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science, WG ‘97, LNCS1335, Springer-Verlag |

Citations: | 11 - 2 self |

### BibTeX

@INPROCEEDINGS{Erlebach97off-lineand,

author = {Thomas Erlebach and Klaus Jansen},

title = {Off-Line and On-Line Call-Scheduling in Stars and Trees},

booktitle = {in Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science, WG ‘97, LNCS1335, Springer-Verlag},

year = {1997},

pages = {195--213},

publisher = {SpringerVerlag}

}

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### Abstract

. Given a communication network and a set of call requests, the goal is to find a minimum makespan schedule for the calls such that the sum of the bandwidth requirements of simultaneously active calls using the same link does not exceed the capacity of that link. In this paper the call-scheduling problem is studied for star and tree networks. Lower and upper bounds on the worst-case performance of List-Scheduling (LS) and variants of it are obtained for call-scheduling with arbitrary bandwidth requirements and either unit call durations or arbitrary call durations. LS does not require advance knowledge of call durations and, hence, is an on-line algorithm. It has performance ratio (competitive ratio) at most 5 in star networks. A variant of LS for calls with unit durations is shown to have performance ratio at most 2 2 3 . In tree networks with n nodes, a variant of LS for calls with unit durations has performance ratio at most 6, and a variant for calls with arbitrary d...

### Citations

417 | Bounds on multiprocessing timing anomalies
- Graham
- 1969
(Show Context)
Citation Context ...specified processor allocations if each task requests one or two processors [11]. One of the earliest heuristics for the solution of scheduling problems was List-Scheduling (LS), introduced by Graham =-=[9]-=-. In the call-scheduling context, the input to LS is a star or tree network G and a set R of call requests arranged in a list L. LS starts to schedule calls at time 0. If there is a call r in L such t... |

112 |
Scheduling parallel machines on-line
- Shmoys, Wein, et al.
- 1995
(Show Context)
Citation Context ...algorithms, i.e., algorithms that can deal with additional call requests that arrive on-line while other calls have already been scheduled, increasing the competitive ratio by no more than a factor 2 =-=[14, 7]-=-. An on-line algorithm has competitive ratio ae if it always produces a schedule with makespan at most a factor ae longer than the optimum (off-line) schedule. If G is a tree, the path P r is already ... |

109 | Competitive non-preemptive call control
- Awerbuch, Bartal, et al.
- 1994
(Show Context)
Citation Context ...Combining these inequalities, we obtain jSj = t r + 1s6 \Delta OPT . ut 3.2 Arbitrary Durations and Arbitrary Bandwidth Requirements Given a tree network T with n nodes, we use a well-known technique =-=[2]-=- based on a tree separator [16] to assign levels to the nodes of T as follows: 1. Choose a node v whose removal splits T into subtrees T 1 ; T 2 ; : : : ; T k with at most n=2 nodes each. Assign node ... |

54 |
Scheduling file transfers
- Coffman, Garey, et al.
- 1985
(Show Context)
Citation Context .... Coffman et al. study a file-transfer scheduling problem that corresponds to call-scheduling in a star with varying edge capacities and calls with unit bandwidth requirements and arbitrary durations =-=[4]-=-. They present complexity results for various restricted versions of the problem, approximation results, and distributed implementations. Many of their results for arbitrary edge capacities and unit b... |

51 | Scheduling of virtual connections in fast networks
- Jansen
(Show Context)
Citation Context ...y OPT = OPT (R) the length of a shortest feasible schedule for R, and by A(R) the length of the schedule produced by algorithmsA. Since it is in general NP-hard to compute a minimum makespan schedule =-=[5]-=-, one is interested in polynomial-time approximation algorithms with provable performance guarantee. An algorithm A has performance ratio at most ae if A(R)sae \Delta OPT (R) for all request sets R. I... |

45 |
On the 1.1 edge-coloring of multigraphs
- Nishizeki, Kashiwagi
- 1990
(Show Context)
Citation Context ... with unit durations (d r = 1 for all r 2 R) and unit bandwidths (b r = 1 for all r 2 R), call-scheduling in a star is equivalent to edgecoloring a multigraph and thus NP-hard [5]. The algorithm from =-=[13]-=- colors any multigraph G with at most b1:1 \Delta OPT (G) + 0:8c colors and can be used for the call-scheduling problem with the same performance guarantee, even in trees [5]. The equivalence between ... |

44 | Complexity of scheduling multiprocessor tasks with prespecified processor allocations
- Hoogeveen, Velde, et al.
- 1994
(Show Context)
Citation Context ...ith unit bandwidth requirements in stars with unit edge capacities is equivalent to scheduling multiprocessor tasks with prespecified processor allocations if each task requests one or two processors =-=[11]-=-. One of the earliest heuristics for the solution of scheduling problems was List-Scheduling (LS), introduced by Graham [9]. In the call-scheduling context, the input to LS is a star or tree network G... |

38 |
Improved bounds for all optical routing
- Aumann, Rabani
- 1995
(Show Context)
Citation Context ...rresponds to a wavelength assignment with the minimum number of distinct wavelengths. Routing and wavelength allocation in all-optical networks have received considerable attention lately, see, e.g., =-=[1]-=- and the references contained in there. A variation of the problem dealing with directed instead of bidirectional calls has also been studied. Here, calls using the same edge can receive the same wave... |

33 | Constrained bipartite edge coloring with applications to wavelength routing. Accepted for ICALP
- KAKLAMANIS, PERSIANO, et al.
(Show Context)
Citation Context ...alls using the same edge can receive the same wavelength if they use the edge in different directions. The best approximation algorithm known up to now requires 5 3 Lmax wavelengths in the worst case =-=[12]-=-. It is known that the bidirectional call-scheduling problem with unit durations and unit bandwidths is NP-hard in trees of arbitrary degree, but solvable in polynomial time in trees whose degree is b... |

32 | On-line routing in all-optical networks
- Bartal, Leonardi
(Show Context)
Citation Context ...he on-line version of the wavelength allocation problem the algorithm is given requests one by one and must assign wavelengths immediately without knowledge about future requests. Bartal and Leonardi =-=[3]-=- obtain deterministic on-line algorithms with competitive ratio O(log n) for networks with n processors whose topology is that of a tree, a tree of rings, or a mesh. In addition, they present a matchi... |

31 | Call scheduling in trees, rings and meshes
- ERLEBACH, JANSEN
- 1997
(Show Context)
Citation Context ...e bidirectional call-scheduling problem with unit durations and unit bandwidths is NP-hard in trees of arbitrary degree, but solvable in polynomial time in trees whose degree is bounded by a constant =-=[5, 6]-=-. The directed version is NP-hard already for binary trees [6]. In the on-line version of the wavelength allocation problem the algorithm is given requests one by one and must assign wavelengths immed... |

28 |
Leeuwen (editor), Handbook of theoretical computer
- van
- 1990
(Show Context)
Citation Context ...we obtain jSj = t r + 1s6 \Delta OPT . ut 3.2 Arbitrary Durations and Arbitrary Bandwidth Requirements Given a tree network T with n nodes, we use a well-known technique [2] based on a tree separator =-=[16]-=- to assign levels to the nodes of T as follows: 1. Choose a node v whose removal splits T into subtrees T 1 ; T 2 ; : : : ; T k with at most n=2 nodes each. Assign node v the level 0. 2. In each subtr... |

19 | Competitive analysis of call admission algorithms that allow delay
- Feldmann, Maggs, et al.
- 1995
(Show Context)
Citation Context ...algorithms, i.e., algorithms that can deal with additional call requests that arrive on-line while other calls have already been scheduled, increasing the competitive ratio by no more than a factor 2 =-=[14, 7]-=-. An on-line algorithm has competitive ratio ae if it always produces a schedule with makespan at most a factor ae longer than the optimum (off-line) schedule. If G is a tree, the path P r is already ... |

13 | Bounds on the performance of scheduling algorithms - Graham - 1976 |

3 |
On-line call admission for high-speed networks (Ph.D
- Feldmann
- 1995
(Show Context)
Citation Context ...ing problem with unit edge capacities and arbitrary bandwidth requirements, however. Previous Work on On-Line Call-Scheduling. Feldmann et al. initiated research on on-line call-scheduling in [7] and =-=[8]-=-. They analyze the GREEDY algorithm (equivalent to LS) and show that running GREEDY once on the calls with bandwidth requirementss1 2 and once on the calls with bandwidth requirements ? 1 2 yields an ... |