## Improved scheduling algorithms for minsum criteria (1996)

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Venue: | Automata, Languages and Programming, volume 1099 of Lecture Notes in Computer Science |

Citations: | 64 - 18 self |

### BibTeX

@INPROCEEDINGS{Chakrabarti96improvedscheduling,

author = {Soumen Chakrabarti and Cynthia A. Phillips and Andreas S. Schulz and David B. Shmoys and Cliff Stein and Joel Wein},

title = {Improved scheduling algorithms for minsum criteria},

booktitle = {Automata, Languages and Programming, volume 1099 of Lecture Notes in Computer Science},

year = {1996},

pages = {646--657},

publisher = {Springer}

}

### Years of Citing Articles

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### Abstract

Abstract. We consider the problem of finding near-optimal solutions for a variety of A/I)-hard scheduling problems for which the objective is to minimize the total weighted completion time. Recent work has led to the development of several techniques that yield constant worst-case bounds in a number of settings. We continue this line of research by providing improved performance guarantees for several of the most basic scheduling models, and by giving the first constant performance guarantee for a number of more realistically constrained scheduling problems. For example, we give an improved performance guarantee for minimizing the total weighted completion time subject to release dates on a single machine, and subject to release dates and/or precedence constraints on identical parallel machines. We also give improved bounds on the power of preemption in scheduling jobs with release dates on parallel machines. We give improved on-line algorithms for many more realistic scheduling models, including environments with parallelizable jobs, jobs contending for shared resources, tree precedence-constrained jobs, as well as shop scheduling models. In several of these cases, we give the first constant performance guarantee achieved on-line. Finally, one of the consequences of our work is the surprising structural property that there are schedules that simultaneously approximate the optimal makespan and the optimal weighted completion time to within small constants. Not only do such schedules exist, but we can find approximations to them with an on-line algorithm. 1

### Citations

194 | Scheduling to minimize average completion time: Off-line and on-line approximation algorithms
- Hall, Schulz, et al.
- 1997
(Show Context)
Citation Context ...st known performance guarantee for minimizing the total weighted completion time subject to release date constraints in either a single-machine or a parallel-machine environment, improving results of =-=[11, 18, 10]-=-. Observe that in Corollary 4, we did not state that the two bounds could be achieved by the same schedule. Indeed, we do not know how to achieve these simultaneously, since a choice of a that is good... |

165 |
Various optimizers for single-stage production
- Smith
- 1956
(Show Context)
Citation Context ...ward CCR-9211494 and a grant from the New York State Science and Technology Foundation, through its Center for Advanced Technology in Telecommunications.647 been known to be polynomial-time solvable =-=[21, 4, 12]-=-; when one adds release dates, precedence constraints, or weights, essentially all versions of the problem become A/P-hard, and until [16, 11, 18] very little was known about approximation algorithms ... |

163 |
A computational study of the job-shop scheduling problem
- Applegate, Cook
- 1991
(Show Context)
Citation Context ... can be scheduled in any order. Minimizing the makespan of job shops is perhaps the most notorious of difficult AlP-hard scheduling problems; even small instances are difficult to solve to optimality =-=[1]-=- and the best approximation algorithms give polylogarithmic performance guarantees [19]. We give the first constant-factor approximations for min-sum shop scheduling with a fixed number of machines m.... |

94 | Openshop Scheduling to Minimize Finish Time
- Gonzdez, Sahni
- 1976
(Show Context)
Citation Context ...s set within makespan (2 + e)D. For an open shop instance a nonpreemptive schedule of length P,~ax + ]-/max ~ (2 T s and a preemptive schedule of length max(Pmax, H~ax) _< (1 + e)D can be constructed =-=[9, 2]-=-. For job shop scheduling we can adapt the known (2 + e)-approximation makespan algorithm for fixed m [19]. Theorem 10. There is a randomized (2.89+e)-approximation algorithm for preemptive open shop ... |

87 | An improved approximation ratio for the minimum latency problem
- Goemans, Kleinberg
- 1998
(Show Context)
Citation Context ... for designing on-line algorithms that minimize the average weighted completion time, by improving and extending a result of Hall, Shmoys, & Wein [11]. By incorporating an idea of Goemans & Kleinberg =-=[8]-=- that exploits randomization in an elegant way, we can improve the performance guarantee of the resulting algorithms; the resulting bounds are quite strong, and in certain cases even improve upon off-... |

82 | The minimum latency problem
- Blum, Chalasani, et al.
- 1994
(Show Context)
Citation Context ...tive, and the maximum completion time objective. The result of Goemans ~c Kleinberg improves upon a result of Blum et al., who present a similar bicriteria result for traveling-salesman type problems =-=[3]-=-; we show that their approach applies to a very general class of scheduling problems. Our framework Greedy-Interval is based on algorithms for the maximum scheduled weight problem: given a deadline D,... |

82 | Improved Approximation Algorithms for Shop Scheduling Problems
- Shmoys, Stein, et al.
- 1994
(Show Context)
Citation Context ...st notorious of difficult AlP-hard scheduling problems; even small instances are difficult to solve to optimality [1] and the best approximation algorithms give polylogarithmic performance guarantees =-=[19]-=-. We give the first constant-factor approximations for min-sum shop scheduling with a fixed number of machines m. No approximation algorithms were known for minimizing average completion time in shop ... |

80 |
Scheduling independent tasks to reduce mean finishing time
- Bruno, Coffman, et al.
- 1974
(Show Context)
Citation Context ...ward CCR-9211494 and a grant from the New York State Science and Technology Foundation, through its Center for Advanced Technology in Telecommunications.647 been known to be polynomial-time solvable =-=[21, 4, 12]-=-; when one adds release dates, precedence constraints, or weights, essentially all versions of the problem become A/P-hard, and until [16, 11, 18] very little was known about approximation algorithms ... |

70 | Bounds on multiprocessor scheduling with resource constraints
- Garey, Graham
- 1975
(Show Context)
Citation Context ...s. We set the weight and size of job j E J to be wj and mjpj, respectively, and then call655 Knapsack, setting J~ = Knapsack(J, mD). Finally, we adapt the list scheduling algorithm of Garey & Graham =-=[7]-=- to schedule J~. Theorem6. The above DualPack routine is a dual (3 + e)-approximation algorithm for the maximum scheduled weight problem. This gives a deterministic on-line (12 + e)-approximation algo... |

50 |
Scheduling malleable and nonmalleable parallel tasks
- Ludwig, Tiwari
- 1994
(Show Context)
Citation Context ...ecedence constraints. The best off-line performance guarantee known for the non-malleable special case, without release dates, is 8.53, due to Turek et al [22]; by applying an idea of Ludwig & Tiwari =-=[15]-=-, this can be extended to the malleable case. Our on-line rain-sum algorithm with release dates has a performance guarantee of 12 + e, and if we allow randomization, a nearly identical guarantee of 8.... |

50 | Scheduling to minimize total weighted completion time: Performance guarantees of LP-based heuristics and lower bounds
- Schulz
(Show Context)
Citation Context ...ne algorithm. 1 Introduction Recently there has been significant progress in giving approximation algorithms to minimize average weighted completion time for a variety of AfP-haxd scheduling problems =-=[16, 11, 18]-=-. Constructing a schedule to minimize average completion time in a one-machine or parallel machine scheduling environment has long * soumen@cs.berkeley.edu. Computer Science Division, U.C. Berkeley, C... |

42 |
On knapsack partitions and a new dynamic programming techniques for trees
- Johnson, Niemi
- 1983
(Show Context)
Citation Context ...l weight at least W* that has total size at most (1 + e)S, where e > 0 is an arbitrarily small constant. To achieve this, we round down each sj by units of cS/n and then use dynamic programming as in =-=[14]-=-. In each of the following subsections, we will give an implementation of DualPack for a specific problem; throughout, we denote the deadline by D and the set of jobs from which we choose by J. All of... |

39 |
Scheduling jobs that arrive over time
- Phillips, Stein, et al.
- 1995
(Show Context)
Citation Context ...ne algorithm. 1 Introduction Recently there has been significant progress in giving approximation algorithms to minimize average weighted completion time for a variety of AfP-haxd scheduling problems =-=[16, 11, 18]-=-. Constructing a schedule to minimize average completion time in a one-machine or parallel machine scheduling environment has long * soumen@cs.berkeley.edu. Computer Science Division, U.C. Berkeley, C... |

39 |
Scheduling parallel tasks to minimize average response time
- Turek, Schwiegelshohn, et al.
- 1994
(Show Context)
Citation Context ... for malleable parallelizable jobs without precedence constraints. The best off-line performance guarantee known for the non-malleable special case, without release dates, is 8.53, due to Turek et al =-=[22]-=-; by applying an idea of Ludwig & Tiwari [15], this can be extended to the malleable case. Our on-line rain-sum algorithm with release dates has a performance guarantee of 12 + e, and if we allow rand... |

35 | Polyhedral approaches to machine scheduling - Queyranne, Schulz - 1994 |

28 | Resource scheduling for parallel database and scienti�c applications
- Chakrabarti, Muthukrishnan
- 1996
(Show Context)
Citation Context ...leable jobs with tree precedence We shall consider perfectly malleable jobs, as in Feldmann et al [6], and out-tree precedence constraints. (A study of precedence and non-malleability is initiated in =-=[5]-=-.) Our DuaIPack routine is as follows. We remove from J any j with PathToRoot(j) > D, set J' = Knapsack(Jr, roD), and list schedule J' as in [6]: let 4) = (vr5 - 1)/2 be the golden ratio; whenever the... |

22 |
Minimizing average flow time with parallel machines
- Horn
- 1973
(Show Context)
Citation Context ...ward CCR-9211494 and a grant from the New York State Science and Technology Foundation, through its Center for Advanced Technology in Telecommunications.647 been known to be polynomial-time solvable =-=[21, 4, 12]-=-; when one adds release dates, precedence constraints, or weights, essentially all versions of the problem become A/P-hard, and until [16, 11, 18] very little was known about approximation algorithms ... |

8 |
On the makespan of a schedule minimizing total completion time for unrelated parallel machines. Unpublished manuscript
- Hurkens, Coster
- 1996
(Show Context)
Citation Context ... N < 2Cf for each job j. This proof can be refined to yield somewhat better constants; the details will be given in the complete version of the paper. In contrast to this result, Hurkens853 & Coster =-=[13]-=- have given a family of unrelated parallel machine instances for which all minimum total completion time schedules have makespan that is an /2(log n) factor greater than the optimal makespan. 3.1 Appl... |

5 | Tobbg'epes utemez'esi probl'em'ak kozel optim'alis megold'asa. Szigma--Mat.-- Kozgazdas'agi Foly'oirat - B'ar'any, Fiala - 1982 |

2 | Scheduling parallel machines with costs - Shmoys, Tardos - 1993 |

1 |
Optimal online scheduline of parallel jobs with dependencies
- Feldmann, Kao, et al.
- 1993
(Show Context)
Citation Context ...and a randomized on-line algorithm with expected performance within 5.78 of optimal. 4.3 Perfectly malleable jobs with tree precedence We shall consider perfectly malleable jobs, as in Feldmann et al =-=[6]-=-, and out-tree precedence constraints. (A study of precedence and non-malleability is initiated in [5].) Our DuaIPack routine is as follows. We remove from J any j with PathToRoot(j) > D, set J' = Kna... |

1 |
TSbbg~pes iitemez~si probl&ms kSzel optim~lis megold~sa. Szigma-Mat.-KSzgazdasdgi FolySirat
- Bs163, Fiala
- 1982
(Show Context)
Citation Context ...s set within makespan (2 + e)D. For an open shop instance a nonpreemptive schedule of length P,~ax + ]-/max ~ (2 T s and a preemptive schedule of length max(Pmax, H~ax) _< (1 + e)D can be constructed =-=[9, 2]-=-. For job shop scheduling we can adapt the known (2 + e)-approximation makespan algorithm for fixed m [19]. Theorem 10. There is a randomized (2.89+e)-approximation algorithm for preemptive open shop ... |