## Online Load Balancing and Network Flow (1993)

Venue: | In Proc. 25th Annual ACM Symposium on Theory of Computing |

Citations: | 35 - 4 self |

### BibTeX

@INPROCEEDINGS{Phillips93onlineload,

author = {Steven Phillips and Jeffery Westbrook},

title = {Online Load Balancing and Network Flow},

booktitle = {In Proc. 25th Annual ACM Symposium on Theory of Computing},

year = {1993},

pages = {402--411},

publisher = {ACM}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper we study two problems that can be viewed as on-line games on a dynamic bipartite graph. The first problem is on-line load balancing with preemption. A centralized scheduler must assign tasks to servers, processing online a sequence of task arrivals and departures. Each task is restricted to run on some subset of the servers. The scheduler attempts to keep the load well-balanced. If preemptive reassignments are dissallowed, Azar, Broder and Karlin [3] proved a lower bound of \Omega\Gamma p n) on the ratio between the maximum load achieved by an on-line algorithm and the optimum off-line maximum load. We show that this ratio can be greatly reduced by an efficient scheduler using only a small amount of rescheduling. We then apply these ideas to network flow. Cheriyan and Hagerup [6] introduced an on-line game on a bipartite graph as a fundamental step in improving algorithms for computing the maximum flow in networks. They described a randomized strategy to play the game. ...

### Citations

543 | A new approach to the maximum flow problem
- GOLDBERG, TARJAN
- 1988
(Show Context)
Citation Context ...ng node kills. Edge kills are closely related to task departures. The number of points scored by B is the number of dynamic tree operations performed by the Goldberg-Tarjan algorithm for maximum flow =-=[9]-=-. The correspondence between the game and the running time for network flow is given by the following theorems from King et al. Theorem 1 Given a strategy to play the node kill game, scoring at most P... |

336 |
Bounds for certain multiprocessing anomalies
- Graham
- 1966
(Show Context)
Citation Context ... factors among both deterministic and randomized algorithms. If for each task the eligible subset is all servers, however, then the competitive ratio falls to 2 \Gamma ffl for some small constant ffl =-=[10, 5]-=-. Azar, Broder and Karlin [3] studied the dynamic load balancing problem when tasks both arrive and depart, but retained the restriction that tasks cannot be preempted. In this version, the picture is... |

165 |
Combinatorial Optimization
- Papadimitriou, Steiglitz
- 1982
(Show Context)
Citation Context ...other extreme, we may rebuild an optimum assignment each time a task arrives or departs. An optimum assignment can be computed in \Theta(n 3 log n) time using binary search and a b-matching algorithm =-=[12]-=-. This results in a ratio of 1, \Theta(m 2 ) reassignments, and \Theta(mn 3 log n) total computation. Our algorithms extend to more general versions of the problem where both tasks and servers may arr... |

98 | On-line load balancing
- AZAR
- 1998
(Show Context)
Citation Context ...d departures. Each task is restricted to run on some subset of the servers. The scheduler attempts to keep the load well-balanced. If preemptive reassignments are dissallowed, Azar, Broder and Karlin =-=[3]-=- proved a lower bound of \Omega\Gamma p n) on the ratio between the maximum load achieved by an on-line algorithm and the optimum off-line maximum load. We show that this ratio can be greatly reduced ... |

95 | The competitiveness of on-line assignments
- Azar, Naor, et al.
- 1995
(Show Context)
Citation Context ...t of tasks that are in R j+1 after the reassignment: these tasks were assigned greedily, without any task departures, so by the log n-competitiveness of the greedy algorithm for static load balancing =-=[4]-=-, the maximum server load is at most (j + 1)` +OPT log ns13 OPT log n=ae after the reassignment. 2 Note that our algorithm belongs to a class of algorithms that does no preemptive rescheduling unless ... |

92 | New Algorithms for an Ancient Scheduling Problem
- Bartal, Fiat, et al.
- 1995
(Show Context)
Citation Context ... factors among both deterministic and randomized algorithms. If for each task the eligible subset is all servers, however, then the competitive ratio falls to 2 \Gamma ffl for some small constant ffl =-=[10, 5]-=-. Azar, Broder and Karlin [3] studied the dynamic load balancing problem when tasks both arrive and depart, but retained the restriction that tasks cannot be preempted. In this version, the picture is... |

57 | On-line load balancing of temporary tasks
- Azar, Kalyanasundaram, et al.
- 1997
(Show Context)
Citation Context ... strong bounds indicate that the performance of an online scheduler may be severely impacted by the lack of information about future tasks. The O( p n) lower bound has recently been shown to be tight =-=[2]-=-. We address the problem of the huge lower bound on the achievable competitive ratio by giving the scheduler a little more power. We study load balancing with task preemption. That is, the scheduler i... |

51 |
Tarjan, A faster deterministic maximum flow algorithm
- King, Rao, et al.
- 1994
(Show Context)
Citation Context ...on-line game on a bipartite graph as a fundamental step in improving algorithms for computing the maximum flow in networks. They described a randomized strategy to play the game. King, Rao and Tarjan =-=[11] studied a-=- modified version of this game, called "node kill", and gave a deterministic strategy. We obtain an improved deterministic algorithm for the node kill game (and hence for maximum flow) in al... |

17 | Generating pseudo-random permutations and maximum flow algorithms
- Alon
- 1990
(Show Context)
Citation Context ...ills is at most O( p nm+ P (n; m)). Cheriyan and Hagerup [6, 7] first introduced a restricted form of this game, in which player A may not redesignate edges, and described a randomized strategy. Alon =-=[1]-=- derandomized this strategy. King et al. extended the game to the form described above and found an improved deterministic strategy. We apply ideas from online load balancing to play the node-kill gam... |

16 |
A randomized maximum-flow algorithm
- Cheriyan, Hagerup
- 1995
(Show Context)
Citation Context ...-line maximum load. We show that this ratio can be greatly reduced by an efficient scheduler using only a small amount of rescheduling. We then apply these ideas to network flow. Cheriyan and Hagerup =-=[6]-=- introduced an on-line game on a bipartite graph as a fundamental step in improving algorithms for computing the maximum flow in networks. They described a randomized strategy to play the game. King, ... |

3 |
Can a maximum flow be computed in o(mn) time
- Cheriyan, Hagerup, et al.
- 1990
(Show Context)
Citation Context ...rem 2 When the node kill game is used for network flows, if at most P (n; m) points are scored in the node kill game, then the number of edge kills is at most O( p nm+ P (n; m)). Cheriyan and Hagerup =-=[6, 7]-=- first introduced a restricted form of this game, in which player A may not redesignate edges, and described a randomized strategy. Alon [1] derandomized this strategy. King et al. extended the game t... |