Better bounds for online load balancing on unrelated machines

  • Authors:

  • Ioannis Caragiannis

  • Affiliations:

  • University of Patras, Rio

  • Venue:
  • Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2008

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Abstract

We study the problem of scheduling permanent jobs on unrelated machines when the objective is to minimize the Lp norm of the machine loads. The problem is known as load balancing under the Lp norm. We present an improved upper bound for the greedy algorithm through simple analysis; this bound is also shown to be best possible within the class of deterministic online algorithms for the problem. We also address the question whether randomization helps online load balancing under Lp norms on unrelated machines; this is a challenging question which is open for more than a decade even for the L2 norm. We provide a positive answer to this question by presenting the first randomized online algorithms which outperform deterministic ones under any (integral) Lp norm for p = 2,…,137. Our algorithms essentially compute in an online manner a fractional solution to the problem and use the fractional values to make random choices. The local optimization criterion used at each step is novel and rather counterintuitive: the values of the fractional variables for each job correspond to flows at an approximate Wardrop equilibrium for an appropriately defined non-atomic congestion game. As corollaries of our analysis and by exploiting the relation between the Lp norm and the makespan of machine loads, we obtain new competitive algorithms for online makespan minimization, making progress in another longstanding open problem.