Allocating weighted jobs in parallel

The classic balls-into-bins game considers the experiment of placing m balls independently and uniformly at random (i.u.r.) in n bins. For m=n , it is well known that the maximum load, i.e., the number of balls in the fullest bin is Θ(log n/log log n) , with high probability. It is also known (see [S2]) that a maximum load of O( m / n ) can be obtained for all m≥ n if each ball is allocated in one (suitably chosen) of two (i.u.r.) bins. Stemann presents a distributed algorithm to find the ``suitable'' bin for each ball. The algorithm uses r communication rounds to achieve a maximum load of \(\max\{\sqrt[r]{\log n}, O(m/n)\}\) , with high probability. Adler et al. [ACMR] show that Stemann's protocol is optimal up to a constant factor for constant r .

[1]  Rajeev Motwani,et al.  Randomized algorithms , 1996, CSUR.

[2]  Bala Kalyanasundaram,et al.  On-Line Load Balancing of Temporary Tasks , 1993, J. Algorithms.

[3]  Michael Mitzenmacher,et al.  Load balancing and density dependent jump Markov processes , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[4]  R.M. Karp, M. Luby, F. Meyer auf der Hei.  Efficient PRAM simulation on a distributed memory machine , 1996 .

[5]  Bala Kalyanasundaram,et al.  On-Line Load Balancing of Temporary Tasks , 1997, J. Algorithms.

[6]  Eli Upfal,et al.  Balanced allocations (extended abstract) , 1994, STOC '94.

[7]  Friedhelm Meyer auf der Heide,et al.  Simple, efficient shared memory simulations , 1993, SPAA '93.

[8]  Michael Mitzenmacher,et al.  On the Analysis of Randomized Load Balancing Schemes , 1997, SPAA '97.

[9]  Friedhelm Meyer auf der Heide,et al.  Exploiting Storage Redundancy to Speed up Randomized Shared Memory Simulations , 1995, Theor. Comput. Sci..

[10]  T. Kurtz.  Approximation of Population Processes , 1987 .

[11]  Micah Adler,et al.  Parallel randomized load balancing , 1995, STOC '95.

[12]  Volker Stemann,et al.  Parallel balanced allocations , 1996, SPAA '96.

[13]  Yossi Azar.  On-line Load Balancing , 1996, Online Algorithms.

[14]  Steven J. Phillips,et al.  Online load balancing and network flow , 1993, STOC.

[15]  Micah Adler,et al.  Parallel randomized load balancing (Preliminary Version). , 1995, STOC 1995.

[16]  Micah Adler,et al.  Analyzing an Infinite Parallel Job Allocation Process , 1998, ESA.

[17]  Friedhelm Meyer auf der Heide,et al.  How to distribute a dictionary in a complete network , 1990, STOC '90.

[18]  Friedhelm Meyer auf der Heide,et al.  Contention Resolution in Hashing Based Shared Memory Simulations , 2000, SIAM J. Comput..