Alistarh, Dan-AdrianIST Austria; Aspnes, James; Bender, Michael; Gelashvili, Rati; Gilbert, Seth
Task allocation is a classic distributed problem in which a set of p potentially faulty processes must cooperate to perform a set of tasks. This paper considers a new dynamic version of the problem, in which tasks are injected adversarially during an asynchronous execution. We give the first asynchronous shared-memory algorithm for dynamic task allocation, and we prove that our solution is optimal within logarithmic factors. The main algorithmic idea is a randomized concurrent data structure called a dynamic to-do tree, which allows processes to pick new tasks to perform at random from the set of available tasks, and to insert tasks at random empty locations in the data structure. Our analysis shows that these properties avoid duplicating work unnecessarily. On the other hand, since the adversary controls the input as well the scheduling, it can induce executions where lots of processes contend for a few available tasks, which is inefficient. However, we prove that every algorithm has the same problem: given an arbitrary input, if OPT is the worst-case complexity of the optimal algorithm on that input, then the expected work complexity of our algorithm on the same input is O(OPT log3 m), where m is an upper bound on the number of tasks that are present in the system at any given time.
Dan Alistarh - This author was supported by the SNF Postdoctoral Fellows Program, NSF grant CCF-1217921, DoE ASCR grant ER26116/DE-SC0008923, and by grants from the Oracle and Intel corporations. James Aspnes - Supported in part by NSF grant CCF-0916389. Michael A. Bender - This research was supported in part by NSF grants CCF 1114809, CCF 1217708, IIS 1247726, and IIS 1251137. Rati Gelashvili - This work was supported in part by NSF grants CCF-1217921, CCF-1301926, DoE ASCR grant ER26116/DE-SC0008923, and by grants from the Oracle and Intel corporations. Seth Gilbert - Supported by Singapore AcRF-2 MOE2011-T2-2-042.
416 - 435
SODA: Symposium on Discrete Algorithms
Alistarh D-A, Aspnes J, Bender M, Gelashvili R, Gilbert S. Dynamic task allocation in asynchronous shared memory. In: SIAM; 2014:416-435. doi:10.1137/1.9781611973402.31
Alistarh, D.-A., Aspnes, J., Bender, M., Gelashvili, R., & Gilbert, S. (2014). Dynamic task allocation in asynchronous shared memory (pp. 416–435). Presented at the SODA: Symposium on Discrete Algorithms, SIAM. https://doi.org/10.1137/1.9781611973402.31
Alistarh, Dan-Adrian, James Aspnes, Michael Bender, Rati Gelashvili, and Seth Gilbert. “Dynamic Task Allocation in Asynchronous Shared Memory,” 416–35. SIAM, 2014. https://doi.org/10.1137/1.9781611973402.31.
D.-A. Alistarh, J. Aspnes, M. Bender, R. Gelashvili, and S. Gilbert, “Dynamic task allocation in asynchronous shared memory,” presented at the SODA: Symposium on Discrete Algorithms, 2014, pp. 416–435.
Alistarh D-A, Aspnes J, Bender M, Gelashvili R, Gilbert S. 2014. Dynamic task allocation in asynchronous shared memory. SODA: Symposium on Discrete Algorithms, 416–435.
Alistarh, Dan-Adrian, et al. Dynamic Task Allocation in Asynchronous Shared Memory. SIAM, 2014, pp. 416–35, doi:10.1137/1.9781611973402.31.