Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, February 07, 2017, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Dan Alistarh

We consider the following random process, implementing a relaxed priority queue: we are given n queues, into which increasingly labeled elements are inserted uniformly at random. To remove an element, we pick two random queues, and remove the element of lower label (higher priority) among the two. The cost of a removal is the *rank* of the removed label among labels still present in any of the queues, that is, the distance from the optimal choice at step. Variants of this strategy are ubiquitous in practical implementations of concurrent priority queues; yet, no guarantees are known for this strategy.

This talk will give a solution to this question, showing that the expected cost of a removal is O( n ), while the expected worst-case cost is O( n log n ), irrespective of the number of steps for which the process runs. These bounds are asymptotically tight. The argument is based on a new connection between heavily loaded balls-into-bins processes and priority scheduling, and extends to the case where insertions are biased toward some of the queues, and removals may alternate between one and two random choices. This extension inspires a new concurrent priority queue implementation, which improves upon the state of the art in terms of throughput by up to 50%.

Joint work with Justin Kopinsky (MIT), Jerry Li (MIT), and Giorgi Nadiradze (ETH Zurich).

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