A priority queue with the time-finger property

Abstract

We present a priority queue that supports insert in worst-case constant time, and delete-min, access-min, delete, and decrease of an element x in worst-case O(log(min{wx,qx})) time, where wx (respectively, qx) is the number of elements that were accessed after (respectively, before) the last access to x and are still in the priority queue at the time when the corresponding operation is performed. (An access to an element is accounted for by any priority-queue operation that involves this element.) Our priority queue then has both the working-set and the queueish properties; and, more strongly, it satisfies these properties in the worst-case sense. From the results in Iacono (2001) [11] and Elmasry et al. (2011) [7], our priority queue also satisfies the static-finger, static-optimality, and unified bounds. Moreover, we modify our priority queue to realize a new unifying property — the time-finger property — which encapsulates both the working-set and the queueish properties.