# Forskning ved Københavns Universitet - Københavns Universitet

## A unifying property for distribution-sensitive priority queues

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt

• Amr Ahmed Abd Elmoneim Elmasry
• Arash Farzan
• John Iacono

We present a priority queue that supports the operations: insert in worst-case constant time, and delete, delete-min, find-min and decrease-key on an element x in worst-case O(lg(min{wx, qx} + 2)) time, where wx (respectively, qx) is the number of elements that were accessed after (respectively, before) the last access of x and are still in the priority queue at the time when the corresponding operation is performed. 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. We also argue that these bounds are the best possible with respect to the considered measures. Moreover, we modify our priority queue to satisfy a new unifying property - the time-finger property - which encapsulates both the working-set and the queueish properties. In addition, we prove that the working-set bound is asymptotically equivalent to the unified bound (which is the minimum per operation among the static-finger, static-optimality, and working-set bounds). This latter result is of tremendous interest by itself as it had gone unnoticed since the introduction of such bounds by Sleater and Tarjan [10]. Together, these results indicate that our priority queue also satisfies the static-finger, the static-optimality and the unified bounds.

Originalsprog Engelsk Combinatorial Algorithms : 22nd International Workshop, IWOCA 2011, Victoria, BC, Canada, July 20-22, 2011, Revised Selected Papers Costas S. Iliopoulos, William F. Smyth 14 Springer 2011 209-222 978-3-642-25010-1 978-3-642-25011-8 https://doi.org/10.1007/978-3-642-25011-8_17 Udgivet - 2011 22nd International Workshop on Combinatorial Algorithms - University of Victoria, Victoria, CanadaVarighed: 20 jun. 2011 → 22 jun. 2011Konferencens nummer: 22

### Konference

Konference 22nd International Workshop on Combinatorial Algorithms 22 University of Victoria Canada Victoria 20/06/2011 → 22/06/2011
Navn Lecture notes in computer science 7056 0302-9743

ID: 172850721