A unified access bound on comparison-based dynamic dictionaries

Authors:
Mihai Bdoiu;Richard Cole;Erik D. Demaine;John Iacono
Affiliations:
MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar Street, Cambridge, MA 02139, USA;Computer Science Department, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA;MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar Street, Cambridge, MA 02139, USA;Department of Computer and Information Science, Polytechnic University, 5 MetroTech Center, Brooklyn, NY 11201, USA
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

We present a dynamic comparison-based search structure that supports insertions, deletions, and searches within the unified bound. The unified bound specifies that it is quick to access an element that is near a recently accessed element. More precisely, if w(y) distinct elements have been accessed since the last access to element y, and d(x,y) denotes the rank distance between x and y among the current set of elements, then the amortized cost to access element x is O(minylog[w(y)+d(x,y)+2]). This property generalizes the working-set and dynamic-finger properties of splay trees.