Dagstuhl Seminar on On-line Algorithms

A Survey of Self-Organizing Data-Structures Susanne Albers and Jeffery Westbrook Self-organizing data structures modify their structure while processing a sequence of operations. The data structure is allowed to be in an arbitrary state, i.e. no global constraint has to be satisfied, but during each operation a simple restructuring rule is applied. The purpose of this restructuring is to guarantee the efficiency of future operations. Typically the restructuring is also done on-line, without knowledge of future operations. In this talk we review important results for self-organizing data structures such as linear lists and binary search trees. The problem of maintaining self-organizing linear lists is also known as the list update problem. First we present results on the competitive ratio of deterministic on-line algorithms for the list update problem. We concentrate on the algorithms Move-To-Front, Transpose, Frequency-Count and Timestamp(0). Then we discuss randomized competitive on-line algorithms that have been developed so far. We also mention lower bounds on the competitiveness that can be achieved by deterministic and randomized on-line algorithms. Finally we give a summary of average case analysis results for the list update problem. In the context of self-organizing binary search trees we discuss restructuring heuristics such as Move-To-Root, Single-Rotation and Splaying. We then concentrate on the Splaying scheme and present important theorems known for splay trees. We also present a series of conjectures and report on progress on these conjectures. Finally we briefly mention how splay trees perform in practice. In the third part of the talk we show that self-organizing binary search trees and in particular linear lists can be used to construct very effective data compression schemes. Competitive Analysis of Distributed Algorithms