Two algorithms for maintaining order in a list
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Journal of Algorithms - Special issue on SODA '95 papers
Adaptive functional programming
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A locality-preserving cache-oblivious dynamic dictionary
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Monads for incremental computing
Proceedings of the seventh ACM SIGPLAN international conference on Functional programming
Fast Updating of Well-Balanced Trees
SWAT '90 Proceedings of the 2nd Scandinavian Workshop on Algorithm Theory
A Tight Lower Bound for On-line Monotonic List Labeling
SWAT '94 Proceedings of the 4th Scandinavian Workshop on Algorithm Theory
A Sparse Table Implementation of Priority Queues
Proceedings of the 8th Colloquium on Automata, Languages and Programming
Two Simplified Algorithms for Maintaining Order in a List
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Maintaining order in a linked list
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Density Control and On-Line Labeling Problems
Density Control and On-Line Labeling Problems
A new method for functional arrays
Journal of Functional Programming
A Tight Lower Bound for Online Monotonic List Labeling
SIAM Journal on Discrete Mathematics
Tight lower bounds for the online labeling problem
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
On online labeling with polynomially many labels
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
On randomized online labeling with polynomially many labels
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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The problem of on-line labelling is one of assigning integer labels in the range 1 to N to an input stream of at most N distinct items, drawn from a linearly ordered set, so that at each step the labels respect the ordering on the items. To maintain this constraint, items may have to be relabelled to accommodate new ones. With T(M, N) denoting the total number of relabellings that have to be performed for the first M inputs, it is known that for any given constant c in the range 0 c T(Nc, N) = Θ(N log N) and T(cN, N) = Θ(N log2N). However, in the case c = 1, when the labelling is called minimal, is known only that T(N, N) = O(N log3N). Existing algorithms for minimal on-line labelling are complicated, and our aim in this paper is to give a simplified and self-contained account of the problem.