Where’s the Winner? Max-Finding and Sorting with Metric Costs
Traditionally, a fundamental assumption in evaluating the performance of algorithms for sorting and selection has been that comparing any two elements costs one unit (of time, work, etc.); the goal of an algorithm is to minimize the total cost incurred. However, a body of recent work has attempted to find ways to weaken this assumption – in particular, new algorithms have been given for these basic problems of searching, sorting and selection, when comparisons between different pairs of elements have different associated costs.
In this paper, we further these investigations, and address the questions of max-finding and sorting when the comparison costs form a metric; i.e., the comparison costs c uv respect the triangle inequality c uv + c vw ≥ c uw for all input elements u,v and w. We give the first results for these problems – specifically, we present
An O(log n)-competitive algorithm for max-finding on general metrics, and we improve on this result to obtain an O(1)-competitive algorithm for the max-finding problem in constant dimensional spaces.
An O(log2 n)-competitive algorithm for sorting in general metric spaces.
- Where’s the Winner? Max-Finding and Sorting with Metric Costs
- Book Title
- Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques
- Book Subtitle
- 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th International Workshop on Randomization and Computation, RANDOM 2005, Berkeley, CA, USA, August 22-24, 2005. Proceedings
- pp 74-85
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Industry Sectors
- eBook Packages
- Editor Affiliations
- 16. Dept. of Computer Science, University of Illinois
- 17. Institute for Computer Science, University of Kiel
- 18. Battelle Bâtiment A, Centre Universitaire d’Informatique
- 19. UC Berkeley
- Author Affiliations
- 20. Dept. of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 15213, USA
- 21. Dept. of Computer Science & Engineering, Indian Institute of Technology, Hauz Khas, New Delhi, India, 110016
To view the rest of this content please follow the download PDF link above.