A New Approach to Competitive Analysis: Approximating the Optimal Competitive Ratio
Please always quote using this URN:urn:nbn:de:0296-matheon-9433
- We propose a new approach to competitive analysis by introducing the novel concept of online approximation schemes. Such scheme algorithmically constructs an online algorithm with a competitive ratio arbitrarily close to the best possible competitive ratio for any online algorithm. We study the problem of scheduling jobs online to minimize the weighted sum of completion times on parallel, related, and unrelated machines, and we derive both deterministic and randomized algorithms which are almost best possible among all online algorithms of the respective settings. Our method relies on an abstract characterization of online algorithms combined with various simplifications and transformations. We also contribute algorithmic means to compute the actual value of the best possible competitive ratio up to an arbitrary accuracy. This strongly contrasts all previous manually obtained competitiveness results for algorithms and, most importantly, it reduces the search for the optimal competitive ratio to a question that a computer can answer. We believe that our method can also be applied to many other problems and yields a completely new and interesting view on online algorithms.
Author: | Elisabeth Günther, Olaf Maurer, Nicole Megow, Andreas Wiese |
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URN: | urn:nbn:de:0296-matheon-9433 |
Referee: | Rolf H. Möhring |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2012/01/07 |
Release Date: | 2012/01/07 |
Tag: | approximation scheme; competitive analysis; online scheduling; sum of weighted completion times |
Institute: | Research Center Matheon |
Technische Universität Berlin | |
MSC-Classification: | 68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section {04 in that areag 68-00 General reference works (handbooks, dictionaries, bibliographies, etc.) / 68-06 Proceedings, conferences, collections, etc. |
Preprint Number: | 844 |