On the Advice Complexity of Online Problems

(Extended Abstract)
  • Hans-Joachim Böckenhauer
  • Dennis Komm
  • Rastislav Královič
  • Richard Královič
  • Tobias Mömke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)

Abstract

In this paper, we investigate to what extent the solution quality of online algorithms can be improved by allowing the algorithm to extract a given amount of information about the input. We consider the recently introduced notion of advice complexity where the algorithm, in addition to being fed the requests one by one, has access to a tape of advice bits that were computed by some oracle function from the complete input. The advice complexity is the number of advice bits read. We introduce an improved model of advice complexity and investigate the connections of advice complexity to the competitive ratio of both deterministic and randomized online algorithms using the paging problem, job shop scheduling, and the routing problem on a line as sample problems. We provide both upper and lower bounds on the advice complexity of all three problems.

Our results for all of these problems show that very small advice (only three bits in the case of paging) already suffices to significantly improve over the best deterministic algorithm. Moreover, to achieve the same competitive ratio as any randomized online algorithm, a logarithmic number of advice bits is sufficient. On the other hand, to obtain optimality, much larger advice is necessary.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Hans-Joachim Böckenhauer
    • 1
  • Dennis Komm
    • 1
  • Rastislav Královič
    • 2
  • Richard Královič
    • 1
  • Tobias Mömke
    • 1
  1. 1.Department of Computer ScienceETH ZurichSwitzerland
  2. 2.Department of Computer ScienceComenius UniversityBratislavaSlovakia

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