New algorithms for online rectangle filling with k-lookahead

  • Authors:
  • Haitao Wang;Amitabh Chaudhary;Danny Z. Chen

  • Affiliations:
  • Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, USA 46556;Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, USA 46556;Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, USA 46556

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2011

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Abstract

We study the online rectangle filling problem which arises in channel aware scheduling of wireless networks, and present deterministic and randomized results for algorithms that are allowed a k-lookahead for k驴2. Our main result is a deterministic min驴{1.848,1+2/(k驴1)}-competitive online algorithm. This is the first algorithm for this problem with a competitive ratio approaching 1 as k approaches +驴. The previous best-known solution for this problem has a competitive ratio of 2 for any k驴2. We also present a randomized online algorithm with a competitive ratio of 1+1/(k+1). Our final result is a closely matching lower bound (also proved in this paper) of $1+1/(\sqrt{k+2}+\sqrt{k+1})^{2}1+1/(4(k+2))$ on the competitive ratio of any randomized online algorithm against an oblivious adversary. These are the first known results for randomized algorithms for this problem.