New algorithms for online rectangle filling with k-lookahead

Abstract

We study the online rectangle filling problem which arises in channel aware scheduling of wireless networks, and present improved deterministic and first known randomized results for algorithms that are allowed a k-lookahead for k ≥ 2. Our main result is a deterministic min {1.848,1 + 2/(k - 1)}-competitive online algorithm. The previous best-known solution for this problem has a competitive ratio of 2 for any k ≥ 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 of 1+1/(√ k+2 + √ k+1)2 > 1+1/(4(k+2)) on the competitive ratio of any randomized online algorithm against an oblivious adversary. © 2008 Springer-Verlag Berlin Heidelberg.