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Lower Bounds on the Competitive Ratio for Mobile User Tracking and Distributed Job Scheduling *
 

Summary: Lower Bounds on the Competitive Ratio for
Mobile User Tracking and Distributed Job Scheduling *
Noga Alon **
Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences,
Tel-Aviv University, Tel Aviv, Israel
Gil Kalai ***
Institute of Mathematics and Computer Science, Hebrew University, Jerusalem, Israel
Moty Ricklin
Computer Science Department, Raymond and Beverly Sackler Faculty of Exact Sciences,
Tel-Aviv University, Tel Aviv, Israel
Larry Stockmeyer
IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, CA 95120,
USA
1
Abstract
We prove a lower bound of (log n/ log log n) on the competitive ratio of any (deterministic
or randomized) distributed algorithm for solving the mobile user problem introduced by
Awerbuch and Peleg [5], on certain networks of n processors. Our lower bound holds for
various networks, including the hypercube, any network with sufficiently large girth, and
any highly expanding graph. A similar (log n/ log log n) lower bound is proved for the

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics