Polylogarithmic Guarantees for Generalized Reordering Buffer Management

In the Generalized Reordering Buffer Management Problem (GRBM) a sequence of items located in a metric space arrives online, and has to be processed by a set of k servers moving within the space. In a single step the first b still unprocessed items from the sequence are accessible, and a scheduling strategy has to select an item and a server. Then the chosen item is processed by moving the chosen server to its location. The goal is to process all items while minimizing the total distance travelled by the servers. This problem was introduced in [Chan, Megow, Sitters, van Stee TCS 12] and has been subsequently studied in an online setting by [Azar, Englert, Gamzu, Kidron STACS 14]. The problem is a natural generalization of two very well-studied problems: the k-server problem for b=1 and the Reordering Buffer Management Problem (RBM) for k=1. In this paper we consider the GRBM problem on a uniform metric in the online version. We show how to obtain a competitive ratio of O(log k(log k+loglog b)) for this problem. Our result is a drastic improvement in the dependency on b compared to the previous best bound of O(√b log k), and is asymptotically optimal for constant k, because Ω(log k + loglog b) is a lower bound for GRBM on uniform metrics.

Authors

• Matthias Englert
• Harald Räcke
• Richard Stotz

Keywords

• Servers
• Color
• Delays
• Extraterrestrial measurements
• Upper bound
• Computer science
• Maximum Norm
• Scheduling Scheme
• Sequence Of Items
• Competitive Ratio
• Time Step
• Lower Bound
• Increase In Intensity
• Unmarked
• Active Period
• Constant Factor
• Previous Phase
• Cost Control
• Group In Phase
• Start Of Phase
• Scheduling Algorithm
• Online Algorithm
• Cost Of Algorithm
• Items In Set
• Dual Solution
• Cost Of Movement
• Explicit Request
• online computing
• reordering buffer management
• randomized algorithms