Online splitting interval scheduling on m identical machines

Authors:
Feifeng Zheng;Bo Liu;Yinfeng Xu;E. Zhang
Affiliations:
School of Management, Xi'an JiaoTong Univ., Xi'an, China and Ministry of Edu. Key Lab for Int. Networks and Network Sec., China and Ministry of Edu. Key Lab for Process Control and Efficiency Eng. ...;School of Management, Xi'an JiaoTong University, Xi'an, China;School of Management, Xi'an JiaoTong Univ., Xi'an, China and Ministry of Edu. Key Lab for Int. Networks and Network Sec., China and Ministry of Edu. Key Lab for Process Control and Efficiency Eng. ...;School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai, China
Venue:
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Year:
2010

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Abstract

This paper investigates online scheduling on m identical machines with splitting intervals, i.e., intervals can be split into pieces arbitrarily and processed simultaneously on different machines. The objective is to maximize the throughput, i.e., the total length of satisfied intervals. Intervals arrive over time and the knowledge of them becomes known upon their arrivals. The decision on splitting and assignment for each interval is made irrecoverably upon its arrival. We first show that any non-split online algorithms cannot have bounded competitive ratios if the ratio of longest to shortest interval length is unbounded. Our main result is giving an online algorithm ES (for Equivalent Split) which has competitive ratio of 2 and 2m-1/m-1 for m = 2 and m ≥ 3, respectively. We further present a lower bound of m/m-1, implying that ES is optimal as m = 2.