NP-hardness of the sorting buffer problem on the uniform metric

Authors:
Yuichi Asahiro;Kenichi Kawahara;Eiji Miyano
Affiliations:
Department of Information Science, Kyushu Sangyo University, Fukuoka 813-8503, Japan;Department of Systems Design and Informatics, Kyushu Institute of Technology, Fukuoka 820-8502, Japan;Department of Systems Design and Informatics, Kyushu Institute of Technology, Fukuoka 820-8502, Japan
Venue:
Discrete Applied Mathematics
Year:
2012

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Abstract

An instance of the sorting buffer problem (SBP) consists of a sequence of requests for service, each of which is specified by a point in a metric space, and a sorting buffer which can store up to a limited number of requests and rearrange them. To serve a request, the server needs to visit the point where serving a request p following the service to a request q requires the cost corresponding to the distance d(p,q) between p and q. The objective of SBP is to serve all input requests in a way that minimizes the total distance traveled by the server by reordering the input sequence. In this paper, we focus our attention to the uniform metric, i.e., the distance d(p,q)=1 if pq, d(p,q)=0 otherwise, and present the first NP-hardness proof for SBP on the uniform metric.