Worst-Case Analysis of Network Design Problem Heuristics
Name
OR-085-78.pdf
Size
1.26 MB
Format
Adobe PDF
Checksum (MD5)
1548d8298a21309b8eabc7d6c09508ab
Author(s)
Wong, Richard T.
Date Issued
December 1978
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 085-78
Abstract
The Optimal Network problem (as defined by Scott [16]) consists of selecting a subset of arcs that minimizes the sum of the shortest paths between all nodes subject to a budget constraint. This paper considers the worst-case behavior of heuristics for this prob'em. Let n be the number of nodes in the network and e be a constant between 0 and 1. For a general class of Optimal Network Problems, we show that the question of finding a solution which is always less than n times the optimal solution is NP-complete. This indicates that all polynomial-time heuristics for the problem most probably have poor worst-case performance. An upper bound for worst-case heuristic performance of 2n times the optimal solution is also derived. For a restricted version of the Optimal Network problem we describe a procedure whose maximum percentage of error is bounded by a constant.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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