Inverse Max+Sum Spanning Tree Problem under Weighted Sum-Type Hamming Distance by Modifying the Max-Weight Vector

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Azad Hampa B.; Baroughi F.

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Journal Paper

Paper Information

Journal: Journal of Operational Research in its Applications Year:2022 | Volume:19 | Issue:2 Page(s): 77-91

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Information Journal Paper

Title

Inverse Max+Sum Spanning Tree Problem under Weighted Sum-Type Hamming Distance by Modifying the Max-Weight Vector

Author(s)

Azad Hampa B. | Baroughi F. | Issue Writer Certificate

Keywords

Max+Sum Spanning Tree ProblemQ4

Inverse OptimizationQ4

Hamming DistanceQ4

Abstract

The max+sum spanning tree problem is to find a spanning tree T* which makes the combined weight “max w(e)+Sum c(e) time” as small as possible, in which a weight w(e) and a cost c(e) are prescribed for each e ͼT. The problem can be solved in O(mlog n) time. In an inverse max+sum spanning tree problem, T0 is a given spanning tree of G, which is not an optimal max+sum spanning tree. Then we modify the weight vector w to w̅ so that T0 becomes a max+sum spanning tree. The goal is to minimize the modification cost ||w̅-w||under Hamming Distance. This paper presents a new solution algorithm for the inverse max+sum spanning tree problem under weighted sum-type Hamming Distance by modifying the max-weight vector with time complexity of O(mlog n). First, we formulate the problem and then present a new solution algorithm for the problem under investigation. Finally, we present a numerical example to illustrate the efficiency of the algorithm.

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