Robust discrete spanning tree problem: local search algorithms

Prabha Sharma (), Sandeep Singh (), Diptesh Ghosh () and R Chandrasekaran ()
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Prabha Sharma: The NorthCap University
Sandeep Singh: The NorthCap University
Diptesh Ghosh: Indian Institute of Management
R Chandrasekaran: University of Texas

OPSEARCH, 2022, vol. 59, issue 2, No 12, 632-644

Abstract: Abstract In this paper the robust spanning tree problem and the relative robust spanning tree problem on an arbitrary graph, whose edge costs vary over a finite set, are considered. All possible combinations of the edge cost form the scenario set. We show that the absolute robust spanning tree problem is polynomially solvable. The relative robust spanning tree problem, when the edge cost of each edge varies over a specified interval, is known to be NP-complete. Status of the relative robust spanning tree problem with edge costs varying over a finite set of values is open. Two local search algorithms, TREE and STAGE2 have been designed for this problem. For graphs with upto 12 nodes our results matched exactly with the optimal solution. For, graphs with 15 nodes computing the exact solution was becoming intractable.

Keywords: Scenario; Absolute robust tree; Relative robust tree; Worst case scenario; Neighbourhood of a tree; Local search; Weak tree (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s12597-021-00538-0

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